TSTP Solution File: SCT171+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT171+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 22:04:27 EDT 2022
% Result : Theorem 1.88s 2.15s
% Output : Refutation 1.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SCT171+2 : TPTP v8.1.0. Released v5.3.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 02:44:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.46/1.72 ============================== Prover9 ===============================
% 1.46/1.72 Prover9 (32) version 2009-11A, November 2009.
% 1.46/1.72 Process 30276 was started by sandbox on n025.cluster.edu,
% 1.46/1.72 Sat Jul 2 02:44:10 2022
% 1.46/1.72 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30123_n025.cluster.edu".
% 1.46/1.72 ============================== end of head ===========================
% 1.46/1.72
% 1.46/1.72 ============================== INPUT =================================
% 1.46/1.72
% 1.46/1.72 % Reading from file /tmp/Prover9_30123_n025.cluster.edu
% 1.46/1.72
% 1.46/1.72 set(prolog_style_variables).
% 1.46/1.72 set(auto2).
% 1.46/1.72 % set(auto2) -> set(auto).
% 1.46/1.72 % set(auto) -> set(auto_inference).
% 1.46/1.72 % set(auto) -> set(auto_setup).
% 1.46/1.72 % set(auto_setup) -> set(predicate_elim).
% 1.46/1.72 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.46/1.72 % set(auto) -> set(auto_limits).
% 1.46/1.72 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.46/1.72 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.46/1.72 % set(auto) -> set(auto_denials).
% 1.46/1.72 % set(auto) -> set(auto_process).
% 1.46/1.72 % set(auto2) -> assign(new_constants, 1).
% 1.46/1.72 % set(auto2) -> assign(fold_denial_max, 3).
% 1.46/1.72 % set(auto2) -> assign(max_weight, "200.000").
% 1.46/1.72 % set(auto2) -> assign(max_hours, 1).
% 1.46/1.72 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.46/1.72 % set(auto2) -> assign(max_seconds, 0).
% 1.46/1.72 % set(auto2) -> assign(max_minutes, 5).
% 1.46/1.72 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.46/1.72 % set(auto2) -> set(sort_initial_sos).
% 1.46/1.72 % set(auto2) -> assign(sos_limit, -1).
% 1.46/1.72 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.46/1.72 % set(auto2) -> assign(max_megs, 400).
% 1.46/1.72 % set(auto2) -> assign(stats, some).
% 1.46/1.72 % set(auto2) -> clear(echo_input).
% 1.46/1.72 % set(auto2) -> set(quiet).
% 1.46/1.72 % set(auto2) -> clear(print_initial_clauses).
% 1.46/1.72 % set(auto2) -> clear(print_given).
% 1.46/1.72 assign(lrs_ticks,-1).
% 1.46/1.72 assign(sos_limit,10000).
% 1.46/1.72 assign(order,kbo).
% 1.46/1.72 set(lex_order_vars).
% 1.46/1.72 clear(print_given).
% 1.46/1.72
% 1.46/1.72 % formulas(sos). % not echoed (885 formulas)
% 1.46/1.72
% 1.46/1.72 ============================== end of input ==========================
% 1.46/1.72
% 1.46/1.72 % From the command line: assign(max_seconds, 300).
% 1.46/1.72
% 1.46/1.72 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.46/1.72
% 1.46/1.72 % Formulas that are not ordinary clauses:
% 1.46/1.72 1 (all B_1_1 all B_2_1 all B_3_1 (is_fun20916972t_bool(B_1_1) & is_Arr723427730le_alt(B_2_1) & is_Arr723427730le_alt(B_3_1) -> is_fun20916972t_bool(arrow_207701375_below(B_1_1,B_2_1,B_3_1)))) # label(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Obelow) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 2 (all B_1_1 all B_2_1 all B_3_1 (is_fun20916972t_bool(B_1_1) & is_Arr723427730le_alt(B_2_1) & is_Arr723427730le_alt(B_3_1) -> is_bool(in_rel1361124802le_alt(B_1_1,B_2_1,B_3_1)))) # label(gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 3 (all B_1_1 (is_fun20916972t_bool(B_1_1) -> is_fun1420103068l_bool(inj_on398823523t_bool(B_1_1)))) # label(gsy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 4 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_1_1) -> is_fun701126715l_bool(pi_Arr1801471756t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 5 (all B_1_1 all B_2_1 (is_fun701126715l_bool(B_1_1) -> is_fun292781289l_bool(pi_fun1555365306t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 6 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_1_1) -> is_fun1420103068l_bool(pi_Pro1873779901t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 7 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_1_1) -> is_fun1084921220e_indi(hilber951314860di_nat(B_1_1,B_2_1)))) # label(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 8 (all B_1_1 (is_fun2015243113i_bool(B_1_1) -> is_fun2015243113i_bool(collec279390863e_indi(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 9 (all B_1_1 (is_fun1568535512t_bool(B_1_1) -> is_fun1568535512t_bool(collect_Product_unit(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Product____Type__Ounit) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 10 (all B_1_1 (is_fun701126715l_bool(B_1_1) -> is_fun701126715l_bool(collec1567922785t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 11 (all B_1_1 (is_fun292781289l_bool(B_1_1) -> is_fun292781289l_bool(collec1517527055t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 12 (all B_1_1 (is_fun1420103068l_bool(B_1_1) -> is_fun1420103068l_bool(collec612883262t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 13 (all B_1_1 (is_fun20916972t_bool(B_1_1) -> is_fun20916972t_bool(collec1376511890le_alt(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 14 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_bool(hAPP_A1120018583t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 15 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun1420103068l_bool(hAPP_A433435097l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 16 (all B_1_1 all B_2_1 (is_Arr723427730le_alt(B_2_1) -> is_fun20916972t_bool(hAPP_A1014090479t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_001) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 17 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_1_1) & is_Arr859726945e_indi(B_2_1) -> is_bool(hAPP_A416869060i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 18 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun701126715l_bool(hAPP_A701636433l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 19 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun292781289l_bool(hAPP_A955165183l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_002) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 20 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun1420103068l_bool(hAPP_A659996934l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_003) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 21 (all B_1_1 all B_2_1 (is_Arr859726945e_indi(B_2_1) -> is_fun20916972t_bool(hAPP_A340536322t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_004) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 22 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 23 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_b2116075462i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 24 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1568535512t_bool(hAPP_b1096750261t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 25 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun701126715l_bool(hAPP_b1461182872l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 26 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun292781289l_bool(hAPP_b651754310l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 27 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1420103068l_bool(hAPP_b805997823l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 28 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun20916972t_bool(hAPP_b763490121t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 29 (all B_1_1 all B_2_1 (is_fun1084921220e_indi(B_1_1) -> is_Arr859726945e_indi(hAPP_n619554777e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 30 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 31 (all B_1_1 all B_2_1 is_fun2015243113i_bool(hAPP_n1600508401i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsu) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 32 (all B_1_1 all B_2_1 is_fun1568535512t_bool(hAPP_n454528608t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 33 (all B_1_1 all B_2_1 (is_fun1568535512t_bool(B_1_1) -> is_bool(hAPP_P1676879539t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 34 (all B_1_1 all B_2_1 is_fun701126715l_bool(hAPP_P667392034l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 35 (all B_1_1 all B_2_1 is_fun292781289l_bool(hAPP_P1305865168l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 36 (all B_1_1 all B_2_1 is_fun1420103068l_bool(hAPP_P288224245l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 37 (all B_1_1 all B_2_1 is_fun20916972t_bool(hAPP_P401722323t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 38 (all B_1_1 all B_2_1 is_bool(hAPP_f212509069l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 39 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_2_1) -> is_bool(hAPP_f160177134l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 40 (all B_1_1 all B_2_1 (is_fun2015243113i_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_f1282033109i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__005) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 41 (all B_1_1 all B_2_1 is_Arr859726945e_indi(hAPP_f350403485e_indi(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__006) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 42 (all B_1_1 all B_2_1 (is_fun701126715l_bool(B_1_1) -> is_bool(hAPP_f1378099862l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__007) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 43 (all B_1_1 all B_2_1 is_fun2015243113i_bool(hAPP_f1570138413i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__008) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 44 (all B_1_1 all B_2_1 is_fun1568535512t_bool(hAPP_f1009478556t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__009) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 45 (all B_1_1 all B_2_1 is_fun1420103068l_bool(hAPP_f1895971544l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__010) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 46 (all B_1_1 all B_2_1 is_fun20916972t_bool(hAPP_f1817389232t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__011) # label(hypothesis) # label(non_clause). [assumption].
% 1.46/1.72 47 (all B_1_1 all B_2_1 is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 48 (all B_1_1 all B_2_1 is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 49 (all B_1_1 all B_2_1 (is_fun1568535512t_bool(B_2_1) -> is_bool(hAPP_f2028818269l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 50 (all B_1_1 all B_2_1 (is_fun1568535512t_bool(B_2_1) -> is_fun1568535512t_bool(hAPP_f427533077t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 51 (all B_1_1 all B_2_1 is_bool(hAPP_f599997089l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 52 (all B_1_1 all B_2_1 is_bool(hAPP_f1898839893l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_012) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 53 (all B_1_1 all B_2_1 is_bool(hAPP_f2016919811l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_013) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 54 (all B_1_1 all B_2_1 (is_fun701126715l_bool(B_2_1) -> is_bool(hAPP_f147218624l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_014) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 55 (all B_1_1 all B_2_1 (is_fun701126715l_bool(B_2_1) -> is_fun701126715l_bool(hAPP_f189058133l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_015) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 56 (all B_1_1 all B_2_1 is_Arr859726945e_indi(hAPP_f2043811403e_indi(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_016) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 57 (all B_1_1 all B_2_1 (is_fun292781289l_bool(B_1_1) -> is_bool(hAPP_f446648900l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_017) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 58 (all B_1_1 all B_2_1 is_fun2015243113i_bool(hAPP_f783549695i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_018) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 59 (all B_1_1 all B_2_1 is_fun1568535512t_bool(hAPP_f1841347694t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_019) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 60 (all B_1_1 all B_2_1 is_bool(hAPP_f1291635206l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_020) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 61 (all B_1_1 all B_2_1 is_bool(hAPP_f67777128l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 62 (all B_1_1 all B_2_1 is_bool(hAPP_f620747982l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 63 (all B_1_1 all B_2_1 is_bool(hAPP_f740740988l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 64 (all B_1_1 all B_2_1 is_bool(hAPP_f937100551l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 65 (all B_1_1 all B_2_1 is_bool(hAPP_f2053170815l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 66 (all B_1_1 all B_2_1 is_bool(hAPP_f1428735377l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 67 (all B_1_1 all B_2_1 is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 68 (all B_1_1 all B_2_1 is_bool(hAPP_f1426445843l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 69 (all B_1_1 all B_2_1 is_bool(hAPP_f537623936l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 70 (all B_1_1 all B_2_1 is_bool(hAPP_f339859954l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 71 (all B_1_1 all B_2_1 is_bool(hAPP_f866114756l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 72 (all B_1_1 all B_2_1 is_bool(hAPP_f1597773170l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 73 (all B_1_1 all B_2_1 is_bool(hAPP_f1965705105l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 74 (all B_1_1 all B_2_1 is_bool(hAPP_f1117143157l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 75 (all B_1_1 all B_2_1 is_bool(hAPP_f882250837l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 76 (all B_1_1 all B_2_1 is_bool(hAPP_f1138659662l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_021) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 77 (all B_1_1 all B_2_1 is_bool(hAPP_f1082951236l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_022) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 78 (all B_1_1 all B_2_1 (is_fun292781289l_bool(B_2_1) -> is_bool(hAPP_f322109294l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_023) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 79 (all B_1_1 all B_2_1 (is_fun292781289l_bool(B_2_1) -> is_fun292781289l_bool(hAPP_f1028172757l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_024) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 80 (all B_1_1 all B_2_1 is_bool(hAPP_f742658307l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 81 (all B_1_1 all B_2_1 is_bool(hAPP_f750478076l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_025) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 82 (all B_1_1 all B_2_1 is_bool(hAPP_f966397426l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_026) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 83 (all B_1_1 all B_2_1 is_bool(hAPP_f1021828400l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 84 (all B_1_1 all B_2_1 is_bool(hAPP_f560261801l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_027) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 85 (all B_1_1 all B_2_1 is_bool(hAPP_f1384787615l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_028) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 86 (all B_1_1 all B_2_1 is_bool(hAPP_f1363425282l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_029) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 87 (all B_1_1 all B_2_1 is_bool(hAPP_f817344902l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 88 (all B_1_1 all B_2_1 (is_fun1420103068l_bool(B_2_1) -> is_bool(hAPP_f560517119l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_030) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 89 (all B_1_1 all B_2_1 (is_fun1420103068l_bool(B_2_1) -> is_fun1420103068l_bool(hAPP_f574392641l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_031) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 90 (all B_1_1 all B_2_1 is_bool(hAPP_f557371893l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_032) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 91 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_Arr859726945e_indi(hAPP_f1283454584e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 92 (all B_1_1 all B_2_1 (is_fun1420103068l_bool(B_1_1) & is_fun20916972t_bool(B_2_1) -> is_bool(hAPP_f1733357041l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___033) # label(hypothesis) # label(non_clause). [assumption].
% 1.46/1.72 93 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun2015243113i_bool(hAPP_f431432850i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___034) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 94 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun1568535512t_bool(hAPP_f649586561t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___035) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 95 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun701126715l_bool(hAPP_f1332130404l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___036) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 96 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun1420103068l_bool(hAPP_f1344932147l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___037) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 97 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_2_1) -> is_fun20916972t_bool(hAPP_f137597973t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___038) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 98 (all B_1_1 all B_2_1 is_Arr859726945e_indi(hAPP_P1645359566e_indi(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 99 (all B_1_1 all B_2_1 (is_fun20916972t_bool(B_1_1) -> is_bool(hAPP_P1813625415t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__039) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 100 (all B_1_1 all B_2_1 is_fun2015243113i_bool(hAPP_P957402556i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__040) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 101 (all B_1_1 all B_2_1 is_fun1568535512t_bool(hAPP_P822772139t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__041) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 102 (all B_1_1 all B_2_1 is_fun1420103068l_bool(hAPP_P1151433609l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__042) # label(hypothesis) # label(non_clause). [assumption].
