TSTP Solution File: SWW473+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW473+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:09 EDT 2022
% Result : Timeout 300.03s 300.22s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW473+3 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 4 11:39:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.60/2.02 ============================== Prover9 ===============================
% 1.60/2.02 Prover9 (32) version 2009-11A, November 2009.
% 1.60/2.02 Process 30965 was started by sandbox2 on n020.cluster.edu,
% 1.60/2.02 Sat Jun 4 11:39:24 2022
% 1.60/2.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30811_n020.cluster.edu".
% 1.60/2.02 ============================== end of head ===========================
% 1.60/2.02
% 1.60/2.02 ============================== INPUT =================================
% 1.60/2.02
% 1.60/2.02 % Reading from file /tmp/Prover9_30811_n020.cluster.edu
% 1.60/2.02
% 1.60/2.02 set(prolog_style_variables).
% 1.60/2.02 set(auto2).
% 1.60/2.02 % set(auto2) -> set(auto).
% 1.60/2.02 % set(auto) -> set(auto_inference).
% 1.60/2.02 % set(auto) -> set(auto_setup).
% 1.60/2.02 % set(auto_setup) -> set(predicate_elim).
% 1.60/2.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.60/2.02 % set(auto) -> set(auto_limits).
% 1.60/2.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.60/2.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.60/2.02 % set(auto) -> set(auto_denials).
% 1.60/2.02 % set(auto) -> set(auto_process).
% 1.60/2.02 % set(auto2) -> assign(new_constants, 1).
% 1.60/2.02 % set(auto2) -> assign(fold_denial_max, 3).
% 1.60/2.02 % set(auto2) -> assign(max_weight, "200.000").
% 1.60/2.02 % set(auto2) -> assign(max_hours, 1).
% 1.60/2.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.60/2.02 % set(auto2) -> assign(max_seconds, 0).
% 1.60/2.02 % set(auto2) -> assign(max_minutes, 5).
% 1.60/2.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.60/2.02 % set(auto2) -> set(sort_initial_sos).
% 1.60/2.02 % set(auto2) -> assign(sos_limit, -1).
% 1.60/2.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.60/2.02 % set(auto2) -> assign(max_megs, 400).
% 1.60/2.02 % set(auto2) -> assign(stats, some).
% 1.60/2.02 % set(auto2) -> clear(echo_input).
% 1.60/2.02 % set(auto2) -> set(quiet).
% 1.60/2.02 % set(auto2) -> clear(print_initial_clauses).
% 1.60/2.02 % set(auto2) -> clear(print_given).
% 1.60/2.02 assign(lrs_ticks,-1).
% 1.60/2.02 assign(sos_limit,10000).
% 1.60/2.02 assign(order,kbo).
% 1.60/2.02 set(lex_order_vars).
% 1.60/2.02 clear(print_given).
% 1.60/2.02
% 1.60/2.02 % formulas(sos). % not echoed (1415 formulas)
% 1.60/2.02
% 1.60/2.02 ============================== end of input ==========================
% 1.60/2.02
% 1.60/2.02 % From the command line: assign(max_seconds, 300).
% 1.60/2.02
% 1.60/2.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.60/2.02
% 1.60/2.02 % Formulas that are not ordinary clauses:
% 1.60/2.02 1 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2_1)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 2 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2_1)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 3 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_1_1) -> is_fun_a_bool(cOMBB_1273333599bool_a(B_1_1,B_2_1)))) # label(gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 4 (all B_1_1 (is_bool(B_1_1) -> is_fun_a_bool(cOMBK_bool_a(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 5 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 6 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 7 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_2_1) -> is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 8 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 9 (all B_1_1 all B_2_1 is_bool(finite_folding_one_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 10 (all B_1_1 all B_2_1 is_bool(finite1282449217_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 11 (all B_1_1 all B_2_1 is_bool(finite1626084323ne_int(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 12 (all B_1_1 all B_2_1 is_bool(finite988810631ne_nat(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 13 (all B_1_1 all B_2_1 is_bool(finite1819937229idem_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 14 (all B_1_1 all B_2_1 is_bool(finite89670078_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 15 (all B_1_1 all B_2_1 is_bool(finite1432773856em_int(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 16 (all B_1_1 all B_2_1 is_bool(finite795500164em_nat(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 17 (all B_1_1 (is_fun_a_bool(B_1_1) -> is_fun_a_bool(collect_a(B_1_1)))) # label(gsy_c_Set_OCollect_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 18 (all B_1_1 (is_fun_pname_bool(B_1_1) -> is_fun_pname_bool(collect_pname(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 19 (all B_1_1 (is_fun949378684l_bool(B_1_1) -> is_fun949378684l_bool(collect_fun_a_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 20 (all B_1_1 (is_fun1661590463l_bool(B_1_1) -> is_fun1661590463l_bool(collec1974731493e_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 21 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun_a_bool(image_a_a(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000t__a_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 22 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun_pname_bool(image_a_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 23 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun949378684l_bool(image_a_fun_a_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 24 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun1661590463l_bool(image_819518260e_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 25 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_a_bool(image_pname_a(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 26 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(image_pname_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 27 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 28 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 29 (all B_1_1 all B_2_1 is_fun_a_bool(image_int_a(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Int__Oint_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 30 (all B_1_1 all B_2_1 is_fun_pname_bool(image_int_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 31 (all B_1_1 all B_2_1 is_fun949378684l_bool(image_int_fun_a_bool(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 32 (all B_1_1 all B_2_1 is_fun1661590463l_bool(image_637364955e_bool(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 33 (all B_1_1 all B_2_1 is_fun_a_bool(image_nat_a(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 34 (all B_1_1 all B_2_1 is_fun_pname_bool(image_nat_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 35 (all B_1_1 all B_2_1 is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 36 (all B_1_1 all B_2_1 is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 37 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_2_1) -> is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 38 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_2_1) -> is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 39 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun_a_bool(image_876012084bool_a(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 40 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 41 (all B_1_1 all B_2_1 is_fun_a_bool(image_fun_int_bool_a(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 42 (all B_1_1 all B_2_1 is_fun_pname_bool(image_62782965_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 43 (all B_1_1 all B_2_1 is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 44 (all B_1_1 all B_2_1 is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 45 (all B_1_1 all B_2_1 (is_a(B_2_1) -> is_a(hAPP_a_a(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000t__a_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 46 (all B_1_1 all B_2_1 (is_fun_a_bool(B_1_1) & is_a(B_2_1) -> is_bool(hAPP_a_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000t__a_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 47 (all B_1_1 all B_2_1 (is_a(B_2_1) -> is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 48 (all B_1_1 all B_2_1 (is_a(B_2_1) -> is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 49 (all B_1_1 all B_2_1 (is_a(B_2_1) -> is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 50 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_a(hAPP_pname_a(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000t__a) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 51 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_pname(hAPP_pname_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 52 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_1_1) & is_pname(B_2_1) -> is_bool(hAPP_pname_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 53 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 54 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 55 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 56 (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].
% 1.60/2.02 57 (all B_1_1 all B_2_1 is_a(hAPP_int_a(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Int__Oint_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 58 (all B_1_1 all B_2_1 is_bool(hAPP_int_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 59 (all B_1_1 all B_2_1 is_fun_a_bool(hAPP_int_fun_a_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 60 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_i7355787e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 61 (all B_1_1 all B_2_1 is_fun949378684l_bool(hAPP_i888906320l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 62 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_i1587699435l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 63 (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(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 64 (all B_1_1 all B_2_1 is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 65 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 66 (all B_1_1 all B_2_1 is_fun949378684l_bool(hAPP_n1414589940l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 67 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_n850744903l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 68 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_a(hAPP_fun_a_bool_a(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 69 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_1_1) & is_fun_a_bool(B_2_1) -> is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 70 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 71 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 72 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 73 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_1_1) & is_fun_pname_bool(B_2_1) -> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 1.60/2.02 74 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 75 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 76 (all B_1_1 all B_2_1 is_bool(hAPP_f448129468l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 77 (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].
% 1.60/2.02 78 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_2_1) -> is_bool(hAPP_f621171935l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 79 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_2_1) -> is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 80 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 81 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 82 (all B_1_1 all B_2_1 is_bool(hAPP_f215623910l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 83 (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].
% 1.60/2.02 84 (all B_1_1 all B_2_1 is_bool(hAPP_f292226953l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 85 (all B_1_1 all B_2_1 is_bool(hAPP_f389811538l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 86 (all B_1_1 all B_2_1 is_bool(hAPP_f1593524852l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 87 (all B_1_1 all B_2_1 is_bool(hAPP_f937997336l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 88 (all B_1_1 (is_fun_a_bool(B_1_1) -> is_fun949378684l_bool(p(B_1_1)))) # label(gsy_v_P) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 89 (all B_1_1 is_a(mgt(B_1_1))) # label(gsy_v_mgt) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 90 (all B_1_1 is_bool(wt(B_1_1))) # label(gsy_v_wt) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 91 (all Ts all G (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Ts),G)) -> hBOOL(hAPP_fun_a_bool_bool(p(G),Ts)))) # label(fact_0_assms_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 92 (all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),A)))))) # label(fact_1_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 93 (all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A)))))) # label(fact_2_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 94 (all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A)))))) # label(fact_3_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 95 (all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A)))))) # label(fact_4_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 96 (all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A)))))) # label(fact_5_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 97 (all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A)))))) # label(fact_6_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 98 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A)))))) # label(fact_7_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 99 (all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),A)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 100 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(H,F_1))))) # label(fact_9_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 101 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(H,F_1))))) # label(fact_10_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 102 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,F_1))))) # label(fact_11_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 103 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(H,F_1))))) # label(fact_12_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 104 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(H,F_1))))) # label(fact_13_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 105 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(H,F_1))))) # label(fact_14_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 106 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(H,F_1))))) # label(fact_15_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 107 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(H,F_1))))) # label(fact_16_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 108 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(H,F_1))))) # label(fact_17_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 109 (all H all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(H,F_1))))) # label(fact_18_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 110 (all H all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(H,F_1))))) # label(fact_19_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 111 (all H all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(H,F_1))))) # label(fact_20_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 112 (all H all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(H,F_1))))) # label(fact_21_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 113 (all H all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(H,F_1))))) # label(fact_22_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 114 (all H all F_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(H,F_1))))) # label(fact_23_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 115 (all H all F_1 (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(H,F_1))))) # label(fact_24_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 116 (all H all F_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(H,F_1))))) # label(fact_25_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 117 (all H all F_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,F_1))))) # label(fact_26_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 118 (all H all F_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(H,F_1))))) # label(fact_27_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 119 (all H all F_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(H,F_1))))) # label(fact_28_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 120 (all H all F_1 (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(H,F_1))))) # label(fact_29_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 121 (all H all F_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(H,F_1))))) # label(fact_30_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 122 (all H all F_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(H,F_1))))) # label(fact_31_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 123 (all H all F_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(H,F_1))))) # label(fact_32_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 124 (all H all F_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(H,F_1))))) # label(fact_33_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 125 (all H all F_1 (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(H,F_1))))) # label(fact_34_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 126 (all H all F_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(H,F_1))))) # label(fact_35_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 127 (all H all F_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(H,F_1))))) # label(fact_36_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 128 (all H all F_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(H,F_1))))) # label(fact_37_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 129 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(H,F_1))))) # label(fact_38_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 130 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(H,F_1))))) # label(fact_39_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 131 (all A_2 all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,A_2),A))))) # label(fact_40_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 132 (all A_2 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_2),A))))) # label(fact_41_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 133 (all A_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A))))) # label(fact_42_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 134 (all A_2 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,A_2),A))))) # label(fact_43_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 135 (all A_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A))))) # label(fact_44_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 136 (all A_2 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A))))) # label(fact_45_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 137 (all A_2 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A))))) # label(fact_46_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 138 (all A_2 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A))))) # label(fact_47_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 139 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_48_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 140 (all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_49_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 141 (all F all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A))))) # label(fact_50_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 142 (all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_51_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 143 (all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_52_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 144 (all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_53_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 145 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_54_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 146 (all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_55_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 147 (all F all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A))))) # label(fact_56_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 148 (all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_57_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 149 (all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_58_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 150 (all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_59_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 151 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_60_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 152 (all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_61_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 153 (all F all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A))))) # label(fact_62_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 154 (all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_63_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 155 (all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_64_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 156 (all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_65_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 157 (all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_66_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 158 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_67_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 159 (all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(F,A))),hAPP_f957591787ol_nat(finite_card_int,A))))) # label(fact_68_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 160 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_69_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 161 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_70_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 162 (all A all B (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,A)),hAPP_f521865025ol_nat(finite1876863882t_bool,B)))))) # label(fact_71_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 163 (all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,B)))))) # label(fact_72_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 164 (all A all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,B)))))) # label(fact_73_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 165 (all A all B (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B)))))) # label(fact_74_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 166 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B)))))) # label(fact_75_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 167 (all A all B (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B)))))) # label(fact_76_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 168 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B)))))) # label(fact_77_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 169 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B)))))) # label(fact_78_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 170 (all A all B (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,B)),hAPP_f521865025ol_nat(finite1876863882t_bool,A))) -> A = B)))) # label(fact_79_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 171 (all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B)),hAPP_f696928925ol_nat(finite346522414t_bool,A))) -> A = B)))) # label(fact_80_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 172 (all A all B (is_fun1661590463l_bool(A) & is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B)),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) -> A = B))))) # label(fact_81_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 173 (all A all B (is_fun949378684l_bool(A) & is_fun949378684l_bool(B) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) -> A = B))))) # label(fact_82_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 174 (all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B)),hAPP_f921600141ol_nat(finite_card_pname,A))) -> A = B))))) # label(fact_83_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 175 (all A all B (is_fun_a_bool(A) & is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B)),hAPP_fun_a_bool_nat(finite_card_a,A))) -> A = B))))) # label(fact_84_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 176 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B)),hAPP_f22106695ol_nat(finite_card_nat,A))) -> A = B)))) # label(fact_85_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 177 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,B)),hAPP_f957591787ol_nat(finite_card_int,A))) -> A = B)))) # label(fact_86_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 178 (all X_1 all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,A)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)))))) # label(fact_87_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 179 (all X_1 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)))))) # label(fact_88_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 180 (all X_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)))))) # label(fact_89_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 181 (all X_1 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)))))) # label(fact_90_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 182 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)))))) # label(fact_91_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 183 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)))))) # label(fact_92_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 184 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)))))) # label(fact_93_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 185 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)))))) # label(fact_94_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 186 (all X_1 all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A)) -> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_f521865025ol_nat(finite1876863882t_bool,A)) & (-hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A)) -> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,A))))) # label(fact_95_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 187 (all X_1 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A)) -> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_f696928925ol_nat(finite346522414t_bool,A)) & (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A)) -> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_96_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 188 (all X_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A)) & (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_97_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 189 (all X_1 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A)) & (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_98_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 190 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f921600141ol_nat(finite_card_pname,A)) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_99_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 191 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_card_nat,A)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_100_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 192 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f957591787ol_nat(finite_card_int,A)) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,A))))) # label(fact_101_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 193 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_fun_a_bool_nat(finite_card_a,A)) & (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_102_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 194 (all X_1 all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> (-hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A)) -> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,A))))) # label(fact_103_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 195 (all X_1 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A)) -> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_104_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 196 (all X_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_105_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 197 (all X_1 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_106_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 198 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_107_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 199 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_108_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 200 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,A))))) # label(fact_109_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 201 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_110_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 202 (all Q_3 all Pa (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_3))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_3)))))) # label(fact_111_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 203 (all Q_3 all Pa (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Pa))) | hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Q_3))) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,Pa),Q_3)))))) # label(fact_112_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 204 (all Q_3 all Pa (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_3))) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_3)))))) # label(fact_113_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 205 (all Q_3 all Pa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_3))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_3)))))) # label(fact_114_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 206 (all Q_3 all Pa (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_3))) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_3)))))) # label(fact_115_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 207 (all Q_3 all Pa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_3))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_3)))))) # label(fact_116_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 208 (all Q_3 all Pa (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_3))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_3)))))) # label(fact_117_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 209 (all Q_3 all Pa (hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Pa))) | hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Q_3))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,Pa),Q_3)))))) # label(fact_118_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 210 (all N all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)))) # label(fact_119_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 211 (all K hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K))))) # label(fact_120_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 212 (all Na hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na)) # label(fact_121_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 213 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_122_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 214 (all Nat_3 all Nat_4 (hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_4) <-> Nat_3 = Nat_4)) # label(fact_123_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 215 (all N hAPP_nat_nat(suc,N) != N) # label(fact_124_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 216 (all N N != hAPP_nat_nat(suc,N)) # label(fact_125_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 217 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) -> M_1 = N))) # label(fact_126_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 218 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))))) # label(fact_127_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 219 (all M_1 all N (M_1 = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)))) # label(fact_128_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 220 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)))) # label(fact_129_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 221 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N))) # label(fact_130_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 222 (all I_1 all J all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),K_1)),J)) # label(fact_131_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 223 (all Pa all Q_3 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_3))))) # label(fact_132_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.02 224 (all Pa all Q_3 (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Pa))) & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Q_3))))) # label(fact_133_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 225 (all Pa all Q_3 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_3))))) # label(fact_134_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 226 (all Pa all Q_3 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_3))))) # label(fact_135_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 227 (all Pa all Q_3 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_3))))) # label(fact_136_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 228 (all Pa all Q_3 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_3))))) # label(fact_137_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 229 (all Pa all Q_3 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_3))))) # label(fact_138_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 230 (all Pa all Q_3 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,Pa),Q_3)))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Pa))) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Q_3))))) # label(fact_139_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 231 (all A_2 all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,A_2),A))) <-> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)))) # label(fact_140_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 232 (all A_2 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_2),A))) <-> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)))) # label(fact_141_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 233 (all A_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)))) # label(fact_142_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 234 (all A_2 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,A_2),A))) <-> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)))) # label(fact_143_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 235 (all A_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)))) # label(fact_144_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 236 (all A_2 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)))) # label(fact_145_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 237 (all A_2 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)))) # label(fact_146_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 238 (all A_2 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A))) <-> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)))) # label(fact_147_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 239 (all A all B (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B)) -> (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))))) # label(fact_148_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 240 (all A all B (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))))) # label(fact_149_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 241 (all A all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))))) # label(fact_150_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 242 (all A all B (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))))) # label(fact_151_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 243 (all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))))) # label(fact_152_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 244 (all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_153_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 245 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_154_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 246 (all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))))) # label(fact_155_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 247 (all A all B (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))))) # label(fact_156_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 248 (all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))))) # label(fact_157_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 249 (all A all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))))) # label(fact_158_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 250 (all A all B (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))))) # label(fact_159_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 251 (all A all B (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))))) # label(fact_160_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 252 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_161_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 253 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_162_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 254 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))))) # label(fact_163_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 255 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)))) # label(fact_164_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 256 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> M_1 = hAPP_nat_nat(suc,N)))) # label(fact_165_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 257 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N))))) # label(fact_166_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 258 (all Na all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M)))) # label(fact_167_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 259 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) | M = hAPP_nat_nat(suc,Na))) # label(fact_168_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 260 (all M all Na (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M)))) # label(fact_169_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 261 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N))) # label(fact_170_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 262 (all M_1 all N all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),K_1)) # label(fact_171_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 263 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) # label(fact_172_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 264 (all Na all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)))))) # label(fact_173_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 265 (all N all K_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)))) # label(fact_174_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 266 (all Na all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K) <-> M = Na)))) # label(fact_175_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 267 (all I_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),I_1)) = I_1)) # label(fact_176_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 268 (all L_1 all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),L_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),L_1))))) # label(fact_177_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 269 (all L_1 all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1))))) # label(fact_178_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 270 (all M_1 all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),M_1))) # label(fact_179_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 271 (all B all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_a_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_180_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 272 (all B all F all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_int_bool_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_181_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 273 (all B all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_nat_bool_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_182_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 274 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_876012084bool_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_183_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 275 (all B all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_a_bool_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_184_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 276 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1512837979t_bool(F,A))) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))))) # label(fact_185_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 277 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_2129980159t_bool(F,A))) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))))) # label(fact_186_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 278 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_187_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 279 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_112932426a_bool(F,A))) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))))) # label(fact_188_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 280 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_189_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 281 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_nat_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_190_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 282 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1556378401t_bool(F,A))) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))))) # label(fact_191_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 283 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_26036933t_bool(F,A))) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))))) # label(fact_192_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 284 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_1655916159e_bool(F,A))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_193_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 285 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_nat_fun_a_bool(F,A))) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))))) # label(fact_194_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 286 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_nat_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_195_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 287 (all B all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_int_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_196_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 288 (all B all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_275383677t_bool(F,A))) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))))) # label(fact_197_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 289 (all B all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_892525857t_bool(F,A))) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))))) # label(fact_198_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 290 (all B all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_637364955e_bool(F,A))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_199_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 291 (all B all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_int_fun_a_bool(F,A))) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))))) # label(fact_200_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 292 (all B all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_int_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_201_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 293 (all B all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_a_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_202_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 294 (all B all F all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_62782965_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_203_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 295 (all B all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1921560913_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_204_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 296 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_205_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 297 (all B all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1854862208_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_206_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 298 (all B all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_a_nat(F,A))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))))) # label(fact_207_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 299 (all B all F all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1431733819ol_nat(F,A))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))))) # label(fact_208_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 300 (all B all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_496248727ol_nat(F,A))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))))) # label(fact_209_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 301 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1551609309ol_nat(F,A))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))))) # label(fact_210_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 302 (all B all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_fun_a_bool_nat(F,A))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))))) # label(fact_211_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 303 (all B all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_a_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_212_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 304 (all B all F all A (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_2069007511ol_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_213_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 305 (all B all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_1133522419ol_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_214_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 306 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_41399353ol_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_215_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 307 (all B all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_fun_a_bool_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_216_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 308 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_217_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 309 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_218_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 310 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_int_bool_a(F,A))) -> (exists C_16 (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16)) & B = image_fun_int_bool_a(F,C_16))))))) # label(fact_219_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 311 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_nat_bool_a(F,A))) -> (exists C_16 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16)) & B = image_fun_nat_bool_a(F,C_16))))))) # label(fact_220_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 312 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_876012084bool_a(F,A))) -> (exists C_16 (is_fun1661590463l_bool(C_16) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16)) & B = image_876012084bool_a(F,C_16))))))) # label(fact_221_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 313 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_a_bool_a(F,A))) -> (exists C_16 (is_fun949378684l_bool(C_16) & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A)) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16)) & B = image_fun_a_bool_a(F,C_16))))))) # label(fact_222_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 314 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_a_a(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_a_a(F,C_16))))))) # label(fact_223_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 315 (all F all A all B (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_a_fun_int_bool(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_a_fun_int_bool(F,C_16)))))) # label(fact_224_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 316 (all F all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_a_fun_nat_bool(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_a_fun_nat_bool(F,C_16)))))) # label(fact_225_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 317 (all F all A all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_819518260e_bool(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_819518260e_bool(F,C_16))))))) # label(fact_226_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 318 (all F all A all B (is_fun949378684l_bool(B) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_a_fun_a_bool(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_a_fun_a_bool(F,C_16))))))) # label(fact_227_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 319 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_a_pname(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_a_pname(F,C_16))))))) # label(fact_228_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 320 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_62782965_pname(F,A))) -> (exists C_16 (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16)) & B = image_62782965_pname(F,C_16))))))) # label(fact_229_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 321 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1921560913_pname(F,A))) -> (exists C_16 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16)) & B = image_1921560913_pname(F,C_16))))))) # label(fact_230_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 322 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A))) -> (exists C_16 (is_fun1661590463l_bool(C_16) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16)) & B = image_1283814551_pname(F,C_16))))))) # label(fact_231_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 323 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1854862208_pname(F,A))) -> (exists C_16 (is_fun949378684l_bool(C_16) & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A)) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16)) & B = image_1854862208_pname(F,C_16))))))) # label(fact_232_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 324 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_a_nat(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_a_nat(F,C_16)))))) # label(fact_233_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 325 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1431733819ol_nat(F,A))) -> (exists C_16 (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16)) & B = image_1431733819ol_nat(F,C_16)))))) # label(fact_234_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 326 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_496248727ol_nat(F,A))) -> (exists C_16 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16)) & B = image_496248727ol_nat(F,C_16)))))) # label(fact_235_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 327 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1551609309ol_nat(F,A))) -> (exists C_16 (is_fun1661590463l_bool(C_16) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16)) & B = image_1551609309ol_nat(F,C_16)))))) # label(fact_236_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 328 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_fun_a_bool_nat(F,A))) -> (exists C_16 (is_fun949378684l_bool(C_16) & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A)) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16)) & B = image_fun_a_bool_nat(F,C_16)))))) # label(fact_237_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 329 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_pname_nat(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_pname_nat(F,C_16)))))) # label(fact_238_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 330 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_a_int(F,A))) -> (exists C_16 (is_fun_a_bool(C_16) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16)) & B = image_a_int(F,C_16)))))) # label(fact_239_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 331 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_2069007511ol_int(F,A))) -> (exists C_16 (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16)) & B = image_2069007511ol_int(F,C_16)))))) # label(fact_240_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 332 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_1133522419ol_int(F,A))) -> (exists C_16 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16)) & B = image_1133522419ol_int(F,C_16)))))) # label(fact_241_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 333 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_41399353ol_int(F,A))) -> (exists C_16 (is_fun1661590463l_bool(C_16) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16)) & B = image_41399353ol_int(F,C_16)))))) # label(fact_242_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 334 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_fun_a_bool_int(F,A))) -> (exists C_16 (is_fun949378684l_bool(C_16) & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A)) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16)) & B = image_fun_a_bool_int(F,C_16)))))) # label(fact_243_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 335 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_pname_int(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_pname_int(F,C_16)))))) # label(fact_244_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 336 (all F all A all B (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1512837979t_bool(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_1512837979t_bool(F,C_16)))))) # label(fact_245_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 337 (all F all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_2129980159t_bool(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_2129980159t_bool(F,C_16)))))) # label(fact_246_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 338 (all F all A all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_47868345e_bool(F,C_16))))))) # label(fact_247_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 339 (all F all A all B (is_fun949378684l_bool(B) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_112932426a_bool(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_112932426a_bool(F,C_16))))))) # label(fact_248_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 340 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_pname_pname(F,C_16))))))) # label(fact_249_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 341 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_nat_a(F,A))) -> (exists C_16 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16)) & B = image_nat_a(F,C_16))))))) # label(fact_250_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 342 (all F all A all B (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1556378401t_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16)) & B = image_1556378401t_bool(F,C_16)))))) # label(fact_251_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 343 (all F all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_26036933t_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16)) & B = image_26036933t_bool(F,C_16)))))) # label(fact_252_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 344 (all F all A all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_1655916159e_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16)) & B = image_1655916159e_bool(F,C_16))))))) # label(fact_253_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 345 (all F all A all B (is_fun949378684l_bool(B) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_nat_fun_a_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16)) & B = image_nat_fun_a_bool(F,C_16))))))) # label(fact_254_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 346 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_nat_pname(F,A))) -> (exists C_16 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16)) & B = image_nat_pname(F,C_16))))))) # label(fact_255_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 347 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_int_a(F,A))) -> (exists C_16 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16)) & B = image_int_a(F,C_16))))))) # label(fact_256_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 348 (all F all A all B (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_275383677t_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16)) & B = image_275383677t_bool(F,C_16)))))) # label(fact_257_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 349 (all F all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_892525857t_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16)) & B = image_892525857t_bool(F,C_16)))))) # label(fact_258_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 350 (all F all A all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_637364955e_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16)) & B = image_637364955e_bool(F,C_16))))))) # label(fact_259_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 351 (all F all A all B (is_fun949378684l_bool(B) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_int_fun_a_bool(F,A))) -> (exists C_16 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16)) & B = image_int_fun_a_bool(F,C_16))))))) # label(fact_260_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 352 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_int_pname(F,A))) -> (exists C_16 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16)) & B = image_int_pname(F,C_16))))))) # label(fact_261_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 353 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A))) -> (exists C_16 (is_fun_pname_bool(C_16) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16)) & B = image_pname_a(F,C_16))))))) # label(fact_262_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 354 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A))) -> (exists C_16 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16)) & B = image_nat_int(F,C_16)))))) # label(fact_263_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 355 (all Na all N_3 all F ((all N_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_1)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,Na)),hAPP_n1025906991e_bool(F,N_3)))))) # label(fact_264_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 356 (all Na all N_3 all F ((all N_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,N_1)),hAPP_nat_bool(F,hAPP_nat_nat(suc,N_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Na)),hAPP_nat_bool(F,N_3)))))) # label(fact_265_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 357 (all Na all N_3 all F ((all N_1 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_1)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,Na)),hAPP_nat_fun_a_bool(F,N_3)))))) # label(fact_266_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 358 (all Na all N_3 all F ((all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_1)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Na)),hAPP_nat_nat(F,N_3)))))) # label(fact_267_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 359 (all Na all N_3 all F ((all N_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,N_1)),hAPP_nat_int(F,hAPP_nat_nat(suc,N_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,Na)),hAPP_nat_int(F,N_3)))))) # label(fact_268_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 360 (all Na all N_3 all F ((all N_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_1)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Na)),hAPP_n1699378549t_bool(F,N_3)))))) # label(fact_269_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 361 (all Na all N_3 all F ((all N_1 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(F,N_1)),hAPP_n1082236369t_bool(F,hAPP_nat_nat(suc,N_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(F,Na)),hAPP_n1082236369t_bool(F,N_3)))))) # label(fact_270_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 362 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,F)),hAPP_n1082236369t_bool(F,X_2))))))))))) # label(fact_271_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 363 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,F)),hAPP_n1699378549t_bool(F,X_2))))))))))) # label(fact_272_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 364 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,F)),hAPP_n1025906991e_bool(F,X_2))))))))))) # label(fact_273_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 365 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,F)),hAPP_nat_fun_a_bool(F,X_2))))))))))) # label(fact_274_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 366 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,F)),hAPP_int_a(F,X_2))))))))))) # label(fact_275_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 367 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,F)),hAPP_i1948725293t_bool(F,X_2))))))))))) # label(fact_276_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 368 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,F)),hAPP_i418383825t_bool(F,X_2))))))))))) # label(fact_277_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 369 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,F)),hAPP_i7355787e_bool(F,X_2))))))))))) # label(fact_278_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 370 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,F)),hAPP_int_fun_a_bool(F,X_2))))))))))) # label(fact_279_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 371 (all F all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_2))))))))))) # label(fact_280_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 372 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,F)),hAPP_nat_int(F,X_2))))))))))) # label(fact_281_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 373 (all A all B_3 all F all X_1 (B_3 = hAPP_nat_int(F,X_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A)))))) # label(fact_282_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 374 (all A all B_3 all F all X_1 (B_3 = hAPP_pname_a(F,X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))))) # label(fact_283_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 375 (all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) -> A = B))) # label(fact_284_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 376 (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_285_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 377 (all A all B (is_fun_a_bool(A) & is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) -> A = B)))) # label(fact_286_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 378 (all C_6 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))))) # label(fact_287_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 379 (all C_6 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))))) # label(fact_288_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 380 (all C_6 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))))) # label(fact_289_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 381 (all C_6 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))))) # label(fact_290_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 382 (all B_3 all A_2 all B ((-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B)) -> A_2 = B_3) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B))))) # label(fact_291_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 383 (all B_3 all A_2 all B ((-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B)) -> A_2 = B_3) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B))))) # label(fact_292_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 384 (all B_3 all A_2 all B ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B)) -> A_2 = B_3) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B))))) # label(fact_293_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 385 (all B_3 all A_2 all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) -> A_2 = B_3) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),B))))) # label(fact_294_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 386 (all A_2 all B_3 all A (is_a(A_2) & is_a(B_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A))) -> (A_2 != B_3 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)))))) # label(fact_295_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 387 (all A_2 all B_3 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),A))) -> (A_2 != B_3 -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))))) # label(fact_296_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 388 (all A_2 all B_3 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),A))) -> (A_2 != B_3 -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))))) # label(fact_297_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 389 (all A_2 all B_3 all A (is_pname(A_2) & is_pname(B_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),A))) -> (A_2 != B_3 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)))))) # label(fact_298_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 390 (all I_2 all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N_1 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(Pa,N_1)))) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K),I_2)))))) # label(fact_299_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 391 (all N all M_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_4)) -> (exists M_2 M_4 = hAPP_nat_nat(suc,M_2)))) # label(fact_300_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 392 (all X_1 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),X_1))) # label(fact_301_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 393 (all X_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),X_1))) # label(fact_302_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 394 (all X_11 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),X_11))) # label(fact_303_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 395 (all X_11 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),X_11))) # label(fact_304_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 396 (all X_1 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),X_1))) # label(fact_305_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 397 (all X_10 all Y_9 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_10),Y_9)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_9),X_10)))) # label(fact_306_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 398 (all X_10 all Y_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),Y_9)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_10)))) # label(fact_307_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 399 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)))) # label(fact_308_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 400 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)))) # label(fact_309_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 401 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)))) # label(fact_310_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 402 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)))) # label(fact_311_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 403 (all X_1 all Y_1 (is_fun_a_bool(X_1) & is_fun_a_bool(Y_1) -> (X_1 = Y_1 <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))))) # label(fact_312_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 404 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)))) # label(fact_313_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 405 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)))) # label(fact_314_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 406 (all X_9 all Y_8 (X_9 = Y_8 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_9),Y_8)))) # label(fact_315_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 407 (all X_9 all Y_8 (X_9 = Y_8 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8)))) # label(fact_316_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 408 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)))) # label(fact_317_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 409 (all Y_1 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_318_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 410 (all Y_1 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_319_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 411 (all Y_1 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_320_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 412 (all Y_1 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_321_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 413 (all Y_1 all X_1 (is_fun_a_bool(Y_1) & is_fun_a_bool(X_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) <-> X_1 = Y_1)))) # label(fact_322_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 414 (all C_6 all A_2 all B_3 (A_2 = B_3 -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_3),C_6)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_6))))) # label(fact_323_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 415 (all C_6 all A_2 all B_3 (A_2 = B_3 -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_3),C_6)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_6))))) # label(fact_324_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 416 (all C_15 all A_21 all B_19 (A_21 = B_19 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_19),C_15)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_21),C_15))))) # label(fact_325_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 417 (all C_15 all A_21 all B_19 (A_21 = B_19 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),C_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),C_15))))) # label(fact_326_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 418 (all C_6 all A_2 all B_3 (A_2 = B_3 -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_3),C_6)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),C_6))))) # label(fact_327_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 419 (all C_6 all A_2 all B_3 (A_2 = B_3 -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),B_3)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),A_2))))) # label(fact_328_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 420 (all C_6 all A_2 all B_3 (A_2 = B_3 -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),B_3)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),A_2))))) # label(fact_329_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 421 (all C_14 all A_20 all B_18 (A_20 = B_18 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),B_18)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),A_20))))) # label(fact_330_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.03 422 (all C_14 all A_20 all B_18 (A_20 = B_18 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),B_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),A_20))))) # label(fact_331_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 423 (all C_6 all A_2 all B_3 (A_2 = B_3 -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),B_3)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),A_2))))) # label(fact_332_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 424 (all C_6 all A_2 all B_3 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_3)) -> (B_3 = C_6 -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_6))))) # label(fact_333_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 425 (all C_6 all A_2 all B_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_3)) -> (B_3 = C_6 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_6))))) # label(fact_334_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 426 (all C_13 all A_19 all B_17 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),B_17)) -> (B_17 = C_13 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),C_13))))) # label(fact_335_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 427 (all C_13 all A_19 all B_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),B_17)) -> (B_17 = C_13 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),C_13))))) # label(fact_336_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 428 (all C_6 all A_2 all B_3 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),B_3)) -> (B_3 = C_6 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),C_6))))) # label(fact_337_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 429 (all C_6 all B_3 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_3),A_2)) -> (B_3 = C_6 -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),A_2))))) # label(fact_338_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 