% 1.46/1.72 103 (all X_2 all Y_2 all L_3 all Z_1 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(Z_1) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),Z_1))) <-> Y_2 != Z_1 & (X_2 = Z_1 -> X_2 != Y_2) & (X_2 != Z_1 -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)))))) # label(fact_4_in__mkbot) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 104 (all X_2 all Y_2 all L_3 all Z_1 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(Z_1) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),Z_1))) <-> X_2 != Z_1 & (Y_2 = Z_1 -> X_2 != Y_2) & (Y_2 != Z_1 -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)))))) # label(fact_5_in__mktop) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 105 (all P_1 all Pa all A_34 all B_32 all Aa all Ba (is_Arr723427730le_alt(A_34) & is_Arr723427730le_alt(B_32) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (A_34 != B_32 -> (Aa != B_32 -> (Ba != A_34 -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof)) -> ((all I_2 (is_Arr859726945e_indi(I_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))))))))))))) # label(fact_6__C2_C) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 106 (all P_1 all Pa all A_34 all B_32 all Aa all Ba (is_Arr723427730le_alt(A_34) & is_Arr723427730le_alt(B_32) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (A_34 != B_32 -> (Aa != B_32 -> (Ba != A_34 -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof)) -> ((all I_2 (is_Arr859726945e_indi(I_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))))))))))))) # label(fact_7__C1_C) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 107 (all P_1 all Pa all Ca all Aa all Ba (is_Arr723427730le_alt(Ca) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (Ba != Ca -> (Aa != Ca -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof)) -> ((all I_2 (is_Arr859726945e_indi(I_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_A340536322t_bool(P_1,I_2)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Ca)),hAPP_f1817389232t_bool(f,P_1)))))))))))) # label(fact_8__C4_C) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 108 (all P_1 all Pa all A_34 all B_32 all Aa all Ba (is_Arr723427730le_alt(A_34) & is_Arr723427730le_alt(B_32) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (A_34 != B_32 -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof)) -> ((all I_2 (is_Arr859726945e_indi(I_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_A340536322t_bool(P_1,I_2)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32)),hAPP_f1817389232t_bool(f,P_1))))))))))) # label(fact_9_pairwise__neutrality) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 109 (all P_1 all Pa all Aa all Ba (is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_1),arrow_583275979e_Prof)) -> ((all I_2 (is_Arr859726945e_indi(I_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I_2))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_A340536322t_bool(P_1,I_2)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),hAPP_f1817389232t_bool(f,P_1)))))))))) # label(fact_10__C3_C) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 110 (all I_2 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A340536322t_bool(p,I_2))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> (hAPP_A1895296483di_nat(h,I_2) = n -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))) & (hAPP_A1895296483di_nat(h,I_2) != n -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))))))) # label(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 111 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) # label(fact_14_PW) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 112 (all Pa ((all X1 hBOOL(hAPP_P1813625415t_bool(Pa,X1))) <-> (all A_1 all B_25 (is_Arr723427730le_alt(A_1) & is_Arr723427730le_alt(B_25) -> hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25))))))) # label(fact_15_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 113 (all A_36 all B_34 all A_35 all B_33 (is_Arr723427730le_alt(A_36) & is_Arr723427730le_alt(B_34) & is_Arr723427730le_alt(A_35) & is_Arr723427730le_alt(B_33) -> (hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_36),B_34) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_35),B_33) -> -(A_36 = A_35 -> B_34 != B_33)))) # label(fact_21_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 114 (all Aa all Ba all A_34 all B_32 (is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) & is_Arr723427730le_alt(A_34) & is_Arr723427730le_alt(B_32) -> (hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_34),B_32) <-> Aa = A_34 & Ba = B_32))) # label(fact_22_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 115 (all Fa (hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,Fa)) <-> (all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) -> (all Xa (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Xa),arrow_583275979e_Prof)) -> (all A_1 all B_25 (is_Arr723427730le_alt(A_1) & is_Arr723427730le_alt(B_25) -> ((all I_2 (is_Arr859726945e_indi(I_2) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(Xa,I_2)))))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,Xa))))))))))))) # label(fact_23_IIA__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 116 (all Fa (hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,Fa)) <-> (all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) -> (all A_1 all B_25 (is_Arr723427730le_alt(A_1) & is_Arr723427730le_alt(B_25) -> ((all I_2 (is_Arr859726945e_indi(I_2) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_2))))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1)))))))))) # label(fact_24_unanimity__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 117 (all X_2 hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2))) # label(fact_25_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 118 (all X_2 hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2))) # label(fact_26_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 119 (all X_2 hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2))) # label(fact_27_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 120 (all X_2 hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2))) # label(fact_28_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 121 (all X_2 hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2))) # label(fact_29_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 122 (all X_2 hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))) # label(fact_30_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 123 (all X_2 hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2))) # label(fact_31_top1I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 124 (all X_2 hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool))) # label(fact_32_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 125 (all X_2 hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool))) # label(fact_33_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 126 (all X_2 hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool))) # label(fact_34_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 127 (all X_2 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool))) # label(fact_35_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 128 (all X_2 hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool))) # label(fact_36_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 129 (all X_2 hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool))) # label(fact_37_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 130 (all X_2 hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool))) # label(fact_38_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 131 (all X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool))) # label(fact_39_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 132 (all X_2 hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool))) # label(fact_40_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 133 (all X_2 hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool))) # label(fact_41_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 134 (all X_2 hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool))) # label(fact_42_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 135 (all X_2 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool))) # label(fact_43_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 136 (all X_2 hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool))) # label(fact_44_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 137 (all X_2 hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool))) # label(fact_45_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 138 (all X_2 hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool))) # label(fact_46_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 139 (all X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool))) # label(fact_47_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 140 (all X_2 (hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_48_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 141 (all X_2 (hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_49_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 142 (all X_2 (hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_50_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 143 (all X_2 (hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_51_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 144 (all X_2 (hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_52_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.72 145 (all X_2 (hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_53_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 146 (all X_2 (hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_54_top__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 147 (all Aa -hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,top_to846262053l_bool),Aa))) # label(fact_55_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 148 (all Aa -hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,top_to935749874l_bool),Aa))) # label(fact_56_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 149 (all Aa -hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,top_to1849101472l_bool),Aa))) # label(fact_57_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 150 (all Aa -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa))) # label(fact_58_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 151 (all Aa -hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,top_to1773227171t_bool),Aa))) # label(fact_59_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 152 (all Aa -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,top_to207207712i_bool),Aa))) # label(fact_60_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 153 (all Aa -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa))) # label(fact_61_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 154 (all Aa -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),Aa))) # label(fact_62_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 155 (all Aa (is_fun1420103068l_bool(Aa) -> (Aa != top_to846262053l_bool <-> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,Aa),top_to846262053l_bool))))) # label(fact_63_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 156 (all Aa (is_fun701126715l_bool(Aa) -> (Aa != top_to935749874l_bool <-> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,Aa),top_to935749874l_bool))))) # label(fact_64_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 157 (all Aa (is_fun292781289l_bool(Aa) -> (Aa != top_to1849101472l_bool <-> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,Aa),top_to1849101472l_bool))))) # label(fact_65_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 158 (all Aa (-(hBOOL(Aa) <-> hBOOL(top_top_bool)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)))) # label(fact_66_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 159 (all Aa (is_fun20916972t_bool(Aa) -> (Aa != top_to1773227171t_bool <-> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,Aa),top_to1773227171t_bool))))) # label(fact_67_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 160 (all Aa (is_fun2015243113i_bool(Aa) -> (Aa != top_to207207712i_bool <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),top_to207207712i_bool))))) # label(fact_68_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 161 (all Aa (is_fun1568535512t_bool(Aa) -> (Aa != top_to1257323279t_bool <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),top_to1257323279t_bool))))) # label(fact_69_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 162 (all Aa (Aa != top_top_fun_nat_bool <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),top_top_fun_nat_bool)))) # label(fact_70_less__top) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 163 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n))),lab)),lba)))) # label(fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 164 (all Na hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_583275979e_Prof))) # label(fact_80_PiProf) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 165 -(all Lab (is_fun20916972t_bool(Lab) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),Lab)) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lab),arrow_912654623le_Lin))))) # label(fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 166 -(all Lba (is_fun20916972t_bool(Lba) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),Lba)) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Lba),arrow_912654623le_Lin))))) # label(fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 167 (all I_2 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> (hAPP_A1895296483di_nat(h,I_2) = n -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))) & (hAPP_A1895296483di_nat(h,I_2) != n -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,e),d)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lab))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),lba))))) # label(fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 168 (all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))))) # label(fact_84_n_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 169 (all X_2 all Y_2 all L_3 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_2) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> (X_2 != Y_2 -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3)) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),X_2)),L_3))))))) # label(fact_85_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 170 (all Aa all Ba all L_3 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),L_3)) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),L_3))))) # label(fact_86_Lin__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 171 (all X_2 all L_3 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,L_3),X_2)),arrow_912654623le_Lin)))) # label(fact_87_mktop__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 172 (all X_2 all L_3 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,L_3),X_2)),arrow_912654623le_Lin)))) # label(fact_88_mkbot__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 173 (all L_3 all X_2 all Y_2 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_2) -> (X_2 != Y_2 -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),X_2),Y_2)),arrow_912654623le_Lin)))))) # label(fact_89_above__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 174 (all L_3 (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,L_3)),arrow_583275979e_Prof)))) # label(fact_90_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 175 (all X_32 all Y_30 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_30)) -> (X_32 != Y_30 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_30),X_32))))) # label(fact_91_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 176 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)))) # label(fact_92_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 177 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)))) # label(fact_93_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 178 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)))) # label(fact_94_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 179 (all X_31 all Y_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_29)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_29),X_31)))) # label(fact_95_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 180 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2))))) # label(fact_96_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 181 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2))))) # label(fact_97_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 182 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2))))) # label(fact_98_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 183 (all Z_9 all Y_28 all X_30 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_28),X_30)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_28)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_30))))) # label(fact_99_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 184 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1))))) # label(fact_100_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 185 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1))))) # label(fact_101_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 186 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1))))) # label(fact_102_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 187 (all Z_8 all X_29 all Y_27 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Y_27)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_27),Z_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Z_8))))) # label(fact_103_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 188 (all Ca all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) -> (Ba = Ca -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa))))) # label(fact_104_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 189 (all Ca all Ba all Aa (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) -> (Ba = Ca -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa))))) # label(fact_105_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 190 (all Ca all Ba all Aa (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) -> (Ba = Ca -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa))))) # label(fact_106_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 191 (all C_24 all B_31 all A_33 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_33)) -> (B_31 = C_24 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_24),A_33))))) # label(fact_107_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 192 (all Ca all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) -> (Ba = Ca -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca))))) # label(fact_108_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 193 (all Ca all Aa all Ba (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) -> (Ba = Ca -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca))))) # label(fact_109_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 194 (all Ca all Aa all Ba (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) -> (Ba = Ca -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca))))) # label(fact_110_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 195 (all C_23 all A_32 all B_30 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),B_30)) -> (B_30 = C_23 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),C_23))))) # label(fact_111_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 196 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa))))) # label(fact_112_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 197 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa))))) # label(fact_113_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 198 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Ba)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ca),Aa))))) # label(fact_114_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 199 (all C_22 all A_31 all B_29 (A_31 = B_29 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),A_31))))) # label(fact_115_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 200 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca))))) # label(fact_116_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 201 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca))))) # label(fact_117_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 202 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Ca)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ca))))) # label(fact_118_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 203 (all C_21 all A_30 all B_28 (A_30 = B_28 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_28),C_21)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_30),C_21))))) # label(fact_119_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 204 (all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)))) # label(fact_120_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 205 (all Ba all Aa (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)))) # label(fact_121_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 206 (all Ba all Aa (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)) -> -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)))) # label(fact_122_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 207 (all B_27 all A_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_27),A_29)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_29),B_27)))) # label(fact_123_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 208 (all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)))) # label(fact_124_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 209 (all Aa all Ba (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)))) # label(fact_125_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 210 (all Aa all Ba (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)) -> -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)))) # label(fact_126_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 211 (all A_28 all B_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_26)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_26),A_28)))) # label(fact_127_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 212 (all Pa all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) -> hBOOL(Pa)))) # label(fact_128_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 213 (all Pa all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) -> hBOOL(Pa)))) # label(fact_129_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 214 (all Pa all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) -> hBOOL(Pa)))) # label(fact_130_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 215 (all Pa all X_2 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) -> hBOOL(Pa)))) # label(fact_131_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 216 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> Y_2 != X_2)) # label(fact_132_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 217 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> Y_2 != X_2)) # label(fact_133_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 218 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> Y_2 != X_2)) # label(fact_134_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 219 (all X_28 all Y_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Y_26)) -> Y_26 != X_28)) # label(fact_135_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 220 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> X_2 != Y_2)) # label(fact_136_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 221 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> X_2 != Y_2)) # label(fact_137_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 222 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> X_2 != Y_2)) # label(fact_138_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 223 (all X_27 all Y_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),Y_25)) -> X_27 != Y_25)) # label(fact_139_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 224 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)))) # label(fact_140_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 225 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)))) # label(fact_141_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 226 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)))) # label(fact_142_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 227 (all X_26 all Y_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_24)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_24),X_26)))) # label(fact_143_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 228 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)))) # label(fact_144_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 229 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)))) # label(fact_145_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 230 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)))) # label(fact_146_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 231 (all X_25 all Y_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_23)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_25)))) # label(fact_147_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 232 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> X_2 != Y_2)) # label(fact_148_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 233 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> X_2 != Y_2)) # label(fact_149_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 234 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> X_2 != Y_2)) # label(fact_150_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 235 (all X_24 all Y_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_22)) -> X_24 != Y_22)) # label(fact_151_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 236 (all X_23 all Y_21 (X_23 != Y_21 -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_21)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_23))))) # label(fact_152_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 237 (all Y_2 all X_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) <-> X_2 = Y_2))) # label(fact_153_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 238 (all X_22 all Y_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_20)) | X_22 = Y_20 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_22)))) # label(fact_154_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 239 (all X_2 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) | X_2 = Y_2)) # label(fact_155_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 240 (all X_2 all Y_2 (X_2 != Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)))) # label(fact_156_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 241 (all X_2 -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2))) # label(fact_157_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 242 (all X_2 -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2))) # label(fact_158_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 243 (all X_2 -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),X_2))) # label(fact_159_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 244 (all X_21 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21))) # label(fact_160_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 245 (all X_2 all A (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) <-> hBOOL(hAPP_A416869060i_bool(A,X_2)))) # label(fact_168_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 246 (all X_2 all A (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) <-> hBOOL(hAPP_bool_bool(A,X_2)))) # label(fact_169_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 247 (all X_2 all A (hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) <-> hBOOL(hAPP_P1676879539t_bool(A,X_2)))) # label(fact_170_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 248 (all X_2 all A (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) <-> hBOOL(hAPP_P1813625415t_bool(A,X_2)))) # label(fact_171_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 249 (all X_2 all A (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) <-> hBOOL(hAPP_f1378099862l_bool(A,X_2)))) # label(fact_172_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 250 (all X_2 all A (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) <-> hBOOL(hAPP_f446648900l_bool(A,X_2)))) # label(fact_173_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 251 (all X_2 all A (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) <-> hBOOL(hAPP_f1733357041l_bool(A,X_2)))) # label(fact_174_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 252 (all X_2 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) <-> hBOOL(hAPP_nat_bool(A,X_2)))) # label(fact_175_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 253 (all Pa (is_fun1568535512t_bool(Pa) -> collect_Product_unit(Pa) = Pa)) # label(fact_176_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 254 (all Pa (is_fun2015243113i_bool(Pa) -> collec279390863e_indi(Pa) = Pa)) # label(fact_177_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 255 (all Pa collect_nat(Pa) = Pa) # label(fact_178_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 256 (all X_2 all Y_2 all L_3 all Aa all Ba (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,L_3),Aa),Ba))) <-> X_2 != Y_2 & (X_2 = Ba -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Y_2)),L_3))) & (X_2 != Ba -> (Y_2 = Ba -> X_2 = Aa | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Aa)),L_3))) & (Y_2 != Ba -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))))))))) # label(fact_179_in__above) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 257 (all S_1 all R_1 (is_fun20916972t_bool(S_1) & is_fun20916972t_bool(R_1) -> ((all X_1 all Xa (is_Arr723427730le_alt(X_1) & is_Arr723427730le_alt(Xa) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),R_1)) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Xa)),S_1))))) <-> R_1 = S_1))) # label(fact_180_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 258 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) # label(fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 259 (all I_2 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_312654597_mktop,hAPP_A340536322t_bool(p,I_2)),e)))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),n)) -> (hAPP_A1895296483di_nat(h,I_2) = n -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_1046586475_above,hAPP_A340536322t_bool(p,I_2)),c),e)))) & (hAPP_A1895296483di_nat(h,I_2) != n -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),e)),hAPP_A1014090479t_bool(hAPP_f102394819t_bool(arrow_163947511_mkbot,hAPP_A340536322t_bool(p,I_2)),e))))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lab))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1895296483di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),lba))))) # label(fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 260 (all X_2 all Y_2 all F (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)) -> (hAPP_A1895296483di_nat(F,X_2) = Y_2 -> hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),Y_2) = X_2)))) # label(fact_184_inv__f__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 261 (all X_2 all Y_2 all F (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) -> (hAPP_nat_nat(F,X_2) = Y_2 -> hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),Y_2) = X_2))) # label(fact_185_inv__f__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 262 (all X_2 all F (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)) -> hAPP_n619554777e_indi(hilber951314860di_nat(top_to207207712i_bool,F),hAPP_A1895296483di_nat(F,X_2)) = X_2))) # label(fact_186_inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 263 (all X_2 all F (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) -> hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),hAPP_nat_nat(F,X_2)) = X_2)) # label(fact_187_inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 264 (all I_1 all Fa (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Fa),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) -> ((all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) -> (all A_1 all B_25 (is_Arr723427730le_alt(A_1) & is_Arr723427730le_alt(B_25) -> (A_1 != B_25 -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_A340536322t_bool(X_1,I_1))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_1),B_25)),hAPP_f1817389232t_bool(Fa,X_1))))))))) -> hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1))))) # label(fact_188_dictatorI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 265 (all X_2 all F all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))))) # label(fact_189_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 266 (all X_2 all F all A all B (hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A,B))) -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B,X_2))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))))) # label(fact_190_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 267 (all X_2 all F all A all B (hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A,B))) -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))))) # label(fact_191_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 268 (all X_2 all F all A all B (hBOOL(hAPP_f1117143157l_bool(hAPP_f2011903565l_bool(member485283698le_alt,F),pi_Pro1208494515le_alt(A,B))) -> (-hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P1931143485le_alt(F,X_2)),hAPP_P401722323t_bool(B,X_2))) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))))) # label(fact_192_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 269 (all X_2 all F all A all B (hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A,B))) -> (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B,X_2))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))))) # label(fact_193_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 270 (all X_2 all F all A all B (hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A,B))) -> (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))))) # label(fact_194_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 271 (all X_2 all F all A all B (hBOOL(hAPP_f866114756l_bool(hAPP_f813426957l_bool(member1044213697t_bool,F),pi_Pro1114473858t_bool(A,B))) -> (-hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1245388556t_bool(F,X_2)),hAPP_P667392034l_bool(B,X_2))) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))))) # label(fact_195_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 272 (all X_2 all F all A all B (hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A,B))) -> (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B,X_2))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))))) # label(fact_196_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 273 (all X_2 all F all A all B (hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A,B))) -> (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))))) # label(fact_197_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 274 (all X_2 all F all A all B (hBOOL(hAPP_f1597773170l_bool(hAPP_f627309453l_bool(member1775405935t_bool,F),pi_Pro831923248t_bool(A,B))) -> (-hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P1157363642t_bool(F,X_2)),hAPP_P1305865168l_bool(B,X_2))) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))))) # label(fact_198_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 275 (all X_2 all F all A all B (hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A,B))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))))) # label(fact_199_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 276 (all X_2 all F all A all B (hBOOL(hAPP_f1965705105l_bool(hAPP_f177302985l_bool(member928589940t_bool,F),pi_Pro1925515229t_bool(A,B))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P401722323t_bool(F,X_2)),hAPP_P288224245l_bool(B,X_2))) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))))) # label(fact_200_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 277 (all X_2 all F all A all B (hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,B))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1895296483di_nat(F,X_2)),hAPP_A1948275303t_bool(B,X_2))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))))) # label(fact_201_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 278 (all X_2 all F all A all B (hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))))) # label(fact_202_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 279 (all X_2 all F all A all B (hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2))) -> -hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))))) # label(fact_203_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 280 (all X_2 all F all A all B (hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A,B))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B,X_2))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))))) # label(fact_204_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 281 (all X_2 all F all A all B (hBOOL(hAPP_f557371893l_bool(hAPP_f785487437l_bool(member1226631410t_unit,F),pi_Pro269694131t_unit(A,B))) -> (-hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P992343101t_unit(F,X_2)),hAPP_P822772139t_bool(B,X_2))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A))))) # label(fact_205_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 282 (all X_2 all F all A all B (hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A,B))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B,X_2))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))))) # label(fact_206_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 283 (all X_2 all F all A all B (hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B,X_2))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))))) # label(fact_207_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 284 (all X_2 all F all A all B (hBOOL(hAPP_f1082951236l_bool(hAPP_f1160956173l_bool(member982489409t_unit,F),pi_fun623621634t_unit(A,B))) -> (-hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f754536332t_unit(F,X_2)),hAPP_f1009478556t_bool(B,X_2))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))))) # label(fact_208_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 285 (all X_2 all F all A all B (hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A,B))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B,X_2))) -> -hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))))) # label(fact_209_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 286 (all X_2 all F all A all B (hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B,X_2))) -> -hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))))) # label(fact_210_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 287 (all X_2 all F all A all B (hBOOL(hAPP_f966397426l_bool(hAPP_f1957108621l_bool(member1941767151t_unit,F),pi_fun1390764464t_unit(A,B))) -> (-hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1716204858t_unit(F,X_2)),hAPP_f1841347694t_bool(B,X_2))) -> -hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A))))) # label(fact_211_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 288 (all X_2 all F all A all B (hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,B))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B,X_2))) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))))) # label(fact_212_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 289 (all X_2 all F all A all B (hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B,X_2))) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))))) # label(fact_213_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 290 (all X_2 all F all A all B (hBOOL(hAPP_f1384787615l_bool(hAPP_f715600357l_bool(member416763266t_unit,F),pi_fun1012573681t_unit(A,B))) -> (-hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1636264423t_unit(F,X_2)),hAPP_f649586561t_bool(B,X_2))) -> -hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A))))) # label(fact_214_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 291 (all X_2 all F all A all B (hBOOL(hAPP_f1428735377l_bool(hAPP_f544923081l_bool(member1801639028e_indi,F),pi_nat1476290531e_indi(A,B))) -> (-hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_n619554777e_indi(F,X_2)),hAPP_n1600508401i_bool(B,X_2))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))))) # label(fact_215_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 292 (all X_2 all F all A all B (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))))) # label(fact_216_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 293 (all X_2 all F all A all B (hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B))) -> (-hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))))) # label(fact_217_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 294 (all X_2 all F all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2))) -> -hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A))))) # label(fact_218_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 295 (all X_2 all F all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) -> (-hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2))) -> -hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A))))) # label(fact_219_PiE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 296 (all Aa all Ba (is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (exists X_1 (is_fun20916972t_bool(X_1) & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),arrow_912654623le_Lin)) & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),X_1))))))) # label(fact_220_complete__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 297 (all A pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool) # label(fact_221_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 298 (all A pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool) # label(fact_222_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 299 (all A pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool)) = top_to935749874l_bool) # label(fact_223_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 300 (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2))) # label(fact_224_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 301 (all X_20 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20))) # label(fact_225_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 302 (all X_2 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2))) # label(fact_226_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 303 (exists N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool))) & (all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))))) & hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba)))))) # label(fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 304 -(all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite354462354e_indi(top_to207207712i_bool))) -> ((all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),M))),lab)),lba)))))) -> -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_f1817389232t_bool(f,hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba))))))) # label(fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 305 (all X_19 all Y_19 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_19)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_19),X_19)))) # label(fact_229_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 306 (all X_2 all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))))) # label(fact_230_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 307 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_2))))) # label(fact_231_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 308 (all Z_7 all Y_18 all X_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_18)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),X_18))))) # label(fact_232_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 309 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_2))))) # label(fact_233_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 310 (all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(X_2) <-> hBOOL(Y_2))))) # label(fact_234_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 311 (all Y_17 all X_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_17)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_17),Y_17)) -> X_17 = Y_17))) # label(fact_235_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 312 (all Y_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) -> X_2 = Y_2))) # label(fact_236_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 313 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_1))))) # label(fact_237_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 314 (all Z_6 all X_16 all Y_16 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Y_16)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),Z_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Z_6))))) # label(fact_238_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 315 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_1))))) # label(fact_239_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 316 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(X_2) <-> hBOOL(Y_2))))) # label(fact_240_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 317 (all X_15 all Y_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_15)) -> X_15 = Y_15))) # label(fact_241_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 318 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) -> X_2 = Y_2))) # label(fact_242_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 319 (all Ca all Ba all Aa (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa)) -> ((hBOOL(Ba) <-> hBOOL(Ca)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa))))) # label(fact_243_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 320 (all C_20 all B_24 all A_27 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_27)) -> (B_24 = C_20 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_27))))) # label(fact_244_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 321 (all Ca all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) -> (Ba = Ca -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa))))) # label(fact_245_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 322 (all Ca all Aa all Ba (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba)) -> ((hBOOL(Ba) <-> hBOOL(Ca)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca))))) # label(fact_246_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 323 (all C_19 all A_26 all B_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_23)) -> (B_23 = C_19 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),C_19))))) # label(fact_247_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 324 (all Ca all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) -> (Ba = Ca -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca))))) # label(fact_248_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 325 (all Ca all Ba all Aa ((hBOOL(Aa) <-> hBOOL(Ba)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa))))) # label(fact_249_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 326 (all C_18 all A_25 all B_22 (A_25 = B_22 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),B_22)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),A_25))))) # label(fact_250_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 327 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa))))) # label(fact_251_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 328 (all Ca all Ba all Aa ((hBOOL(Aa) <-> hBOOL(Ba)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca))))) # label(fact_252_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 329 (all C_17 all A_24 all B_21 (A_24 = B_21 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_21),C_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_24),C_17))))) # label(fact_253_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 330 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca))))) # label(fact_254_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 331 (all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) <-> (hBOOL(X_2) <-> hBOOL(Y_2))))) # label(fact_255_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 332 (all Y_2 all X_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) <-> X_2 = Y_2))) # label(fact_256_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 333 (all Y_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) <-> X_2 = Y_2))) # label(fact_257_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 334 (all X_2 all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))))) # label(fact_258_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 335 (all Y_2 all X_2 ((hBOOL(X_2) <-> hBOOL(Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)))) # label(fact_259_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 336 (all X_14 all Y_14 (X_14 = Y_14 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_14)))) # label(fact_260_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 337 (all X_2 all Y_2 (X_2 = Y_2 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)))) # label(fact_261_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 338 (all Y_2 all X_2 ((hBOOL(X_2) <-> hBOOL(Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)))) # label(fact_262_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 339 (all X_2 all Y_2 (X_2 = Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)))) # label(fact_263_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 340 (all X_2 all Y_2 (X_2 = Y_2 <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)))) # label(fact_264_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.73 341 (all X_13 all Y_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),Y_13)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13)))) # label(fact_265_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 342 (all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) <-> (all X_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1)))))) # label(fact_266_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 343 (all X_2 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)))) # label(fact_267_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 344 (all X_2 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)))) # label(fact_268_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 345 (all X_12 all Y_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Y_12)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_12)))) # label(fact_269_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 346 (all X_2 all Y_2 (is_fun1568535512t_bool(X_2) & is_fun1568535512t_bool(Y_2) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) & X_2 != Y_2))) # label(fact_270_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 347 (all X_2 all Y_2 (is_fun2015243113i_bool(X_2) & is_fun2015243113i_bool(Y_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) & X_2 != Y_2))) # label(fact_271_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 348 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) & -(hBOOL(X_2) <-> hBOOL(Y_2)))) # label(fact_272_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 349 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) & X_2 != Y_2)) # label(fact_273_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 350 (all X_2 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) & X_2 != Y_2)) # label(fact_274_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 351 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) & -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)))) # label(fact_275_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 352 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) & -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2)))) # label(fact_276_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 353 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) & -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)))) # label(fact_277_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 354 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)))) # label(fact_278_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 355 (all X_2 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)))) # label(fact_279_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 356 (all X_2 all Y_2 (is_fun1568535512t_bool(X_2) & is_fun1568535512t_bool(Y_2) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) | X_2 = Y_2))) # label(fact_280_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 357 (all X_2 all Y_2 (is_fun2015243113i_bool(X_2) & is_fun2015243113i_bool(Y_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) | X_2 = Y_2))) # label(fact_281_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 358 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) | (hBOOL(X_2) <-> hBOOL(Y_2)))) # label(fact_282_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 359 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) | X_2 = Y_2)) # label(fact_283_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 360 (all X_2 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) | X_2 = Y_2)) # label(fact_284_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 361 (all X_11 all Y_11 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_11)))) # label(fact_285_leI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 362 (all Y_10 all X_10 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_10)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10)))) # label(fact_286_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 363 (all X_2 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) <-> X_2 = Y_2))) # label(fact_287_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 364 (all Aa all Ba (is_fun1568535512t_bool(Aa) & is_fun1568535512t_bool(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)))))) # label(fact_288_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 365 (all Aa all Ba (is_fun2015243113i_bool(Aa) & is_fun2015243113i_bool(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)))))) # label(fact_289_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 366 (all Ba all Aa (-(hBOOL(Aa) <-> hBOOL(Ba)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba))))) # label(fact_290_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 367 (all Aa all Ba (Aa != Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))))) # label(fact_291_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 368 (all A_23 all B_20 (A_23 != B_20 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),B_20)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_23),B_20))))) # label(fact_292_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 369 (all Aa all Ba (is_fun1568535512t_bool(Aa) & is_fun1568535512t_bool(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)))))) # label(fact_293_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 370 (all Aa all Ba (is_fun2015243113i_bool(Aa) & is_fun2015243113i_bool(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)))))) # label(fact_294_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 371 (all Ba all Aa (-(hBOOL(Aa) <-> hBOOL(Ba)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa))))) # label(fact_295_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 372 (all Aa all Ba (Aa != Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))))) # label(fact_296_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 373 (all A_22 all B_19 (A_22 != B_19 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_22)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_22))))) # label(fact_297_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 374 (all Y_9 all X_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_9)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9)))) # label(fact_298_leD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 375 (all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)))) # label(fact_299_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 376 (all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)))) # label(fact_300_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 377 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)))) # label(fact_301_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 378 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)))) # label(fact_302_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 379 (all X_8 all Y_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_8)))) # label(fact_303_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 380 (all X_2 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) <-> X_2 = Y_2))) # label(fact_304_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 381 (all X_2 all Y_2 (is_fun1568535512t_bool(X_2) & is_fun1568535512t_bool(Y_2) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) | X_2 = Y_2))) # label(fact_305_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 382 (all X_2 all Y_2 (is_fun2015243113i_bool(X_2) & is_fun2015243113i_bool(Y_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) | X_2 = Y_2))) # label(fact_306_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 383 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) | (hBOOL(X_2) <-> hBOOL(Y_2)))) # label(fact_307_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 384 (all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) | X_2 = Y_2)) # label(fact_308_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 385 (all X_7 all Y_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_7)) | X_7 = Y_7)) # label(fact_309_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 386 (all Aa all Ba (is_fun1568535512t_bool(Aa) & is_fun1568535512t_bool(Ba) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba)) -> (Aa != Ba -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)))))) # label(fact_310_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 387 (all Aa all Ba (is_fun2015243113i_bool(Aa) & is_fun2015243113i_bool(Ba) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),Ba)) -> (Aa != Ba -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Aa),Ba)))))) # label(fact_311_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 388 (all Aa all Ba (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba)) -> (-(hBOOL(Aa) <-> hBOOL(Ba)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba))))) # label(fact_312_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 389 (all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) -> (Aa != Ba -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))))) # label(fact_313_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 390 (all A_21 all B_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_18)) -> (A_21 != B_18 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),B_18))))) # label(fact_314_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 391 (all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) -> (Aa != Ba -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))))) # label(fact_315_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 392 (all Ba all Aa (is_fun1568535512t_bool(Ba) & is_fun1568535512t_bool(Aa) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa)) -> (Aa != Ba -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)))))) # label(fact_316_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 393 (all Ba all Aa (is_fun2015243113i_bool(Ba) & is_fun2015243113i_bool(Aa) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Ba),Aa)) -> (Aa != Ba -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Ba),Aa)))))) # label(fact_317_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 394 (all B_17 all A_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_20)) -> (A_20 != B_17 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_20))))) # label(fact_318_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 395 (all Ba all Aa (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa)) -> (-(hBOOL(Aa) <-> hBOOL(Ba)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa))))) # label(fact_319_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 396 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1))))) # label(fact_320_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 397 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1))))) # label(fact_321_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 398 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Y_2)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),Z_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1))))) # label(fact_322_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 399 (all Z_5 all X_6 all Y_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Z_5))))) # label(fact_323_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 400 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1))))) # label(fact_324_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 401 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2))))) # label(fact_325_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 402 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2))))) # label(fact_326_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 403 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),X_2)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Z_1),Y_2)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2))))) # label(fact_327_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 404 (all Z_4 all Y_5 all X_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_5),X_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_4),Y_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),X_5))))) # label(fact_328_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 405 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2))))) # label(fact_329_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 406 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1))))) # label(fact_330_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 407 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1))))) # label(fact_331_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 408 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,X_2),Y_2)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Y_2),Z_1)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,X_2),Z_1))))) # label(fact_332_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 409 (all Z_3 all X_4 all Y_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),Z_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Z_3))))) # label(fact_333_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 410 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),Z_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1))))) # label(fact_334_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 411 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2))))) # label(fact_335_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 412 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2))))) # label(fact_336_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 413 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Y_2),X_2)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),Y_2)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,Z_1),X_2))))) # label(fact_337_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 414 (all Z_2 all Y_3 all X_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_3))))) # label(fact_338_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 415 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2))))) # label(fact_339_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 416 (all Aa hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool))) # label(fact_340_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 417 (all Aa hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,Aa),top_to846262053l_bool))) # label(fact_341_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 418 (all Aa hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,Aa),top_to1849101472l_bool))) # label(fact_342_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 419 (all Aa hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,Aa),top_to935749874l_bool))) # label(fact_343_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 420 (all Aa hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,Aa),top_to1773227171t_bool))) # label(fact_344_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 421 (all Aa hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool))) # label(fact_345_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 422 (all Aa hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool))) # label(fact_346_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 423 (all Aa hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,Aa),top_to207207712i_bool))) # label(fact_347_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 424 (all Aa (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa)) <-> (hBOOL(Aa) <-> hBOOL(top_top_bool)))) # label(fact_348_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 425 (all Aa (is_fun1420103068l_bool(Aa) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa)) <-> Aa = top_to846262053l_bool))) # label(fact_349_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 426 (all Aa (is_fun292781289l_bool(Aa) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa)) <-> Aa = top_to1849101472l_bool))) # label(fact_350_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 427 (all Aa (is_fun701126715l_bool(Aa) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa)) <-> Aa = top_to935749874l_bool))) # label(fact_351_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 428 (all Aa (is_fun20916972t_bool(Aa) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa)) <-> Aa = top_to1773227171t_bool))) # label(fact_352_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 429 (all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa)) <-> Aa = top_top_fun_nat_bool)) # label(fact_353_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 430 (all Aa (is_fun1568535512t_bool(Aa) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa)) <-> Aa = top_to1257323279t_bool))) # label(fact_354_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 431 (all Aa (is_fun2015243113i_bool(Aa) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa)) <-> Aa = top_to207207712i_bool))) # label(fact_355_top__unique) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 432 (all Aa (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa)) -> (hBOOL(Aa) <-> hBOOL(top_top_bool)))) # label(fact_356_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 433 (all Aa (is_fun1420103068l_bool(Aa) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,top_to846262053l_bool),Aa)) -> Aa = top_to846262053l_bool))) # label(fact_357_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 434 (all Aa (is_fun292781289l_bool(Aa) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,top_to1849101472l_bool),Aa)) -> Aa = top_to1849101472l_bool))) # label(fact_358_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 435 (all Aa (is_fun701126715l_bool(Aa) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,top_to935749874l_bool),Aa)) -> Aa = top_to935749874l_bool))) # label(fact_359_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 436 (all Aa (is_fun20916972t_bool(Aa) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,top_to1773227171t_bool),Aa)) -> Aa = top_to1773227171t_bool))) # label(fact_360_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 437 (all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa)) -> Aa = top_top_fun_nat_bool)) # label(fact_361_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 438 (all Aa (is_fun1568535512t_bool(Aa) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa)) -> Aa = top_to1257323279t_bool))) # label(fact_362_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 439 (all Aa (is_fun2015243113i_bool(Aa) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,top_to207207712i_bool),Aa)) -> Aa = top_to207207712i_bool))) # label(fact_363_top__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 440 (all F all A (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) <-> (all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),A)) -> (hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Xa) -> X_1 = Xa))))))) # label(fact_364_inj__on__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 441 (all F all A (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) <-> (all X_1 (is_Arr859726945e_indi(X_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A)) -> (all Xa (is_Arr859726945e_indi(Xa) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Xa),A)) -> (hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Xa) -> X_1 = Xa))))))))) # label(fact_365_inj__on__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 442 (all X_2 all Y_2 all F all A (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) -> (X_2 != Y_2 -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A)) -> hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2)))))) # label(fact_366_inj__on__contraD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 443 (all X_2 all Y_2 all F all A (is_Arr859726945e_indi(X_2) & is_Arr859726945e_indi(Y_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) -> (X_2 != Y_2 -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A)) -> hAPP_A1895296483di_nat(F,X_2) != hAPP_A1895296483di_nat(F,Y_2))))))) # label(fact_367_inj__on__contraD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 444 (all Y_2 all X_2 all F all A (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A)) -> (hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) <-> X_2 = Y_2))))) # label(fact_368_inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 445 (all Y_2 all X_2 all F all A (is_Arr859726945e_indi(Y_2) & is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A)) -> (hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2) <-> X_2 = Y_2)))))) # label(fact_369_inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 446 (all X_2 all Y_2 all F all A (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) -> (hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A)) -> X_2 = Y_2))))) # label(fact_370_inj__onD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 447 (all X_2 all Y_2 all F all A (is_Arr859726945e_indi(X_2) & is_Arr859726945e_indi(Y_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) -> (hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),A)) -> X_2 = Y_2)))))) # label(fact_371_inj__onD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 448 (all X_2 all F all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B,X_2)))))) # label(fact_372_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 449 (all X_2 all F all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B,X_2)))))) # label(fact_373_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 450 (all X_2 all F all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B,X_2)))))) # label(fact_374_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 451 (all A hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A))) # label(fact_376_inj__on__id2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 452 (all X_2 all F all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),B))))) # label(fact_377_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 453 (all X_2 all F all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),B))))) # label(fact_378_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 454 (all X_2 all F all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),B))))) # label(fact_379_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 455 (all Fa all I_1 (hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_1)) <-> (all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),arrow_583275979e_Prof)) -> hAPP_f1817389232t_bool(Fa,X_1) = hAPP_A340536322t_bool(X_1,I_1))))) # label(fact_380_dictator__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 456 (all X_2 all Y_2 all F (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) -> (hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) <-> X_2 = Y_2))) # label(fact_381_inj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 457 (all X_2 all Y_2 all F (is_Arr859726945e_indi(X_2) & is_Arr859726945e_indi(Y_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)) -> (hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2) <-> X_2 = Y_2)))) # label(fact_382_inj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 458 (all X_2 all Y_2 all F (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) -> (hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) -> X_2 = Y_2))) # label(fact_383_injD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 459 (all X_2 all Y_2 all F (is_Arr859726945e_indi(X_2) & is_Arr859726945e_indi(Y_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)) -> (hAPP_A1895296483di_nat(F,X_2) = hAPP_A1895296483di_nat(F,Y_2) -> X_2 = Y_2)))) # label(fact_384_injD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 460 (all X_2 all F all A (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hAPP_nat_nat(hilber195283148at_nat(A,F),hAPP_nat_nat(F,X_2)) = X_2))) # label(fact_385_inv__into__f__f) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 461 (all X_2 all F all A (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> hAPP_n619554777e_indi(hilber951314860di_nat(A,F),hAPP_A1895296483di_nat(F,X_2)) = X_2)))) # label(fact_386_inv__into__f__f) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 462 (all Y_2 all X_2 all F all A (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (hAPP_nat_nat(F,X_2) = Y_2 -> hAPP_nat_nat(hilber195283148at_nat(A,F),Y_2) = X_2)))) # label(fact_387_inv__into__f__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 463 (all Y_2 all X_2 all F all A (is_Arr859726945e_indi(X_2) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> (hAPP_A1895296483di_nat(F,X_2) = Y_2 -> hAPP_n619554777e_indi(hilber951314860di_nat(A,F),Y_2) = X_2))))) # label(fact_388_inv__into__f__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 464 (all F all B all A ((all X_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1))))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))))) # label(fact_389_Pi__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 465 (all F all B all A ((all X_1 (is_Arr859726945e_indi(X_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1)))))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))))) # label(fact_390_Pi__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 466 (all F all B all A ((all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1))))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))))) # label(fact_391_Pi__I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 467 (all G all F (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) -> ((all X_1 hAPP_nat_nat(F,hAPP_nat_nat(G,X_1)) = X_1) -> hilber195283148at_nat(top_top_fun_nat_bool,F) = G))) # label(fact_392_inj__imp__inv__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 468 (all G all F (is_fun1084921220e_indi(G) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)) -> ((all X_1 hAPP_A1895296483di_nat(F,hAPP_n619554777e_indi(G,X_1)) = X_1) -> hilber951314860di_nat(top_to207207712i_bool,F) = G)))) # label(fact_393_inj__imp__inv__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 469 (all A_19 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),one_one_nat)))) # label(fact_394_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 470 (all C_16 all D_3 all A_18 all B_16 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),B_16)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_16),D_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3)))))) # label(fact_395_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 471 (all C_15 all D_2 all A_17 all B_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),B_15)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_15),D_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2)))))) # label(fact_396_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 472 (all F ((all X_1 all Y_1 (hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1) -> X_1 = Y_1)) -> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)))) # label(fact_397_injI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 473 (all F ((all X_1 all Y_1 (is_Arr859726945e_indi(X_1) & is_Arr859726945e_indi(Y_1) -> (hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1) -> X_1 = Y_1))) -> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),top_to207207712i_bool)))) # label(fact_398_injI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 474 (all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) & -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F)))) # label(fact_399_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 475 (all F all G (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,F),G)) <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) & -hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,G),F)))) # label(fact_400_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 476 (all F all G (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,F),G)) <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,F),G)) & -hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,G),F)))) # label(fact_401_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 477 (all B all A_16 all A (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A_16),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A_16,B))))) # label(fact_402_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 478 (all B all A_16 all A (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A_16),A)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A_16,B))))) # label(fact_403_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 479 (all B all A_16 all A (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A_16),A)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A_16,B))))) # label(fact_404_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 480 (all R_1 all S_1 (hBOOL(hAPP_f212509069l_bool(hAPP_f2078760383l_bool(ord_le319160163t_bool,hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),R_1)),hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(cOMBB_333235735le_alt(cOMBC_943734388l_bool),hAPP_f1747206697l_bool(cOMBB_885534287le_alt(cOMBB_711698847le_alt(member720722004le_alt)),produc1456060119le_alt))),S_1))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)))) # label(fact_405_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 481 (all A hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),top_to846262053l_bool))) # label(fact_406_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 482 (all A hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),top_to1849101472l_bool))) # label(fact_407_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 483 (all A hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),top_to935749874l_bool))) # label(fact_408_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 484 (all A hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),top_to1773227171t_bool))) # label(fact_409_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 485 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool))) # label(fact_410_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 486 (all A hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool))) # label(fact_411_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 487 (all A hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),top_to207207712i_bool))) # label(fact_412_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 488 (all A all F all B (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))))) # label(fact_413_subset__inj__on) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 489 (all A all F all B (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) -> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A))))) # label(fact_414_subset__inj__on) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 490 (all B_14 all A_15 all C_14 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_15) -> B_14 = C_14)) # label(fact_415_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 491 (all A_14 all B_13 all C_13 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_13) -> B_13 = C_13)) # label(fact_416_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 492 (all A_13 all B_12 all C_12 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_12) -> B_12 = C_12)) # label(fact_417_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 493 (all Ba all Aa all Ca (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa) <-> Ba = Ca)) # label(fact_418_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 494 (all Aa all Ba all Ca (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca) <-> Ba = Ca)) # label(fact_419_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 495 (all A_12 all B_11 all C_11 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11))) # label(fact_420_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 