430 (all C_6 all B_3 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_3),A_2)) -> (B_3 = C_6 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),A_2))))) # label(fact_339_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 431 (all C_12 all B_16 all A_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_16),A_18)) -> (B_16 = C_12 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),A_18))))) # label(fact_340_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 432 (all C_12 all B_16 all A_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_16),A_18)) -> (B_16 = C_12 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_12),A_18))))) # label(fact_341_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 433 (all C_6 all B_3 all A_2 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_3),A_2)) -> (B_3 = C_6 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),A_2))))) # label(fact_342_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 434 (all X_1 all Y_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> X_1 = Y_1))) # label(fact_343_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 435 (all X_1 all Y_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> X_1 = Y_1))) # label(fact_344_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 436 (all X_8 all Y_7 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_8),Y_7)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_7),X_8)) -> X_8 = Y_7))) # label(fact_345_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 437 (all X_8 all Y_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_7)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8)) -> X_8 = Y_7))) # label(fact_346_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 438 (all X_1 all Y_1 (is_fun_a_bool(X_1) & is_fun_a_bool(Y_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1)) -> X_1 = Y_1)))) # label(fact_347_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 439 (all Z_2 all X_1 all Y_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),Z_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Z_2))))) # label(fact_348_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 440 (all Z_2 all X_1 all Y_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),Z_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Z_2))))) # label(fact_349_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 441 (all Z_6 all X_7 all Y_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Y_6)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_6),Z_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Z_6))))) # label(fact_350_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 442 (all Z_6 all X_7 all Y_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Z_6))))) # label(fact_351_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 443 (all Z_2 all X_1 all Y_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),Z_2)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Z_2))))) # label(fact_352_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 444 (all Y_1 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) -> X_1 = Y_1))) # label(fact_353_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 445 (all Y_1 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) -> X_1 = Y_1))) # label(fact_354_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 446 (all Y_5 all X_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_6)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_6),Y_5)) -> X_6 = Y_5))) # label(fact_355_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 447 (all Y_5 all X_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5)) -> X_6 = Y_5))) # label(fact_356_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 448 (all Y_1 all X_1 (is_fun_a_bool(Y_1) & is_fun_a_bool(X_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) -> X_1 = Y_1)))) # label(fact_357_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 449 (all Z_2 all Y_1 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),Y_1)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),X_1))))) # label(fact_358_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 450 (all Z_2 all Y_1 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_1))))) # label(fact_359_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 451 (all Z_5 all Y_4 all X_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_4),X_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),Y_4)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),X_5))))) # label(fact_360_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 452 (all Z_5 all Y_4 all X_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),Y_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),X_5))))) # label(fact_361_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 453 (all Z_2 all Y_1 all X_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_2),Y_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_2),X_1))))) # label(fact_362_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 454 (all X_4 all Y_3 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_4),Y_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_3),X_4)))) # label(fact_363_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 455 (all X_4 all Y_3 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_4)))) # label(fact_364_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 456 (all A_2 all B hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)))) # label(fact_365_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 457 (all A_2 all B hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)))) # label(fact_366_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 458 (all A_2 all B hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)))) # label(fact_367_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 459 (all A_2 all B hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B)))) # label(fact_368_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 460 (all A_2 all B hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B)))) # label(fact_369_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 461 (all A_2 all B hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B)))) # label(fact_370_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 462 (all A_2 all B hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B)))) # label(fact_371_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 463 (all A_2 all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B)))) # label(fact_372_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 464 (all A_2 all Pa hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),collect_a(Pa)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2))),Pa))) # label(fact_373_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 465 (all A_2 all Pa hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),collect_int(Pa)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2))),Pa))) # label(fact_374_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 466 (all A_2 all Pa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),collect_nat(Pa)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2))),Pa))) # label(fact_375_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 467 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) <-> hBOOL(hAPP_int_bool(A,X_1)))) # label(fact_376_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 468 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_nat_bool(A,X_1)))) # label(fact_377_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 469 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) <-> hBOOL(hAPP_a_bool(A,X_1)))) # label(fact_378_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 470 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) <-> hBOOL(hAPP_pname_bool(A,X_1)))) # label(fact_379_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 471 (all Pa collect_int(Pa) = Pa) # label(fact_380_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 472 (all Pa collect_nat(Pa) = Pa) # label(fact_381_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 473 (all X_1 all A hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) # label(fact_382_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 474 (all X_1 all Y_1 all A hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),A)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A))) # label(fact_383_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 475 (all A_2 all B_3 all A (is_a(A_2) & is_a(B_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A))) <-> A_2 = B_3 | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))))) # label(fact_384_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 476 (all A_2 all B_3 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),A))) <-> A_2 = B_3 | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)))) # label(fact_385_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 477 (all A_2 all B_3 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),A))) <-> A_2 = B_3 | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)))) # label(fact_386_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 478 (all A_2 all B_3 all A (is_pname(A_2) & is_pname(B_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),A))) <-> A_2 = B_3 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))))) # label(fact_387_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 479 (all Y_1 all A all X_1 (is_a(Y_1) & is_a(X_1) -> (hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),A),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_a_bool(A,X_1))))) # label(fact_388_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 480 (all B all X_1 all A (is_fun_a_bool(B) & is_fun_a_bool(A) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) -> (hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B) <-> A = B))))) # label(fact_389_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 481 (all B all X_1 all A (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B) <-> A = B)))) # label(fact_390_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 482 (all B all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B) <-> A = B)))) # label(fact_391_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 483 (all B all X_1 all A (is_fun_pname_bool(B) & is_fun_pname_bool(A) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B) <-> A = B))))) # label(fact_392_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 484 (all B_3 all A_2 all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B))))) # label(fact_393_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 485 (all B_3 all A_2 all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B))))) # label(fact_394_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 486 (all B_3 all A_2 all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B))))) # label(fact_395_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 487 (all B_3 all A_2 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),B))))) # label(fact_396_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 488 (all A_2 all A (is_fun_a_bool(A) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) -> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A) = A))) # label(fact_397_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 489 (all A_2 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A) = A)) # label(fact_398_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 490 (all A_2 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A) = A)) # label(fact_399_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 491 (all A_2 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A) = A))) # label(fact_400_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 492 (all A hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),A))) # label(fact_401_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 493 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A))) # label(fact_402_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 494 (all A hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),A))) # label(fact_403_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 495 (all A all B (A = B <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)))) # label(fact_404_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 496 (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_405_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 497 (all A all B (is_fun_a_bool(A) & is_fun_a_bool(B) -> (A = B <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))))) # label(fact_406_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 498 (all A all B (A = B -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)))) # label(fact_407_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 499 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_408_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 500 (all A all B (A = B -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)))) # label(fact_409_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 501 (all A all B (A = B -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)))) # label(fact_410_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 502 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)))) # label(fact_411_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 503 (all A all B (A = B -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)))) # label(fact_412_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 504 (all X_1 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))))) # label(fact_413_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 505 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_414_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 506 (all X_1 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))))) # label(fact_415_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 507 (all X_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_416_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 508 (all B all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))))) # label(fact_417_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 509 (all B all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_418_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 510 (all B all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))))) # label(fact_419_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 511 (all B all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_420_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 512 (all X_1 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))))) # label(fact_421_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 513 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_422_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 514 (all X_1 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))))) # label(fact_423_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 515 (all X_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_424_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 516 (all C_11 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_11)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_11))))) # label(fact_425_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 517 (all C_11 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_11)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_11))))) # label(fact_426_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 518 (all C_11 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C_11)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C_11))))) # label(fact_427_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 519 (all A all B (A = B -> -(hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))))) # label(fact_428_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 520 (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_429_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 521 (all A all B (A = B -> -(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))))) # label(fact_430_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 522 (all Z_2 all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Z_2),image_nat_int(F,A))) <-> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & Z_2 = hAPP_nat_int(F,X_2))))) # label(fact_431_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 523 (all Z_2 all F all A (is_a(Z_2) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_2),image_pname_a(F,A))) <-> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & Z_2 = hAPP_pname_a(F,X_2)))))) # label(fact_432_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 524 (all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A))))) # label(fact_433_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 525 (all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),image_pname_a(F,A))))) # label(fact_434_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 526 (all B_3 all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (B_3 = hAPP_nat_int(F,X_1) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A)))))) # label(fact_435_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 527 (all B_3 all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (B_3 = hAPP_pname_a(F,X_1) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))))) # label(fact_436_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 528 (all X_2 all Xa hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa)))) # label(fact_437_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 529 (all X_2 all Xa hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),Xa) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X_2)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),Xa)))) # label(fact_438_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 530 (all X_2 all Xa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa)))) # label(fact_439_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 531 (all X_2 all Xa hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa)))) # label(fact_440_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 532 (all F all G_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G_1,X_2)))))) # label(fact_441_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 533 (all F all G_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G_1,X_2)))))) # label(fact_442_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 534 (all F all G_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) <-> (all X_2 (is_a(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_2)),hAPP_a_bool(G_1,X_2))))))) # label(fact_443_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 535 (all X_1 all F all G_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G_1,X_1))))) # label(fact_444_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 536 (all X_1 all F all G_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G_1,X_1))))) # label(fact_445_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 537 (all X_1 all F all G_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_1)),hAPP_a_bool(G_1,X_1))))) # label(fact_446_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 538 (all X_1 all F all G_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G_1,X_1))))) # label(fact_447_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 539 (all X_1 all F all G_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G_1,X_1))))) # label(fact_448_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 540 (all X_1 all F all G_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_1)),hAPP_a_bool(G_1,X_1))))) # label(fact_449_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 541 (all B all A_2 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)))) # label(fact_450_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 542 (all B all A_2 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)))) # label(fact_451_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 543 (all B all A_2 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)))) # label(fact_452_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 544 (all X_1 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B)) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)))) # label(fact_453_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 545 (all X_1 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)))) # label(fact_454_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 546 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B)) <-> 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_455_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 547 (all X_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_456_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 