496 (all X_2 (one_one_nat = X_2 <-> X_2 = one_one_nat)) # label(fact_421_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 497 (all C_10 all A_11 all B_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_10))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_11),B_10)))) # label(fact_422_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 498 (all A_10 all C_9 all B_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_10),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_9))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),B_9)))) # label(fact_423_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 499 (all C_8 all D_1 all A_9 all B_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_8),D_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1)))))) # label(fact_424_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 500 (all C_7 all A_8 all B_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7))))) # label(fact_425_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 501 (all C_6 all A_7 all B_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6))))) # label(fact_426_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 502 (all Ca all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_427_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 503 (all Aa all Ca all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_428_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 504 (all C_5 all A_6 all B_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),A_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),B_5))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_5)))) # label(fact_429_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 505 (all A_5 all C_4 all B_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_5),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),C_4))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_5),B_4)))) # label(fact_430_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 506 (all C_3 all D all A_4 all B_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),B_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),D)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_4),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D)))))) # label(fact_431_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 507 (all C_2 all A_3 all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),A_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2))))) # label(fact_432_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 508 (all C_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1))))) # label(fact_433_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 509 (all Ca all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_434_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 510 (all Aa all Ca all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_435_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 511 (all F all G ((all X_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)))) # label(fact_436_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 512 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> A = B))) # label(fact_437_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 513 (all Ca all A all B (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B))))) # label(fact_438_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 514 (all Ca all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B))))) # label(fact_439_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 515 (all Ca all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B))))) # label(fact_440_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 516 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_441_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 517 (all Ca all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B))))) # label(fact_442_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 518 (all Ca all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B))))) # label(fact_443_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 519 (all Ca all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B))))) # label(fact_444_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 520 (all Ca all A all B (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B))))) # label(fact_445_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 521 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) & A != B)) # label(fact_446_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 522 (all A all B (is_fun1568535512t_bool(A) & is_fun1568535512t_bool(B) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) & A != B))) # label(fact_447_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 523 (all A all B (is_fun2015243113i_bool(A) & is_fun2015243113i_bool(B) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) & A != B))) # label(fact_448_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 524 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) | A = B)) # label(fact_449_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 525 (all A all B (is_fun1568535512t_bool(A) & is_fun1568535512t_bool(B) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) | A = B))) # label(fact_450_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 526 (all A all B (is_fun2015243113i_bool(A) & is_fun2015243113i_bool(B) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) | A = B))) # label(fact_451_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 527 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_452_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 528 (all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)))) # label(fact_453_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 529 (all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)))) # label(fact_454_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 530 (all C all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C))))) # label(fact_455_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 531 (all C all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),C)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C))))) # label(fact_456_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 532 (all C all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,B),C)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C))))) # label(fact_457_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 533 (all C all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C))))) # label(fact_458_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 534 (all C all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C))))) # label(fact_459_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 535 (all C all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C))))) # label(fact_460_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 536 (all A all B (A = B -> -(hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))))) # label(fact_461_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 537 (all C all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C))))) # label(fact_462_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 538 (all X_2 all A all B (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B))))) # label(fact_463_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 539 (all X_2 all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B))))) # label(fact_464_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 540 (all X_2 all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B))))) # label(fact_465_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 541 (all X_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))))) # label(fact_466_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 542 (all X_2 all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B))))) # label(fact_467_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 543 (all X_2 all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B))))) # label(fact_468_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 544 (all X_2 all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B))))) # label(fact_469_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 545 (all X_2 all A all B (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B))))) # label(fact_470_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 546 (all B all X_2 all A (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B))))) # label(fact_471_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 547 (all B all X_2 all A (hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B))))) # label(fact_472_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 548 (all B all X_2 all A (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B))))) # label(fact_473_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 549 (all B all X_2 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))))) # label(fact_474_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 550 (all B all X_2 all A (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B))))) # label(fact_475_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.74 551 (all B all X_2 all A (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B))))) # label(fact_476_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 552 (all B all X_2 all A (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B))))) # label(fact_477_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 553 (all B all X_2 all A (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B))))) # label(fact_478_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 554 (all X_2 all Pa all Q_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1)) -> (hBOOL(hAPP_nat_bool(Pa,X_2)) -> hBOOL(hAPP_nat_bool(Q_1,X_2))))) # label(fact_479_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 555 (all X_2 all A all B (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B))))) # label(fact_480_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 556 (all X_2 all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B))))) # label(fact_481_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 557 (all X_2 all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),B))))) # label(fact_482_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 558 (all X_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))))) # label(fact_483_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 559 (all X_2 all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),B))))) # label(fact_484_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 560 (all X_2 all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),B))))) # label(fact_485_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 561 (all X_2 all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),B))))) # label(fact_486_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 562 (all X_2 all A all B (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),B))))) # label(fact_487_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 563 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)))) # label(fact_488_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 564 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_489_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 565 (all Q_1 all Pa all X_2 (hBOOL(hAPP_nat_bool(Pa,X_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1)) -> hBOOL(hAPP_nat_bool(Q_1,X_2))))) # label(fact_490_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 566 (all A all B (A = B <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)))) # label(fact_491_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 567 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A))) # label(fact_492_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 568 (all R_1 all S_1 (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1))) <-> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1)))) # label(fact_493_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 569 (all R_1 all S_1 (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),R_1)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),S_1))) <-> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,R_1),S_1)))) # label(fact_494_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 570 (all R_1 all S_1 (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),R_1)),hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,member161528657e_indi),S_1))) <-> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,R_1),S_1)))) # label(fact_495_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 571 (all R_1 all S_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)))) # label(fact_496_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 572 (all R_1 all S_1 (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),R_1)),hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,member1704306684t_bool),S_1))) <-> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,R_1),S_1)))) # label(fact_497_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 573 (all R_1 all S_1 (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),R_1)),hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,member1619170513t_bool),S_1))) <-> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,R_1),S_1)))) # label(fact_498_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 574 (all R_1 all S_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),R_1)),hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,member1265098019t_bool),S_1))) <-> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,R_1),S_1)))) # label(fact_499_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 575 (all R_1 all S_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),R_1)),hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,member720722004le_alt),S_1))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,R_1),S_1)))) # label(fact_500_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 576 (all B all C all A ((all X_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1122857141l_bool(B,X_1)),hAPP_P1122857141l_bool(C,X_1))))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,pi_Pro1873779901t_bool(A,B)),pi_Pro1873779901t_bool(A,C))))) # label(fact_501_Pi__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 577 (all B all C all A ((all X_1 (is_Arr859726945e_indi(X_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_A659996934l_bool(B,X_1)),hAPP_A659996934l_bool(C,X_1)))))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,pi_Arr1801471756t_bool(A,B)),pi_Arr1801471756t_bool(A,C))))) # label(fact_502_Pi__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 578 (all B all C all A ((all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,hAPP_f1895971544l_bool(B,X_1)),hAPP_f1895971544l_bool(C,X_1))))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,pi_fun1555365306t_bool(A,B)),pi_fun1555365306t_bool(A,C))))) # label(fact_503_Pi__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 579 (all B all A ((all X_1 (is_bool(X_1) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),B))))) -> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)))) # label(fact_504_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 580 (all B all A ((all X_1 (hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),B)))) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)))) # label(fact_505_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 581 (all B all A ((all X_1 (is_Arr859726945e_indi(X_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),B))))) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1028202352i_bool,A),B)))) # label(fact_506_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 582 (all B all A ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_507_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 583 (all B all A ((all X_1 (is_fun20916972t_bool(X_1) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),B))))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1079191765l_bool,A),B)))) # label(fact_508_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 584 (all B all A ((all X_1 (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),B)))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le2143686384l_bool,A),B)))) # label(fact_509_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 585 (all B all A ((all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),B)))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le1482529602l_bool,A),B)))) # label(fact_510_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 586 (all B all A ((all X_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),B)))) -> hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le64728819t_bool,A),B)))) # label(fact_511_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 587 (all Ca all A all B (hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le197158773l_bool,A),B)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B))))) # label(fact_512_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 588 (all Ca all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B))))) # label(fact_513_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 589 (all Ca all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),A)) -> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Ca),B))))) # label(fact_514_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 590 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_515_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 591 (all Ca all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1700034367l_bool(ord_le1260664009l_bool,A),B)) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Ca),B))))) # label(fact_516_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 592 (all Ca all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f1216491309l_bool(ord_le1141238780l_bool,A),B)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),A)) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Ca),B))))) # label(fact_517_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 593 (all Ca all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f1547458257l_bool(ord_le194694222l_bool,A),B)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),A)) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Ca),B))))) # label(fact_518_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 594 (all Ca all A all B (hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(ord_le2113500159t_bool,A),B)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),A)) -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Ca),B))))) # label(fact_519_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 595 (all C all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C))))) # label(fact_520_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 596 (all C all A all B (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B)) -> (hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C)) -> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C))))) # label(fact_521_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 597 (all C all A all B (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),B)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,B),C)) -> hBOOL(hAPP_f160177134l_bool(hAPP_f563440173l_bool(ord_le1791992956i_bool,A),C))))) # label(fact_522_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 598 (all X_2 all Y_2 all L_3 all Aa all Ba (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_2) & is_Arr723427730le_alt(Aa) & is_Arr723427730le_alt(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),arrow_207701375_below(L_3,Aa,Ba))) <-> X_2 != Y_2 & (Y_2 = Aa -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Ba)),L_3))) & (Y_2 != Aa -> (X_2 = Aa -> Y_2 = Ba | hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Y_2)),L_3))) & (X_2 != Aa -> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),L_3))))))))) # label(fact_523_in__below) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 599 (all M_2 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))))) # label(fact_524_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 600 (all M_2 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_525_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 601 (all M_2 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)))) # label(fact_526_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 602 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_527_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 603 (all M_4 all Na (M_4 != Na <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)))) # label(fact_528_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 604 (all X all Y (X != Y -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X))))) # label(fact_529_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 605 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_530_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 606 (all N_1 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2)) -> M_2 != N_1)) # label(fact_531_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 607 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_532_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 608 (all Pa all M_4 all Na ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4))) -> ((M_4 = Na -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)))))) # label(fact_533_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 609 (all M_2 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2)) # label(fact_534_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 610 (all X all Y all Z hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z))) # label(fact_535_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 611 (all M_2 all N_1 all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1))) # label(fact_536_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 612 (all K all M_4 all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na) <-> M_4 = Na)) # label(fact_537_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 613 (all M_4 all K all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K) <-> M_4 = Na)) # label(fact_538_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 614 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1))) # label(fact_539_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 615 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)))) # label(fact_540_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 616 (all M_2 all N_1 (M_2 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_541_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 617 (all K_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_1))))) # label(fact_542_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 618 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)) -> M_2 = N_1))) # label(fact_543_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 619 (all L_3 all X_2 all Y_2 (is_Arr723427730le_alt(X_2) & is_Arr723427730le_alt(Y_2) -> (X_2 != Y_2 -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_3),arrow_912654623le_Lin)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,arrow_207701375_below(L_3,X_2,Y_2)),arrow_912654623le_Lin)))))) # label(fact_544_below__Lin) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 620 (all K all N_2 hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),N_2))) # label(fact_545_inj__on__add__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 621 (all I all J_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),I))) # label(fact_546_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 622 (all J_2 all I -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),I))) # label(fact_547_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 623 (all K all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)))) # label(fact_548_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 624 (all M_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))))) # label(fact_549_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 625 (all M_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))))) # label(fact_550_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 626 (all K_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))))) # label(fact_551_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 627 (all K_1 all L_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2)))))) # label(fact_552_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 628 (all M_2 all N_1 all K_1 all L_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))))) # label(fact_553_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 629 (all I all J_2 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1)))) # label(fact_554_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 630 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) & M_4 != Na)) # label(fact_555_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 631 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) | M_4 = Na)) # label(fact_556_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 632 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_557_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 633 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> (M_2 != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))))) # label(fact_558_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 634 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) | M_2 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_559_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 635 (all N_1 all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)))) # label(fact_560_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 636 (all N_1 all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2)))) # label(fact_561_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 637 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) <-> (exists K_2 Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2)))) # label(fact_562_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 638 (all K all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)))) # label(fact_563_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 639 (all M_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))))) # label(fact_564_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 640 (all M_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))))) # label(fact_565_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 641 (all K_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))))) # label(fact_566_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 642 (all K_1 all L_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2)))))) # label(fact_567_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 643 (all M_4 all K all F ((all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M_4)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K)))))) # label(fact_568_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 644 (all I_1 all J_1 all F ((all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1)))))) # label(fact_569_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 645 (all Z all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_570_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 646 (all Y all X all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_571_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 647 (all Y all X all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_572_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 648 (all Z all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_573_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 649 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)))) # label(fact_574_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 650 (all R_1 all X_2 all Y_2 (hBOOL(in_rel1361124802le_alt(R_1,X_2,Y_2)) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1)))) # label(fact_575_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 651 (all F all B all A ((all X_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),B)))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))))) # label(fact_576_funcsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 652 (all F all B all A ((all X_1 (is_Arr859726945e_indi(X_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),B))))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))))) # label(fact_577_funcsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 653 (all F all B all A ((all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),B)))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))))) # label(fact_578_funcsetI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 654 (exists L_1 (is_fun20916972t_bool(L_1) & hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin)))) # label(fact_579_linear__alt) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 655 (all B all G all F all A ((all W (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,W),A)) -> (hBOOL(hAPP_P1813625415t_bool(F,W)) <-> hBOOL(hAPP_P1813625415t_bool(G,W))))) -> (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))) <-> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,G),pi_Pro1873779901t_bool(A,B)))))) # label(fact_580_Pi__cong) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 656 (all B all F all G all A ((all W (is_Arr859726945e_indi(W) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,W),A)) -> hAPP_A340536322t_bool(F,W) = hAPP_A340536322t_bool(G,W)))) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))) <-> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(A,B)))))) # label(fact_581_Pi__cong) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 657 (all B all F all G all A ((all W (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,W),A)) -> hAPP_f1817389232t_bool(F,W) = hAPP_f1817389232t_bool(G,W))) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))) <-> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(A,B)))))) # label(fact_582_Pi__cong) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 658 (all F all B all A ((all X_1 (hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A)) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B,X_1))))) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,B))))) # label(fact_583_Pi__I_H) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 659 (all F all B all A ((all X_1 (is_Arr859726945e_indi(X_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B,X_1)))))) -> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,B))))) # label(fact_584_Pi__I_H) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 660 (all F all B all A ((all X_1 (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A)) -> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B,X_1))))) -> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,B))))) # label(fact_585_Pi__I_H) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 661 (all F all A all B (hBOOL(hAPP_f1426445843l_bool(hAPP_f2040535501l_bool(member_fun_nat_nat,F),pi_nat_nat(A,hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,B)))) -> (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite_card_nat(A)),finite_card_nat(B))))))) # label(fact_586_card__inj) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 662 (all F all A all B (hBOOL(hAPP_f599997089l_bool(hAPP_f758593513l_bool(member873781636di_nat,F),pi_Arr604548589di_nat(A,hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,B)))) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite_card_nat(B))))))) # label(fact_587_card__inj) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 663 (all F all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) -> (hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A)) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1044330389le_alt(A)),finite_card_bool(B))))))) # label(fact_588_card__inj) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 664 (all F all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) -> (hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A)) -> (hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite354462354e_indi(A)),finite945540987t_bool(B))))))) # label(fact_589_card__inj) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 665 (all F all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) -> (hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A)) -> (hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1524925796t_bool(A)),finite945540987t_bool(B))))))) # label(fact_590_card__inj) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 666 (all F all A ((all X_1 all Y_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_1),A)) -> (hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1) -> X_1 = Y_1)))) -> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)))) # label(fact_591_inj__onI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 667 (all F all A ((all X_1 all Y_1 (is_Arr859726945e_indi(X_1) & is_Arr859726945e_indi(Y_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A)) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_1),A)) -> (hAPP_A1895296483di_nat(F,X_1) = hAPP_A1895296483di_nat(F,Y_1) -> X_1 = Y_1))))) -> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)))) # label(fact_592_inj__onI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 668 (all F all G all A ((all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_nat_nat(F,A_1) = hAPP_nat_nat(G,A_1))) -> (hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) <-> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(G),A))))) # label(fact_593_inj__on__cong) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 669 (all F all G all A ((all A_1 (is_Arr859726945e_indi(A_1) -> (hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,A_1),A)) -> hAPP_A1895296483di_nat(F,A_1) = hAPP_A1895296483di_nat(G,A_1)))) -> (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(F),A)) <-> hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(G),A))))) # label(fact_594_inj__on__cong) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 670 (all G all F all A all B (hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B)))) -> (hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(F),A)) -> (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(B,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,A)))) -> (hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(G),B)) -> (hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A)) -> (hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,B)) -> finite945540987t_bool(A) = finite354462354e_indi(B)))))))) # label(fact_596_card__bij) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 671 (all G all F all A all B (hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,F),pi_fun328162388t_bool(A,hAPP_f23348649l_bool(cOMBK_761999167t_bool,B)))) -> (hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(F),A)) -> (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(B,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,A)))) -> (hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(G),B)) -> (hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,A)) -> (hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,B)) -> finite945540987t_bool(A) = finite1524925796t_bool(B)))))))) # label(fact_597_card__bij) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 672 (all G all F all A all B (hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B)))) -> (hBOOL(hAPP_f1733357041l_bool(inj_on398823523t_bool(F),A)) -> (hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,G),pi_boo1542163389le_alt(B,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,A)))) -> (hBOOL(hAPP_f387058535l_bool(inj_on67207011le_alt(G),B)) -> (hBOOL(hAPP_f1733357041l_bool(finite955821396le_alt,A)) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B)) -> finite1044330389le_alt(A) = finite_card_bool(B)))))))) # label(fact_598_card__bij) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 673 (all G all F all A all B (hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B)))) -> (hBOOL(hAPP_f160177134l_bool(inj_on1507564774t_bool(F),A)) -> (hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,G),pi_fun596906370e_indi(B,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,A)))) -> (hBOOL(hAPP_f560517119l_bool(inj_on302999388e_indi(G),B)) -> (hBOOL(hAPP_f160177134l_bool(finite921964625e_indi,A)) -> (hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B)) -> finite354462354e_indi(A) = finite945540987t_bool(B)))))))) # label(fact_599_card__bij) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 674 (all G all F all A all B (hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B)))) -> (hBOOL(hAPP_f147218624l_bool(inj_on1962565012t_bool(F),A)) -> (hBOOL(hAPP_f1363425282l_bool(hAPP_f1980578603l_bool(member363954533t_bool,G),pi_fun328162388t_bool(B,hAPP_f23348649l_bool(cOMBK_761999167t_bool,A)))) -> (hBOOL(hAPP_f560517119l_bool(inj_on735362094t_bool(G),B)) -> (hBOOL(hAPP_f147218624l_bool(finite1323840035t_bool,A)) -> (hBOOL(hAPP_f560517119l_bool(finite274731772t_bool,B)) -> finite1524925796t_bool(A) = finite945540987t_bool(B)))))))) # label(fact_600_card__bij) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 675 (all K hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K))))) # label(fact_601_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 676 (all K hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K))))) # label(fact_602_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 677 (all Na finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na) # label(fact_604_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 678 (all Pa all I_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))))) # label(fact_606_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 679 (all N_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) <-> (exists M all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)))))) # label(fact_607_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 680 (all N_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) <-> (exists M all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M)))))) # label(fact_608_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 681 (all U all F ((all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(F,N)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U)))))) # label(fact_609_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 682 (all Na all N_2 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)))) # label(fact_610_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 683 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_611_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 684 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_612_le0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 685 (all N_1 (N_1 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_613_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 686 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> N_1 != zero_zero_nat)) # label(fact_614_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 687 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_615_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 688 (all Na (Na != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)))) # label(fact_616_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 689 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_617_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 690 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1) # label(fact_618_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 691 (all M_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2) # label(fact_619_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 692 (all M_4 all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = zero_zero_nat <-> M_4 = zero_zero_nat & Na = zero_zero_nat)) # label(fact_620_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 693 (all M_2 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = M_2 -> N_1 = zero_zero_nat)) # label(fact_621_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 694 (all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat)) <-> Na = zero_zero_nat)) # label(fact_622_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 695 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_623_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 696 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_4)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)))) # label(fact_624_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 697 (all Na all Pa (-hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(Pa,Na)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),Na)) & (all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2)) -> -hBOOL(hAPP_nat_bool(Pa,I_2)))) & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat)))))))) # label(fact_625_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 698 (all Na all Pa (-hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(Pa,Na)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) & (all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) -> -hBOOL(hAPP_nat_bool(Pa,I_2)))) & hBOOL(hAPP_nat_bool(Pa,K_2))))))) # label(fact_626_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 699 (all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) & hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2) = J_2)))) # label(fact_627_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 700 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1)))) # label(fact_628_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 701 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1))))) # label(fact_629_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 702 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1)))) # label(fact_630_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 703 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1))) # label(fact_631_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 704 (all M_4 all Na (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)))) # label(fact_632_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 705 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) | M_4 = hAPP_nat_nat(suc,Na))) # label(fact_633_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 706 (all Na all M_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_4))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_4)))) # label(fact_634_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 707 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))))) # label(fact_635_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 708 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> M_2 = hAPP_nat_nat(suc,N_1)))) # label(fact_636_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 709 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_637_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 710 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_638_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 711 (all Nat_4 all Nat_3 (hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3) <-> Nat_4 = Nat_3)) # label(fact_639_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 712 (all N_1 hAPP_nat_nat(suc,N_1) != N_1) # label(fact_640_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 713 (all N_1 N_1 != hAPP_nat_nat(suc,N_1)) # label(fact_641_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 714 (all M_2 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1))) # label(fact_642_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 715 (all M_2 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1))) # label(fact_643_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 716 (all M_2 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1))) # label(fact_644_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 717 (all M_4 all Na (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))))) # label(fact_645_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 718 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) | M_4 = Na)) # label(fact_646_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 719 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_4)),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)))) # label(fact_647_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 720 (all Na all M_4 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) <-> Na = M_4))) # label(fact_648_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 721 (all N_1 all M_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_2))) -> M_2 = N_1))) # label(fact_649_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 722 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))))) # label(fact_650_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 723 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> (hAPP_nat_nat(suc,M_2) != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1))))) # label(fact_651_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 724 (all K_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1))))) # label(fact_652_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 725 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> M_2 = N_1))) # label(fact_653_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 726 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)))) # label(fact_654_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 727 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)))) # label(fact_655_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 728 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)))) # label(fact_657_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 729 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) <-> Na = M_4))) # label(fact_658_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 730 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)))) # label(fact_659_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 731 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))))) # label(fact_660_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 732 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_4)),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)))) # label(fact_661_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 733 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)))) # label(fact_662_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 734 (all Na all M_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)))) # label(fact_663_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 735 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) <-> (exists K_2 Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2))))) # label(fact_664_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 736 (all I all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I))))) # label(fact_665_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 737 (all I all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_2))))) # label(fact_666_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 738 (all M_4 all Na (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) <-> M_4 = hAPP_nat_nat(suc,zero_zero_nat) & Na = zero_zero_nat | M_4 = zero_zero_nat & Na = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_667_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 739 (all M_4 all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = hAPP_nat_nat(suc,zero_zero_nat) <-> M_4 = hAPP_nat_nat(suc,zero_zero_nat) & Na = zero_zero_nat | M_4 = zero_zero_nat & Na = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_668_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 740 (all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) <-> (exists M Na = hAPP_nat_nat(suc,M)))) # label(fact_669_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 741 (all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat))) <-> Na = zero_zero_nat)) # label(fact_670_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 742 (all M_4 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na))) <-> M_4 = zero_zero_nat | (exists J (M_4 = hAPP_nat_nat(suc,J) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),Na)))))) # label(fact_671_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 743 (all N_2 hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2))) # label(fact_672_inj__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 744 (all M_2 hAPP_nat_nat(suc,M_2) != zero_zero_nat) # label(fact_673_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 745 (all M_2 zero_zero_nat != hAPP_nat_nat(suc,M_2)) # label(fact_674_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 746 (all Nat_2 hAPP_nat_nat(suc,Nat_2) != zero_zero_nat) # label(fact_675_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 747 (all M_2 hAPP_nat_nat(suc,M_2) != zero_zero_nat) # label(fact_676_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 748 (all Nat_1 zero_zero_nat != hAPP_nat_nat(suc,Nat_1)) # label(fact_677_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 749 (all M_2 zero_zero_nat != hAPP_nat_nat(suc,M_2)) # label(fact_678_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 750 (all X_1 hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1))) # label(fact_679_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 751 (all Na finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na)) # label(fact_680_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 752 (all I_1 all M_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> hAPP_nat_nat(suc,finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))))) # label(fact_681_card__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 753 (all I_1 all M_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) != zero_zero_nat)) # label(fact_682_card__less) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 754 (all I_1 all M_3 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))))) # label(fact_683_card__less__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 755 (all Pa all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hBOOL(hAPP_nat_bool(Pa,J_1)) -> ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) -> (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2))) -> hBOOL(hAPP_nat_bool(Pa,I_2))))) -> hBOOL(hAPP_nat_bool(Pa,I_1)))))) # label(fact_684_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 756 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> (exists K_2 N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2))))) # label(fact_685_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.75 757 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (exists M N_1 = hAPP_nat_nat(suc,M)))) # label(fact_686_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 758 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1)) # label(fact_687_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 759 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)) # label(fact_688_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 760 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1)) -> (exists M M_1 = hAPP_nat_nat(suc,M)))) # label(fact_689_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 761 (all I all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1)) -> (K_1 != hAPP_nat_nat(suc,I) -> -(all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> K_1 != hAPP_nat_nat(suc,J)))))) # label(fact_690_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 762 (all I all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1)) -> -(all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> K_1 != hAPP_nat_nat(suc,J))))) # label(fact_691_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 763 (all N_1 (N_1 != zero_zero_nat -> (exists M N_1 = hAPP_nat_nat(suc,M)))) # label(fact_692_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 764 (all Y (Y != zero_zero_nat -> -(all Nat Y != hAPP_nat_nat(suc,Nat)))) # label(fact_693_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 765 (all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))) -> hBOOL(hAPP_nat_bool(Pa,N)))) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))))) # label(fact_694_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 766 (all Na all Pa (hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> ((all N (hBOOL(hAPP_nat_bool(Pa,N)) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))))) -> hBOOL(hAPP_nat_bool(Pa,Na))))) # label(fact_695_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 767 (all L all U hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U)))) # label(fact_697_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 768 -(all H (hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(H),top_to207207712i_bool)) -> image_837079859di_nat(H,top_to207207712i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite354462354e_indi(top_to207207712i_bool)))) # label(fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 769 (all A all K (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A))))) -> A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A))))) # label(fact_699_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 770 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 771 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 772 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 773 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 774 (all P hAPP_nat_nat(cOMBI_nat,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 775 (all X all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 776 (all X all Y (X != Y | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 777 (all P all Q (is_bool(P) -> hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 778 (all P all Q (is_bool(P) -> hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 779 (all P all Q all R hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 780 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 781 (all P all Q all R hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 782 (all P all Q hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 783 (all P all Q (is_bool(P) -> hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 784 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 785 (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].