548 (all B all X_1 all A (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B))) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))))) # label(fact_457_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 549 (all B all X_1 all A (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))))) # label(fact_458_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 550 (all B all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))))) # label(fact_459_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 551 (all B all X_1 all A (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))))) # label(fact_460_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 552 (all B_3 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B))))) # label(fact_461_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 553 (all B_3 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B))))) # label(fact_462_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 554 (all B_3 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,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B))))) # label(fact_463_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 555 (all A_2 all C_11 all D_4 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_11),D_4)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),C_11)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),D_4))))) # label(fact_464_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 556 (all A_2 all C_11 all D_4 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_11),D_4)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),C_11)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),D_4))))) # label(fact_465_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 557 (all A_2 all C_11 all D_4 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_11),D_4)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),C_11)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),D_4))))) # label(fact_466_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 558 (all F all A_2 all B image_nat_int(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,A_2)),image_nat_int(F,B))) # label(fact_467_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 559 (all F all A_2 all B image_pname_a(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(F,A_2)),image_pname_a(F,B))) # label(fact_468_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 560 (all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A)) = image_nat_int(F,A))) # label(fact_469_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 561 (all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(F,X_1)),image_pname_a(F,A)) = image_pname_a(F,A))) # label(fact_470_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 562 (all B all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A))) <-> (exists AA (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A)) & B = image_nat_int(F,AA))))) # label(fact_471_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 563 (all B all F all A (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A))) <-> (exists AA (is_fun_pname_bool(AA) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A)) & B = image_pname_a(F,AA)))))) # label(fact_472_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 564 (all F all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),image_nat_int(F,B))))) # label(fact_473_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 565 (all F all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),image_pname_a(F,B))))) # label(fact_474_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 566 (all B_3 all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A))) -> -(all X_2 (B_3 = hAPP_nat_int(F,X_2) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)))))) # label(fact_475_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 567 (all B_3 all F all A (is_a(B_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A))) -> -(all X_2 (is_pname(X_2) -> (B_3 = hAPP_pname_a(F,X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)))))))) # label(fact_476_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 568 (all B all A ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)))) # label(fact_477_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 569 (all B all A ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_478_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 570 (all B all A ((all X_2 (is_a(X_2) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)))) # label(fact_479_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 571 (all B all A ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_480_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 572 (all F all B all A ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_2)),B)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),B)))) # label(fact_481_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 573 (all F all B all A ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_2)),B))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),B)))) # label(fact_482_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 574 (all F all G_1 ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G_1,X_2)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)))) # label(fact_483_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 575 (all F all G_1 ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G_1,X_2)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)))) # label(fact_484_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 576 (all F all G_1 ((all X_2 (is_a(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_2)),hAPP_a_bool(G_1,X_2))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)))) # label(fact_485_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 577 (all N_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) <-> (exists M_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),M_2)))))) # label(fact_486_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 578 (all G all C_6 (hBOOL(wt(C_6)) -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),u)) -> hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X_2)),bot_bot_fun_a_bool)))))) -> hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(C_6)),bot_bot_fun_a_bool)))))) # label(fact_487_assms_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 579 (all A_2 all B_3 all C_6 all D_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_3) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_6),D_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_6),D_1))))) # label(fact_488_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 580 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na)) <-> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M)),Na)))) # label(fact_489_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 581 (all A_2 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),bot_bot_fun_int_bool))) # label(fact_490_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 582 (all A_2 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),bot_bot_fun_nat_bool))) # label(fact_491_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 583 (all A_2 -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),bot_bot_fun_a_bool))) # label(fact_492_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 584 (all A_2 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool))) # label(fact_493_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 585 (all B all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))) # label(fact_494_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 586 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_495_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 587 (all B all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_496_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 588 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A))) # label(fact_501_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 589 (all A hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A))) # label(fact_502_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 590 (all A hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A))) # label(fact_503_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 591 (all A_2 all A (A = bot_bot_fun_int_bool -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)))) # label(fact_504_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 592 (all A_2 all A (A = bot_bot_fun_nat_bool -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)))) # label(fact_505_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 593 (all A_2 all A (A = bot_bot_fun_a_bool -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)))) # label(fact_506_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 594 (all A_2 all A (A = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)))) # label(fact_507_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 595 (all Pa (collect_int(Pa) = bot_bot_fun_int_bool <-> (all X_2 -hBOOL(hAPP_int_bool(Pa,X_2))))) # label(fact_508_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 596 (all Pa (collect_nat(Pa) = bot_bot_fun_nat_bool <-> (all X_2 -hBOOL(hAPP_nat_bool(Pa,X_2))))) # label(fact_509_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 597 (all Pa (collect_a(Pa) = bot_bot_fun_a_bool <-> (all X_2 (is_a(X_2) -> -hBOOL(hAPP_a_bool(Pa,X_2)))))) # label(fact_510_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 598 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),A) = bot_bot_fun_nat_bool) # label(fact_511_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 599 (all A hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),A) = bot_bot_fun_int_bool) # label(fact_512_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 600 (all A hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),A) = bot_bot_fun_a_bool) # label(fact_513_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 601 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),bot_bot_fun_nat_bool) = A) # label(fact_514_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 602 (all A hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),bot_bot_fun_int_bool) = A) # label(fact_515_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 603 (all A (is_fun_a_bool(A) -> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),bot_bot_fun_a_bool) = A)) # label(fact_516_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 604 (all C_6 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),bot_bot_fun_int_bool))) # label(fact_517_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 605 (all C_6 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),bot_bot_fun_nat_bool))) # label(fact_518_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 606 (all C_6 -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),bot_bot_fun_a_bool))) # label(fact_519_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 607 (all C_6 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),bot_bo844097828e_bool))) # label(fact_520_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 608 (all Pa (bot_bot_fun_int_bool = collect_int(Pa) <-> (all X_2 -hBOOL(hAPP_int_bool(Pa,X_2))))) # label(fact_521_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 609 (all Pa (bot_bot_fun_nat_bool = collect_nat(Pa) <-> (all X_2 -hBOOL(hAPP_nat_bool(Pa,X_2))))) # label(fact_522_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 610 (all Pa (bot_bot_fun_a_bool = collect_a(Pa) <-> (all X_2 (is_a(X_2) -> -hBOOL(hAPP_a_bool(Pa,X_2)))))) # label(fact_523_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 611 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A) = bot_bot_fun_nat_bool) # label(fact_524_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 612 (all A hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),A) = bot_bot_fun_int_bool) # label(fact_525_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 613 (all A hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),A) = bot_bot_fun_a_bool) # label(fact_526_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 614 (all A ((exists X_2 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))) <-> A != bot_bot_fun_int_bool)) # label(fact_527_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 615 (all A ((exists X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))) <-> A != bot_bot_fun_nat_bool)) # label(fact_528_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 616 (all A (is_fun_a_bool(A) -> ((exists X_2 (is_a(X_2) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)))) <-> A != bot_bot_fun_a_bool))) # label(fact_529_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 617 (all A (is_fun_pname_bool(A) -> ((exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)))) <-> A != bot_bo844097828e_bool))) # label(fact_530_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 618 (all A ((all X_2 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))) <-> A = bot_bot_fun_int_bool)) # label(fact_531_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 619 (all A ((all X_2 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))) <-> A = bot_bot_fun_nat_bool)) # label(fact_532_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 620 (all A (is_fun_a_bool(A) -> ((all X_2 (is_a(X_2) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)))) <-> A = bot_bot_fun_a_bool))) # label(fact_533_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 621 (all A (is_fun_pname_bool(A) -> ((all X_2 (is_pname(X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)))) <-> A = bot_bo844097828e_bool))) # label(fact_534_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 622 (all X_1 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_535_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 623 (all X_1 (hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_536_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 624 (all X_1 (hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_537_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 625 (all X_2 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_541_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 626 (all X_2 (hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_542_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 627 (all X_2 (hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_543_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 628 (all A_2 all A (is_fun_a_bool(A) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) -> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) = A))) # label(fact_544_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 629 (all A_2 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) = A)) # label(fact_545_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 630 (all A_2 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) = A)) # label(fact_546_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 631 (all A_2 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) = A))) # label(fact_547_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 632 (all X_1 all A (is_fun_a_bool(A) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = A))) # label(fact_548_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 633 (all X_1 all A (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = A)) # label(fact_549_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 634 (all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = A)) # label(fact_550_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 635 (all X_1 all A (is_fun_pname_bool(A) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A))) # label(fact_551_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 636 (all A_2 all A hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A)) # label(fact_552_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 637 (all A_2 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A)) # label(fact_553_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 638 (all A_2 all A hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A)) # label(fact_554_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 639 (all A all A_2 all B hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))),B)) # label(fact_555_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 640 (all A all A_2 all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))),B)) # label(fact_556_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 641 (all A all A_2 all B hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))),B)) # label(fact_557_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 642 (all A all A_2 all B hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) # label(fact_558_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 643 (all A all A_2 all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) # label(fact_559_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 644 (all A all A_2 all B hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) # label(fact_560_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 645 (all A all X_1 all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B)))))) # label(fact_561_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 646 (all A all X_1 all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)))))) # label(fact_562_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 647 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)))))) # label(fact_563_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 648 (all A all X_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))))) # label(fact_564_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 649 (all A all X_1 all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B))) <-> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))),B))) & (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))))) # label(fact_565_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.04 650 (all A all X_1 all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B))) <-> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B))) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))))) # label(fact_566_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 651 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) <-> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))))) # label(fact_567_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 652 (all A all X_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) <-> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))))) # label(fact_568_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 653 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))))) # label(fact_569_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 654 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_570_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 655 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_571_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 656 (all A all X_1 all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) -> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) # label(fact_572_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 657 (all A all X_1 all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) # label(fact_573_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 658 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) # label(fact_574_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 659 (all A all X_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) # label(fact_575_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 660 (all A all X_1 all B ((hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) -> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)) & (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) -> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))))) # label(fact_576_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 661 (all A all X_1 all B ((hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))) # label(fact_577_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 662 (all A all X_1 all B ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_578_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 663 (all A all X_1 all B ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_579_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 664 (all C_11 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_11)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_11),A)) = A))) # label(fact_580_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 665 (all C_11 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_11)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_11),A)) = A))) # label(fact_581_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 666 (all C_11 all A all B (is_fun_a_bool(A) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C_11)) -> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,B),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,C_11),A)) = A)))) # label(fact_582_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 667 (all D_4 all B all A all C_11 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_11)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,D_4),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_11),D_4)))))) # label(fact_583_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 668 (all D_4 all B all A all C_11 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_11)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,D_4),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_11),D_4)))))) # label(fact_584_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 669 (all D_4 all B all A all C_11 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C_11)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,D_4),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,C_11),D_4)))))) # label(fact_585_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 670 (all A all B hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),A))) # label(fact_586_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 671 (all A all B hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),A))) # label(fact_587_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 672 (all A all B hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),A))) # label(fact_588_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 673 (all A_2 all B_3 (is_a(A_2) & is_a(B_3) -> (hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),bot_bot_fun_a_bool) -> A_2 = B_3))) # label(fact_589_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 674 (all A_2 all B_3 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),bot_bot_fun_nat_bool) -> A_2 = B_3)) # label(fact_590_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 675 (all A_2 all B_3 (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),bot_bot_fun_int_bool) -> A_2 = B_3)) # label(fact_591_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 676 (all B_3 all A_2 (is_a(B_3) & is_a(A_2) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) -> B_3 = A_2))) # label(fact_592_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 677 (all B_3 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) -> B_3 = A_2)) # label(fact_593_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 678 (all B_3 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) -> B_3 = A_2)) # label(fact_594_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 679 (all B_3 all A_2 (is_pname(B_3) & is_pname(A_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) -> B_3 = A_2))) # label(fact_595_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 680 (all A_2 all B_3 all C_6 all D_1 (is_a(A_2) & is_a(B_3) & is_a(C_6) & is_a(D_1) -> (hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,D_1),bot_bot_fun_a_bool)) <-> A_2 = C_6 & B_3 = D_1 | A_2 = D_1 & B_3 = C_6))) # label(fact_596_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 681 (all A_2 all B_3 all C_6 all D_1 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_6),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_1),bot_bot_fun_nat_bool)) <-> A_2 = C_6 & B_3 = D_1 | A_2 = D_1 & B_3 = C_6)) # label(fact_597_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 682 (all A_2 all B_3 all C_6 all D_1 (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,D_1),bot_bot_fun_int_bool)) <-> A_2 = C_6 & B_3 = D_1 | A_2 = D_1 & B_3 = C_6)) # label(fact_598_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 683 (all B_3 all A_2 (is_a(B_3) & is_a(A_2) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) <-> B_3 = A_2))) # label(fact_599_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 684 (all B_3 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) <-> B_3 = A_2)) # label(fact_600_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 685 (all B_3 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) <-> B_3 = A_2)) # label(fact_601_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 686 (all B_3 all A_2 (is_pname(B_3) & is_pname(A_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) <-> B_3 = A_2))) # label(fact_602_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 687 (all A_2 all A hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A) != bot_bot_fun_a_bool) # label(fact_603_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 688 (all A_2 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A) != bot_bot_fun_nat_bool) # label(fact_604_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 689 (all A_2 all A hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A) != bot_bot_fun_int_bool) # label(fact_605_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 690 (all A_2 all A bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A)) # label(fact_606_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 691 (all A_2 all A bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A)) # label(fact_607_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 692 (all A_2 all A bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A)) # label(fact_608_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 693 (all A (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),bot_bot_fun_nat_bool)) <-> A = bot_bot_fun_nat_bool)) # label(fact_609_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 694 (all A (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),bot_bot_fun_int_bool)) <-> A = bot_bot_fun_int_bool)) # label(fact_610_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 695 (all A (is_fun_a_bool(A) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),bot_bot_fun_a_bool)) <-> A = bot_bot_fun_a_bool))) # label(fact_611_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 696 (all F all A (image_nat_int(F,A) = bot_bot_fun_int_bool <-> A = bot_bot_fun_nat_bool)) # label(fact_612_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 697 (all F all A (is_fun_pname_bool(A) -> (image_pname_a(F,A) = bot_bot_fun_a_bool <-> A = bot_bo844097828e_bool))) # label(fact_613_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 698 (all F image_nat_int(F,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool) # label(fact_614_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 699 (all F image_pname_a(F,bot_bo844097828e_bool) = bot_bot_fun_a_bool) # label(fact_615_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 700 (all F all A (bot_bot_fun_int_bool = image_nat_int(F,A) <-> A = bot_bot_fun_nat_bool)) # label(fact_616_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 701 (all F all A (is_fun_pname_bool(A) -> (bot_bot_fun_a_bool = image_pname_a(F,A) <-> A = bot_bo844097828e_bool))) # label(fact_617_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 702 (all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool)) -> A_2 = bot_bot_fun_nat_bool)) # label(fact_618_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 703 (all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool)) -> A_2 = bot_bot_fun_int_bool)) # label(fact_619_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 704 (all A_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),bot_bot_nat)) -> A_17 = bot_bot_nat)) # label(fact_620_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 705 (all A_2 (is_fun_a_bool(A_2) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),bot_bot_fun_a_bool)) -> A_2 = bot_bot_fun_a_bool))) # label(fact_621_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 706 (all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool)) <-> A_2 = bot_bot_fun_nat_bool)) # label(fact_622_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 707 (all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool)) <-> A_2 = bot_bot_fun_int_bool)) # label(fact_623_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 708 (all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),bot_bot_nat)) <-> A_2 = bot_bot_nat)) # label(fact_624_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 709 (all A_2 (is_fun_a_bool(A_2) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),bot_bot_fun_a_bool)) <-> A_2 = bot_bot_fun_a_bool))) # label(fact_625_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 710 (all A_2 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_2))) # label(fact_626_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 711 (all A_2 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_2))) # label(fact_627_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 712 (all A_16 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_16))) # label(fact_628_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 713 (all A_2 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_2))) # label(fact_629_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 714 (all Pa all A_2 ((hBOOL(hAPP_a_bool(Pa,A_2)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),Pa)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)) & (-hBOOL(hAPP_a_bool(Pa,A_2)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),Pa)) = bot_bot_fun_a_bool))) # label(fact_630_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 715 (all Pa all A_2 ((hBOOL(hAPP_int_bool(Pa,A_2)) -> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)) & (-hBOOL(hAPP_int_bool(Pa,A_2)) -> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),Pa)) = bot_bot_fun_int_bool))) # label(fact_631_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 716 (all Pa all A_2 ((hBOOL(hAPP_nat_bool(Pa,A_2)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_2)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),Pa)) = bot_bot_fun_nat_bool))) # label(fact_632_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 717 (all Pa all A_2 ((hBOOL(hAPP_a_bool(Pa,A_2)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_2)),Pa)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)) & (-hBOOL(hAPP_a_bool(Pa,A_2)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_2)),Pa)) = bot_bot_fun_a_bool))) # label(fact_633_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 718 (all Pa all A_2 ((hBOOL(hAPP_int_bool(Pa,A_2)) -> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,A_2)),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)) & (-hBOOL(hAPP_int_bool(Pa,A_2)) -> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,A_2)),Pa)) = bot_bot_fun_int_bool))) # label(fact_634_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 719 (all Pa all A_2 ((hBOOL(hAPP_nat_bool(Pa,A_2)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_2)),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_2)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_2)),Pa)) = bot_bot_fun_nat_bool))) # label(fact_635_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 720 (all A_2 collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)) # label(fact_636_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 721 (all A_2 collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)) # label(fact_637_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 722 (all A_2 collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) # label(fact_638_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 723 (all A_2 collect_a(hAPP_a_fun_a_bool(fequal_a,A_2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)) # label(fact_639_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 724 (all A_2 collect_int(hAPP_i1948725293t_bool(fequal_int,A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)) # label(fact_640_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 725 (all A_2 collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) # label(fact_641_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 726 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,A)))) # label(fact_642_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 727 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,A)))) # label(fact_643_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 728 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,A)))) # label(fact_644_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 729 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,A)))) # label(fact_645_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 730 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))))) # label(fact_646_card__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 731 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))) # label(fact_647_card__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 732 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))) # label(fact_648_card__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 733 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))))) # label(fact_649_card__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 734 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_650_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 735 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A))))) # label(fact_651_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 736 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_652_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 737 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_653_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 738 (all A all A_2 all B (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)))) <-> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))))) # label(fact_654_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 739 (all A all A_2 all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))) # label(fact_655_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 740 (all A all A_2 all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_656_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 741 (all A all A_2 all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_657_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 742 (all F all A all B hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(F,A)),image_nat_int(F,B))),image_nat_int(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_658_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 743 (all F all A all B hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(F,A)),image_pname_a(F,B))),image_pname_a(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_659_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 744 (all A all X_1 (is_fun_a_bool(A) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) -> A = bot_bot_fun_a_bool | A = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) # label(fact_660_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 745 (all A all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) -> A = bot_bot_fun_nat_bool | A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) # label(fact_661_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 746 (all A all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) -> A = bot_bot_fun_int_bool | A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) # label(fact_662_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 747 (all F1 all F2 all Nat_3 hAPP_nat_nat(nat_case_nat(F1,F2),hAPP_nat_nat(suc,Nat_3)) = hAPP_nat_nat(F2,Nat_3)) # label(fact_663_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 748 (all F1 all F2 all Nat_3 (hBOOL(hAPP_nat_bool(nat_case_bool(F1,F2),hAPP_nat_nat(suc,Nat_3))) <-> hBOOL(hAPP_nat_bool(F2,Nat_3)))) # label(fact_664_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 749 (all C_6 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> image_nat_int(cOMBK_int_nat(C_6),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),bot_bot_fun_int_bool))) # label(fact_665_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 750 (all C_6 all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> image_pname_a(cOMBK_a_pname(C_6),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),bot_bot_fun_a_bool))) # label(fact_666_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 751 (all C_6 all A ((A = bot_bot_fun_nat_bool -> image_nat_int(cOMBK_int_nat(C_6),A) = bot_bot_fun_int_bool) & (A != bot_bot_fun_nat_bool -> image_nat_int(cOMBK_int_nat(C_6),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),bot_bot_fun_int_bool)))) # label(fact_667_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 752 (all C_6 all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> image_pname_a(cOMBK_a_pname(C_6),A) = bot_bot_fun_a_bool) & (A != bot_bo844097828e_bool -> image_pname_a(cOMBK_a_pname(C_6),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),bot_bot_fun_a_bool)))) # label(fact_668_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 753 (all A_2 all B_3 all C_6 all D_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_3) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_6),D_1) -> (A_2 = B_3 <-> C_6 = D_1))) # label(fact_669_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 754 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B))))) # label(fact_670_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 755 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B))))) # label(fact_671_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 756 (all A all B (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B))))) # label(fact_672_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 757 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B))))) # label(fact_673_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 758 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))))) # label(fact_674_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 759 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))))) # label(fact_675_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 760 (all A all B (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))))) # label(fact_676_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 761 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))))) # label(fact_677_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 762 (all Pa all A all F_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F_1),A)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool)) -> ((all A_14 all F_2 (is_a(A_14) & is_fun_a_bool(F_2) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),F_2)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,F_2)) -> hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),F_2))))))))) -> hBOOL(hAPP_fun_a_bool_bool(Pa,F_1))))))) # label(fact_678_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 763 (all Pa all A all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F_1),A)) -> (hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) -> ((all A_14 all F_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),F_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,F_2)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),F_2)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,F_1))))))) # label(fact_679_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 764 (all Pa all A all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F_1),A)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all A_14 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1))))))) # label(fact_680_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 765 (all Pa all A all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool)) -> ((all A_14 all F_2 (is_pname(A_14) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,F_2)) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),F_2))))))))) -> hBOOL(hAPP_f1664156314l_bool(Pa,F_1))))))) # label(fact_681_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 766 (all Pn all G (hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,Pn)),G)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(Pn)))),bot_bot_fun_a_bool))) -> hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,Pn)),bot_bot_fun_a_bool))))) # label(fact_682_assms_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 767 (all Pa all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,A)) -> ((all A_14 all A_15 (is_a(A_14) & is_fun_a_bool(A_15) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_15)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),A_15)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,A_15)) -> hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A_15),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),bot_bot_fun_a_bool))))))))) -> hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool)))))) # label(fact_683_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 768 (all Pa all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(Pa,A)) -> ((all A_14 all A_15 