% 1.46/1.76 786 (all P all Q all R hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 787 (all P all Q all R hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,P),Q),R) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 788 (all P all Q all R hAPP_A416869060i_bool(hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A1948275303t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 789 (all P all Q hAPP_A1948275303t_bool(hAPP_f1393414918t_bool(cOMBK_1662914336e_indi,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 790 (all P all Q all R hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(P),Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 791 (all P all Q all R hAPP_P1676879539t_bool(hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,P),Q),R) = hAPP_f2028818269l_bool(hAPP_P607165281l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 792 (all P all Q all R hAPP_A1948275303t_bool(hAPP_f1882280879t_bool(cOMBB_552200224e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1895296483di_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 793 (all P all Q (is_bool(P) -> hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 794 (all X all Y (is_fun20916972t_bool(X) -> hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fTrue),X),Y) = X)) # label(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 795 (all X all Y (is_fun20916972t_bool(Y) -> hAPP_f137597973t_bool(hAPP_f1000663785t_bool(hAPP_b910261233t_bool(if_fun1158274329t_bool,fFalse),X),Y) = Y)) # label(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 796 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 797 (all P all Q all R hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f651290349i_bool(cOMBC_264525026l_bool,P),Q),R) = hAPP_f160177134l_bool(hAPP_A45661955l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_044) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 798 (all P all Q (is_bool(P) -> hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 799 (all P all Q hAPP_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_alt,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 800 (all P all Q (is_fun20916972t_bool(P) -> hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 801 (all P all Q (is_fun20916972t_bool(P) -> hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_045) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 802 (all P all Q all R hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_A433435097l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 803 (all P all Q (is_bool(P) -> hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 804 (all P all Q (is_fun2015243113i_bool(P) -> hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 805 (all P all Q (is_fun1420103068l_bool(P) -> hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 806 (all P all Q all R hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,P),Q),R) = hAPP_A1014090479t_bool(hAPP_A85603248t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_046) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 807 (all P all Q all R hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,P),Q),R) = hAPP_f1068593625t_bool(hAPP_A64811457t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_047) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 808 (all P all Q all R hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f1152614183t_bool(cOMBC_420816290l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 809 (all P all Q all R hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,P),Q),R) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_048) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 810 (all P all Q all R hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f1692576003l_bool(cOMBC_344067350l_bool,P),Q),R) = hAPP_f560517119l_bool(hAPP_f1332197581l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 811 (all P all Q all R hAPP_A433435097l_bool(hAPP_f1656652505l_bool(cOMBB_711698847le_alt(P),Q),R) = hAPP_P1151433609l_bool(P,hAPP_A1561816353le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 812 (all P all Q all R hAPP_A340536322t_bool(hAPP_f590186314t_bool(hAPP_f1975142533t_bool(cOMBC_1894996001t_bool,P),Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_049) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 813 (all P all Q all R hAPP_A340536322t_bool(cOMBS_178315313t_bool(P,Q),R) = hAPP_f137597973t_bool(hAPP_A1906804694t_bool(P,R),hAPP_A340536322t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 814 (all P all Q (is_bool(P) -> hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 815 (all P all Q (is_fun701126715l_bool(P) -> hAPP_f1332130404l_bool(hAPP_f23348649l_bool(cOMBK_761999167t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 816 (all P all Q (is_fun1420103068l_bool(P) -> hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_050) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 817 (all P all Q all R hAPP_A85603248t_bool(hAPP_f2027600413t_bool(cOMBB_640263118e_indi(P),Q),R) = hAPP_f102394819t_bool(P,hAPP_A340536322t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 818 (all P all Q all R hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f1500902601l_bool(cOMBC_1722249314l_bool,P),Q),R) = hAPP_f147218624l_bool(hAPP_f621397159l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.76 819 (all P all Q all R hAPP_A643475905l_bool(hAPP_f1747206697l_bool(cOMBB_885534287le_alt(P),Q),R) = hAPP_f1656652505l_bool(P,hAPP_A1171966089le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15 820 (all P all Q all R hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(cOMBB_930893948e_indi(P),Q),R) = hAPP_f684072049t_bool(P,hAPP_A340536322t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_051) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15 821 (all P all Q all R hAPP_A1906804694t_bool(hAPP_f1898540574t_bool(hAPP_f1283354413t_bool(cOMBC_1373788917t_bool,P),Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_052) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15 822 (all P all Q all R hAPP_A1906804694t_bool(cOMBS_995062533t_bool(P,Q),R) = hAPP_f1000663785t_bool(hAPP_A725195434t_bool(P,R),hAPP_A340536322t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_053) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15 823 (all P all Q all R hAPP_A64811457t_bool(hAPP_f1092358369t_bool(cOMBB_333235735le_alt(P),Q),R) = hAPP_f372913425t_bool(P,hAPP_A643475905l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___054) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15 824 (all P all Q all R hAPP_A725195434t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(P),Q),R) = hAPP_b910261233t_bool(P,hAPP_A416869060i_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15 825 (all P all Q all R hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f863441901l_bool(cOMBC_1528317666l_bool,P),Q),R) = hAPP_f322109294l_bool(hAPP_f881677315l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15
% 1.88/2.15 ============================== end of process non-clausal formulas ===
% 1.88/2.15
% 1.88/2.15 ============================== PROCESS INITIAL CLAUSES ===============
% 1.88/2.15
% 1.88/2.15 ============================== PREDICATE ELIMINATION =================
% 1.88/2.15 826 -is_fun1084921220e_indi(A) | is_Arr859726945e_indi(hAPP_n619554777e_indi(A,B)) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) # label(axiom). [clausify(29)].
% 1.88/2.15 827 -is_fun2015243113i_bool(A) | is_fun1084921220e_indi(hilber951314860di_nat(A,B)) # label(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt) # label(axiom). [clausify(7)].
% 1.88/2.15 Derived: is_Arr859726945e_indi(hAPP_n619554777e_indi(hilber951314860di_nat(A,B),C)) | -is_fun2015243113i_bool(A). [resolve(826,a,827,b)].
% 1.88/2.15 828 -is_fun1084921220e_indi(A) | -hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(B),top_to207207712i_bool)) | hAPP_A1895296483di_nat(B,hAPP_n619554777e_indi(A,f34(A,B))) != f34(A,B) | hilber951314860di_nat(top_to207207712i_bool,B) = A # label(fact_393_inj__imp__inv__eq) # label(axiom). [clausify(468)].
% 1.88/2.15 Derived: -hBOOL(hAPP_f160177134l_bool(inj_on1331630279di_nat(A),top_to207207712i_bool)) | hAPP_A1895296483di_nat(A,hAPP_n619554777e_indi(hilber951314860di_nat(B,C),f34(hilber951314860di_nat(B,C),A))) != f34(hilber951314860di_nat(B,C),A) | hilber951314860di_nat(top_to207207712i_bool,A) = hilber951314860di_nat(B,C) | -is_fun2015243113i_bool(B). [resolve(828,a,827,b)].
% 1.88/2.15
% 1.88/2.15 ============================== end predicate elimination =============
% 1.88/2.15
% 1.88/2.15 Auto_denials: (non-Horn, no changes).
% 1.88/2.15
% 1.88/2.15 Term ordering decisions:
% 1.88/2.15 Function symbol KB weights: member720722004le_alt=1. produc1456060119le_alt=1. ord_less_nat=1. ord_less_eq_nat=1. plus_plus_nat=1. member1265098019t_bool=1. e=1. suc=1. h=1. member1704306684t_bool=1. n=1. p=1. c=1. ord_le1568362934t_bool=1. zero_zero_nat=1. arrow_583275979e_Prof=1. ord_less_eq_bool=1. f=1. arrow_912654623le_Lin=1. member161528657e_indi=1. member_nat=1. member1619170513t_bool=1. ord_le1791992956i_bool=1. ord_le1976645739t_bool=1. ord_le382113706t_bool=1. a=1. b=1. ord_le1028202352i_bool=1. arrow_1046586475_above=1. ord_le1874503007t_bool=1. d=1. top_to207207712i_bool=1. member_bool=1. arrow_163947511_mkbot=1. top_top_bool=1. arrow_312654597_mktop=1. if_fun1158274329t_bool=1. cOMBC_70761414t_bool=1. lba=1. cOMBC_325526267t_bool=1. one_one_nat=1. ord_less_bool=1. member_Product_unit=1. lab=1. top_top_fun_nat_bool=1. ord_le1079191765l_bool=1. ord_le1482529602l_bool=1. top_to846262053l_bool=1. ord_le2143686384l_bool=1. ord_le64728819t_bool=1. top_to1257323279t_bool=1. top_to1849101472l_bool=1. top_to935749874l_bool=1. top_to1773227171t_bool=1. arrow_885770895le_IIA=1. cOMBK_1918246033t_bool=1. finite_finite_nat=1. cOMBC_1373788917t_bool=1. cOMBC_1894996001t_bool=1. fTrue=1. fequal_nat=1. ord_le742797417l_bool=1. cOMBC_1377016489t_bool=1. cOMBC_nat_nat_bool=1. cOMBK_350223551e_indi=1. arrow_1549387998ctator=1. arrow_1550141362nimity=1. cOMBC_226598744l_bool=1. fconj=1. cOMBK_1673635960le_alt=1. finite274731772t_bool=1. cOMBC_1455277858l_bool=1. cOMBC_1528317666l_bool=1. cOMBC_1722249314l_bool=1. cOMBC_2133163426l_bool=1. cOMBC_264525026l_bool=1. cOMBC_344067350l_bool=1. cOMBC_420816290l_bool=1. cOMBC_441619036t_bool=1. cOMBC_943734388l_bool=1. fFalse=1. arrow_1486210539le_alt=1. cOMBK_1399131793t_bool=1. cOMBK_761999167t_bool=1. finite921964625e_indi=1. member1935624595e_indi=1. top_to1647826457l_bool=1. bool=1. cOMBC_nat_nat_nat=1. cOMBI_nat=1. cOMBK_1391252605e_indi=1. cOMBK_1662914336e_indi=1. cOMBK_1685845624l_bool=1. cOMBK_1733734784le_alt=1. cOMBK_577652221t_bool=1. cOMBK_583454926ol_nat=1. cOMBK_715978704t_bool=1. cOMBK_776703103e_indi=1. cOMBK_776847951t_bool=1. cOMBK_790042732t_unit=1. cOMBK_bool_nat=1. finite1323840035t_bool=1. finite955821396le_alt=1. finite_finite_bool=1. member300433020le_alt=1. member363954533t_bool=1. member873781636di_nat=1. ord_le1141238780l_bool=1. ord_le1260664009l_bool=1. ord_le194694222l_bool=1. ord_le2113500159t_bool=1. ord_le319160163t_bool=1. arrow_132732488e_indi=1. member1024687843t_unit=1. member1024929995t_bool=1. member104322770t_bool=1. member1044213697t_bool=1. member1226631410t_unit=1. member1258284266t_bool=1. member1402889547l_bool=1. member1618799570e_indi=1. member1775405935t_bool=1. member1801639028e_indi=1. member1941767151t_unit=1. member2021375116l_bool=1. member219620739le_alt=1. member220564739e_indi=1. member234310528e_indi=1. member416763266t_unit=1. member48503289l_bool=1. member485283698le_alt=1. member689634176t_bool=1. member87760213it_nat=1. member928589940t_bool=1. member930088569t_bool=1. member982489409t_unit=1. member_fun_bool_nat=1. member_fun_nat_bool=1. member_fun_nat_nat=1. ord_le197158773l_bool=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. hAPP_nat_bool=1. hAPP_n1699378549t_bool=1. hAPP_f1733357041l_bool=1. hAPP_P1151433609l_bool=1. hAPP_A1171966089le_alt=1. hAPP_A1561816353le_alt=1. hAPP_nat_nat=1. hAPP_f54304608l_bool=1. hAPP_f160177134l_bool=1. hAPP_nat_fun_nat_nat=1. hAPP_f147218624l_bool=1. hAPP_f103356543l_bool=1. hAPP_A340536322t_bool=1. hAPP_f560517119l_bool=1. hAPP_f621397159l_bool=1. hAPP_bool_bool=1. hAPP_f2028818269l_bool=1. hAPP_b589554111l_bool=1. hAPP_A1895296483di_nat=1. hAPP_f1817389232t_bool=1. hAPP_f1332197581l_bool=1. hAPP_f563440173l_bool=1. hAPP_f272527115l_bool=1. hAPP_A1014090479t_bool=1. hAPP_f322109294l_bool=1. hAPP_A45661955l_bool=1. hAPP_f881677315l_bool=1. hAPP_n215258509l_bool=1. hAPP_f387058535l_bool=1. hAPP_f102394819t_bool=1. pi_Arr1801471756t_bool=1. hAPP_A28770973t_bool=1. hAPP_f684072049t_bool=1. pi_fun1555365306t_bool=1. hAPP_n1600508401i_bool=1. hAPP_b1787118453l_bool=1. hAPP_f1882280879t_bool=1. hAPP_f1931036015t_bool=1. hAPP_f446648900l_bool=1. hAPP_f595617317i_bool=1. hAPP_A630236912t_bool=1. hAPP_f832306437t_bool=1. pi_Pro1873779901t_bool=1. hAPP_P1813625415t_bool=1. hAPP_P607165281l_bool=1. hAPP_f1700034367l_bool=1. hAPP_f1547458257l_bool=1. cOMBS_178315313t_bool=1. cOMBS_995062533t_bool=1. hAPP_f1344932147l_bool=1. hAPP_f2027600413t_bool=1. hAPP_f1216491309l_bool=1. hAPP_A416869060i_bool=1. hAPP_f633903640l_bool=1. hAPP_f590186314t_bool=1. hAPP_f612708895l_bool=1. hAPP_f1283354413t_bool=1. hAPP_f1898540574t_bool=1. hAPP_f1975142533t_bool=1. hAPP_A711952286t_bool=1. hAPP_f1044120523t_bool=1. hAPP_f114580065t_bool=1. hAPP_f229349961t_bool=1. hAPP_f783549695i_bool=1. hilber951314860di_nat=1. hAPP_f137597973t_bool=1. hAPP_f1639180358l_bool=1. hAPP_f1378099862l_bool=1. hAPP_f1722879237t_bool=1. hAPP_f800510211t_bool=1. hAPP_A659996934l_bool=1. hAPP_P1676879539t_bool=1. hAPP_f1895971544l_bool=1. hAPP_n619554777e_indi=1. hAPP_P1122857141l_bool=1. hAPP_f719005683l_bool=1. cOMBS_nat_bool_bool=1. hAPP_b763490121t_bool=1. hAPP_f1028172757l_bool=1. hAPP_f1146629647l_bool=1. hAPP_f1282033109i_bool=1. hAPP_f189058133l_bool=1. hAPP_f427533077t_bool=1. hAPP_f574392641l_bool=1. hAPP_f1092358369t_bool=1. hAPP_f1152614183t_bool=1. hAPP_f1458726223t_bool=1. hAPP_f1500902601l_bool=1. hAPP_f1692576003l_bool=1. hAPP_f1747206697l_bool=1. hAPP_f1840820673t_bool=1. hAPP_f1996228283l_bool=1. hAPP_f651290349i_bool=1. hAPP_f775987425t_bool=1. hAPP_f863441901l_bool=1. hAPP_f961197973l_bool=1. hilber195283148at_nat=1. hAPP_A1906804694t_bool=1. hAPP_A1948275303t_bool=1. hAPP_b1461182872l_bool=1. hAPP_b651754310l_bool=1. hAPP_b805997823l_bool=1. hAPP_f1000663785t_bool=1. hAPP_f1021828400l_bool=1. hAPP_A433435097l_bool=1. hAPP_A725195434t_bool=1. hAPP_A85603248t_bool=1. hAPP_P401722323t_bool=1. hAPP_b1013836512t_bool=1. hAPP_b1096750261t_bool=1. hAPP_b2116075462i_bool=1. hAPP_b910261233t_bool=1. hAPP_f1077635369i_bool=1. hAPP_f1363425282l_bool=1. hAPP_f2022872455l_bool=1. hAPP_f2053170815l_bool=1. hAPP_f212509069l_bool=1. hAPP_f23348649l_bool=1. hAPP_f431432850i_bool=1. hAPP_f599997089l_bool=1. hAPP_f66927821l_bool=1. hAPP_n1006566506l_bool=1. pi_fun596906370e_indi=1. hAPP_A1120018583t_bool=1. hAPP_A1202525278t_bool=1. hAPP_A643475905l_bool=1. hAPP_A64811457t_bool=1. hAPP_A701636433l_bool=1. hAPP_A955165183l_bool=1. hAPP_P1305865168l_bool=1. hAPP_P1645359566e_indi=1. hAPP_P288224245l_bool=1. hAPP_P667392034l_bool=1. hAPP_P822772139t_bool=1. hAPP_P957402556i_bool=1. hAPP_f1009478556t_bool=1. hAPP_f1068593625t_bool=1. hAPP_f1082951236l_bool=1. hAPP_f1117143157l_bool=1. hAPP_f1138659662l_bool=1. hAPP_f1283454584e_indi=1. hAPP_f1291635206l_bool=1. hAPP_f1332130404l_bool=1. hAPP_f1384787615l_bool=1. hAPP_f1393414918t_bool=1. hAPP_f1426445843l_bool=1. hAPP_f1428735377l_bool=1. hAPP_f1570138413i_bool=1. hAPP_f1570313510t_bool=1. hAPP_f1597773170l_bool=1. hAPP_f1637334154l_bool=1. hAPP_f1656652505l_bool=1. hAPP_f1841347694t_bool=1. hAPP_f1898839893l_bool=1. hAPP_f1965705105l_bool=1. hAPP_f1980578603l_bool=1. hAPP_f2016919811l_bool=1. hAPP_f2043811403e_indi=1. hAPP_f2078760383l_bool=1. hAPP_f339859954l_bool=1. hAPP_f350403485e_indi=1. hAPP_f372913425t_bool=1. hAPP_f416620757at_nat=1. hAPP_f452450509l_bool=1. hAPP_f537623936l_bool=1. hAPP_f557371893l_bool=1. hAPP_f560261801l_bool=1. hAPP_f581841297t_bool=1. hAPP_f618557131t_bool=1. hAPP_f620747982l_bool=1. hAPP_f649586561t_bool=1. hAPP_f67777128l_bool=1. hAPP_f740740988l_bool=1. hAPP_f742658307l_bool=1. hAPP_f750478076l_bool=1. hAPP_f758593513l_bool=1. hAPP_f817344902l_bool=1. hAPP_f866114756l_bool=1. hAPP_f882250837l_bool=1. hAPP_f937100551l_bool=1. hAPP_f966397426l_bool=1. hAPP_n454528608t_bool=1. image_837079859di_nat=1. pi_Arr604548589di_nat=1. pi_boo1542163389le_alt=1. pi_fun328162388t_bool=1. fun=1. hAPP_A1433148491t_bool=1. hAPP_A1781286015t_bool=1. hAPP_A503573454le_alt=1. hAPP_A739031709t_bool=1. hAPP_P1157363642t_bool=1. hAPP_P1245388556t_bool=1. hAPP_P1931143485le_alt=1. hAPP_P32877782t_bool=1. hAPP_P426034740it_nat=1. hAPP_P992343101t_unit=1. hAPP_b1482008903le_alt=1. hAPP_b327863236t_bool=1. hAPP_b821377302t_bool=1. hAPP_bool_nat=1. hAPP_f1063991245l_bool=1. hAPP_f1140532045l_bool=1. hAPP_f1160956173l_bool=1. hAPP_f1171266041l_bool=1. hAPP_f1234917389l_bool=1. hAPP_f1338606733l_bool=1. hAPP_f1387788301l_bool=1. hAPP_f144393719l_bool=1. hAPP_f1518101645l_bool=1. hAPP_f1598887207l_bool=1. hAPP_f1636264423t_unit=1. hAPP_f1716204858t_unit=1. hAPP_f177302985l_bool=1. hAPP_f1836999501l_bool=1. hAPP_f1950626059l_bool=1. hAPP_f1951378235l_bool=1. hAPP_f1957108621l_bool=1. hAPP_f2011903565l_bool=1. hAPP_f2040535501l_bool=1. hAPP_f2087408397l_bool=1. hAPP_f2134766349l_bool=1. hAPP_f544923081l_bool=1. hAPP_f591334822l_bool=1. hAPP_f627309453l_bool=1. hAPP_f715600357l_bool=1. hAPP_f721327224l_bool=1. hAPP_f749156301l_bool=1. hAPP_f754536332t_unit=1. hAPP_f785487437l_bool=1. hAPP_f812095627l_bool=1. hAPP_f813426957l_bool=1. hAPP_f840347317l_bool=1. hAPP_n633340360t_unit=1. pi_Arr1064242500le_alt=1. pi_Arr656802323t_bool=1. pi_Arr742795713t_bool=1. pi_Pro1114473858t_bool=1. pi_Pro1208494515le_alt=1. pi_Pro1925515229t_bool=1. pi_Pro269694131t_unit=1. pi_Pro58544964e_indi=1. pi_Pro831923248t_bool=1. pi_Product_unit_nat=1. pi_boo1746012499t_bool=1. pi_boo679625100t_bool=1. pi_boo68262458t_bool=1. pi_bool_nat=1. pi_fun1012573681t_unit=1. pi_fun1236347660l_bool=1. pi_fun1353458625e_indi=1. pi_fun1390764464t_unit=1. pi_fun187048122l_bool=1. pi_fun268174099e_indi=1. pi_fun568395771l_bool=1. pi_fun623621634t_unit=1. pi_nat1476290531e_indi=1. pi_nat_Product_unit=1. pi_nat_bool=1. pi_nat_nat=1. product_prod=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f33=1. f34=1. f39=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f51=1. f65=1. f66=1. f67=1. f68=1. f72=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f82=1. f84=1. f86=1. f87=1. f88=1. f91=1. f92=1. inj_on1331630279di_nat=1. inj_on_nat_nat=1. cOMBB_552200224e_indi=1. cOMBB_810329756e_indi=1. cOMBB_640263118e_indi=1. collect_nat=1. cOMBB_930893948e_indi=1. finite_card_nat=1. finite354462354e_indi=1. cOMBB_1015721476ol_nat=1. finite945540987t_bool=1. cOMBB_333235735le_alt=1. cOMBB_711698847le_alt=1. cOMBB_885534287le_alt=1. ord_at4362885an_nat=1. cOMBB_1146692694ol_nat=1. collec279390863e_indi=1. collect_Product_unit=1. finite1524925796t_bool=1. inj_on1507564774t_bool=1. inj_on1962565012t_bool=1. inj_on398823523t_bool=1. cOMBB_800536526ol_nat=1. collec1376511890le_alt=1. collec1517527055t_bool=1. collec1567922785t_bool=1. collec612883262t_bool=1. finite1044330389le_alt=1. finite_card_bool=1. inj_on302999388e_indi=1. inj_on735362094t_bool=1. finite1949902593t_unit=1. inj_on67207011le_alt=1. undefi1052853330e_indi=1. undefi1471133025le_alt=1. undefi541132219t_bool=1. undefined_bool=1. f6=1. f7=1. f8=1. f10=1. f11=1. f12=1. f13=1. f15=1. f16=1. f17=1. f35=1. f36=1. f37=1. f38=1. f71=1. f73=1. f81=1. f85=1. f89=1. f90=1. arrow_207701375_below=1. in_rel1361124802le_alt=1. f30=1. f31=1. f32=1. f40=1. f41=1. f42=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f62=1. f63=1. f64=1. f69=1. f70=1. f83=1. f5=1. f14=1. f59=1. f60=1. f61=1. f3=1. f9=1. f1=1. f2=1. f4=1.
% 1.88/2.15
% 1.88/2.15 ============================== PROOF =================================
% 1.88/2.15 % SZS status Theorem
% 1.88/2.15 % SZS output start Refutation
% 1.88/2.15
% 1.88/2.15 % Proof 1 at 0.57 (+ 0.02) seconds.
% 1.88/2.15 % Length of proof is 6.
% 1.88/2.15 % Level of proof is 3.
% 1.88/2.15 % Maximum clause weight is 65.000.
% 1.88/2.15 % Given clauses 0.
% 1.88/2.15
% 1.88/2.15 111 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) <-> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) # label(fact_14_PW) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.15 1009 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) # label(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) # label(axiom). [assumption].
% 1.88/2.15 1010 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) | -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) # label(fact_14_PW) # label(axiom). [clausify(111)].
% 1.88/2.15 1011 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))). [copy(1010),unit_del(b,1009)].
% 1.88/2.15 1876 -hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) # label(conj_0) # label(negated_conjecture). [assumption].
% 1.88/2.15 1877 $F. [copy(1876),unit_del(a,1011)].
% 1.88/2.15
% 1.88/2.15 % SZS output end Refutation
% 1.88/2.15 ============================== end of proof ==========================
% 1.88/2.15
% 1.88/2.15 ============================== STATISTICS ============================
% 1.88/2.15
% 1.88/2.15 Given=0. Generated=1315. Kept=922. proofs=1.
% 1.88/2.15 Usable=0. Sos=0. Demods=61. Limbo=922, Disabled=1318. Hints=0.
% 1.88/2.15 Megabytes=15.22.
% 1.88/2.15 User_CPU=0.57, System_CPU=0.02, Wall_clock=1.
% 1.88/2.15
% 1.88/2.15 ============================== end of statistics =====================
% 1.88/2.15
% 1.88/2.15 ============================== end of search =========================
% 1.88/2.15
% 1.88/2.15 THEOREM PROVED
% 1.88/2.15 % SZS status Theorem
% 1.88/2.15
% 1.88/2.15 Exiting with 1 proof.
% 1.88/2.15
% 1.88/2.15 Process 30276 exit (max_proofs) Sat Jul 2 02:44:11 2022
% 1.88/2.15 Prover9 interrupted
%------------------------------------------------------------------------------