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_15)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),A_15)) -> (hBOOL(hAPP_f448129468l_bool(Pa,A_15)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_15),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),bot_bot_fun_int_bool)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)))))) # label(fact_684_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 769 (all Pa all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A)) -> ((all A_14 all A_15 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_15)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),A_15)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A_15)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_15),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),bot_bot_fun_nat_bool)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)))))) # label(fact_685_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 770 (all Pa all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,A)) -> ((all A_14 all A_15 (is_pname(A_14) & is_fun_pname_bool(A_15) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_15)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),A_15)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,A_15)) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_15),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),bot_bo844097828e_bool))))))))) -> hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool)))))) # label(fact_686_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 771 (all Pa all F_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool)) -> ((all X_2 all F_2 (is_a(X_2) & is_fun_a_bool(F_2) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),F_2)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,F_2)) -> hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),F_2)))))))) -> hBOOL(hAPP_fun_a_bool_bool(Pa,F_1)))))) # label(fact_687_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 772 (all Pa all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> (hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,F_2)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,F_1)))))) # label(fact_688_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 773 (all Pa all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1)))))) # label(fact_689_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 774 (all Pa all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool)) -> ((all X_2 all F_2 (is_pname(X_2) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,F_2)) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2)))))))) -> hBOOL(hAPP_f1664156314l_bool(Pa,F_1)))))) # label(fact_690_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 775 (all A_2 (is_fun_a_bool(A_2) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_2)) <-> A_2 = bot_bot_fun_a_bool | (exists A_15 exists A_14 (is_fun_a_bool(A_15) & is_a(A_14) & A_2 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),A_15) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_15))))))) # label(fact_691_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 776 (all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) <-> A_2 = bot_bot_fun_int_bool | (exists A_15 exists A_14 (A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),A_15) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_15)))))) # label(fact_692_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 777 (all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) <-> A_2 = bot_bot_fun_nat_bool | (exists A_15 exists A_14 (A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),A_15) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_15)))))) # label(fact_693_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 778 (all A_2 (is_fun_pname_bool(A_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_2)) <-> A_2 = bot_bo844097828e_bool | (exists A_15 exists A_14 (is_fun_pname_bool(A_15) & is_pname(A_14) & A_2 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),A_15) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_15))))))) # label(fact_694_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 779 (all U all F ((all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F,N_1)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,F)),U)))))) # label(fact_695_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 780 (all X_1 (is_a(X_1) -> hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = X_1)) # label(fact_696_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 781 (all X_1 hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1) # label(fact_697_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 782 (all X_1 hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1) # label(fact_698_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 783 (all A (is_fun_a_bool(A) -> (A != bot_bot_fun_a_bool <-> (exists X_2 exists B_15 (is_a(X_2) & is_fun_a_bool(B_15) & A = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),B_15) & -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B_15))))))) # label(fact_699_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 784 (all A (A != bot_bot_fun_int_bool <-> (exists X_2 exists B_15 (A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),B_15) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_15)))))) # label(fact_700_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 785 (all A (A != bot_bot_fun_nat_bool <-> (exists X_2 exists B_15 (A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_15) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_15)))))) # label(fact_701_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 786 (all A (is_fun_pname_bool(A) -> (A != bot_bo844097828e_bool <-> (exists X_2 exists B_15 (is_pname(X_2) & is_fun_pname_bool(B_15) & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_15) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_15))))))) # label(fact_702_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 787 (all Pn (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn),u)) -> hBOOL(wt(the_com(body(Pn)))))) # label(fact_703_assms_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 788 (all C_6 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) -> -(hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))))) # label(fact_704_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 789 (all C_6 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))))) # label(fact_705_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 790 (all C_6 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) -> -(hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))))) # label(fact_706_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 791 (all C_6 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))))) # label(fact_707_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 792 (all B all C_6 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))))) # label(fact_708_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 793 (all B all C_6 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))))) # label(fact_709_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 794 (all B all C_6 all A (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))))) # label(fact_710_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 795 (all B all C_6 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))))) # label(fact_711_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 796 (all C_6 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B)))) # label(fact_712_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 797 (all C_6 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B)))) # label(fact_713_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 798 (all C_6 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B)))) # label(fact_714_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 799 (all C_6 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B)))) # label(fact_715_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 800 (all C_6 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)))) # label(fact_716_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 801 (all C_6 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)))) # label(fact_717_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 802 (all C_6 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)))) # label(fact_718_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 803 (all C_6 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)))) # label(fact_719_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 804 (all C_6 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B)))) # label(fact_720_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 805 (all C_6 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B)))) # label(fact_721_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 806 (all C_6 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) & -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B)))) # label(fact_722_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 807 (all C_6 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B)))) # label(fact_723_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 808 (all A all B hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B))))) # label(fact_724_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 809 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B))))) # label(fact_725_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 810 (all A all B hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B))))) # label(fact_726_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 811 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))))) # label(fact_727_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 812 (all X_1 all A all F all F_1 (is_a(X_1) -> (hBOOL(finite_folding_one_a(F,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool -> hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = X_1) & (hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool -> hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))))))))) # label(fact_728_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 813 (all X_1 all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = X_1) & (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))))) # label(fact_729_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 814 (all X_1 all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_730_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 815 (all X_1 all A all F all F_1 (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = X_1) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))))))) # label(fact_731_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 816 (all X_1 all A all F all F_1 (is_a(X_1) -> (hBOOL(finite_folding_one_a(F,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> (hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool -> hAPP_fun_a_bool_a(F_1,A) = X_1) & (hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool -> hAPP_fun_a_bool_a(F_1,A) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))))))))) # label(fact_732_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 817 (all X_1 all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,A) = X_1) & (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,A) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))))) # label(fact_733_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 818 (all X_1 all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,A) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))))) # label(fact_734_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 819 (all X_1 all A all F all F_1 (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,A) = X_1) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,A) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))))))))) # label(fact_735_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 820 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),one_one_nat)) & (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,A)))) # label(fact_736_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 821 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),one_one_nat)) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,A)))) # label(fact_737_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 822 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),one_one_nat)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,A)))) # label(fact_738_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 823 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),one_one_nat)) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,A)))) # label(fact_739_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.05 824 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),one_one_nat)))) # label(fact_740_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 825 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),one_one_nat)))) # label(fact_741_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 826 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),one_one_nat)))) # label(fact_742_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 827 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),one_one_nat)))) # label(fact_743_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 828 (all X_1 (one_one_int = X_1 <-> X_1 = one_one_int)) # label(fact_744_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 829 (all X_1 (one_one_nat = X_1 <-> X_1 = one_one_nat)) # label(fact_745_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 830 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N)),one_one_nat) = N) # label(fact_746_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 831 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N)) # label(fact_747_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 832 (all X_1 all F all F_1 (is_a(X_1) -> (hBOOL(finite_folding_one_a(F,F_1)) -> hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = X_1))) # label(fact_748_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 833 (all X_1 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1)) # label(fact_749_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 834 (all X_1 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1)) # label(fact_750_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 835 (all B all A_2 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))),one_one_nat))))) # label(fact_751_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 836 (all B all A_2 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))),one_one_nat))))) # label(fact_752_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 837 (all B all A_2 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))),one_one_nat))))) # label(fact_753_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 838 (all B all A_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))),one_one_nat))))) # label(fact_754_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 839 (all X_1 all A all F all F_1 (is_fun_a_bool(A) -> (hBOOL(finite_folding_one_a(F,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> (A != bot_bot_fun_a_bool -> hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,A)))))))) # label(fact_755_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 840 (all X_1 all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (A != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A))))))) # label(fact_756_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 841 (all X_1 all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A))))))) # label(fact_757_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 842 (all X_1 all A all F all F_1 (is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (A != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,A)))))))) # label(fact_758_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 843 (all A all F all F_1 (is_fun_a_bool(A) -> (hBOOL(finite_folding_one_a(F,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (A != bot_bot_fun_a_bool -> ((all X_2 all Y_2 (is_a(X_2) & is_a(Y_2) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(F,X_2),Y_2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_2),bot_bot_fun_a_bool)))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(F_1,A)),A)))))))) # label(fact_759_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 844 (all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (A != bot_bot_fun_int_bool -> ((all X_2 all Y_2 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_2),bot_bot_fun_int_bool))))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(F_1,A)),A))))))) # label(fact_760_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 845 (all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> ((all X_2 all Y_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_2),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A)),A))))))) # label(fact_761_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 846 (all A all F all F_1 (is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> ((all X_2 all Y_2 (is_pname(X_2) & is_pname(Y_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(F_1,A)),A)))))))) # label(fact_762_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 847 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hAPP_fun_a_bool_nat(finite_card_a,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))))))) # label(fact_763_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 848 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(finite_card_int,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_764_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 849 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_765_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 850 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f921600141ol_nat(finite_card_pname,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))))) # label(fact_766_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 851 (all X_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))))) # label(fact_767_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 852 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))) # label(fact_768_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 853 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))) # label(fact_769_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 854 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))))) # label(fact_770_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 855 (all B all A all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (B != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) -> hAPP_int_int(hAPP_int_fun_int_int(F,hAPP_f1594865479ol_int(F_1,B)),hAPP_f1594865479ol_int(F_1,A)) = hAPP_f1594865479ol_int(F_1,A)))))) # label(fact_771_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 856 (all B all A all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (B != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,B)),hAPP_f22106695ol_nat(F_1,A)) = hAPP_f22106695ol_nat(F_1,A)))))) # label(fact_772_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 857 (all B all A all F all F_1 (is_fun_pname_bool(B) -> (hBOOL(finite89670078_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (B != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,B)),hAPP_f1297739591_pname(F_1,A)) = hAPP_f1297739591_pname(F_1,A))))))) # label(fact_773_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 858 (all B all A all F all F_1 (is_fun_a_bool(B) -> (hBOOL(finite1819937229idem_a(F,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (B != bot_bot_fun_a_bool -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) -> hAPP_a_a(hAPP_a_fun_a_a(F,hAPP_fun_a_bool_a(F_1,B)),hAPP_fun_a_bool_a(F_1,A)) = hAPP_fun_a_bool_a(F_1,A))))))) # label(fact_774_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 859 (all X_1 all A all F all F_1 (is_fun_a_bool(A) -> (hBOOL(finite1819937229idem_a(F,F_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (A != bot_bot_fun_a_bool -> hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,A))))))) # label(fact_775_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 860 (all X_1 all A all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (A != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A)))))) # label(fact_776_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 861 (all X_1 all A all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A)))))) # label(fact_777_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 862 (all X_1 all A all F all F_1 (is_fun_pname_bool(A) -> (hBOOL(finite89670078_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,A))))))) # label(fact_778_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 863 (all Pa all F_1 (is_fun_a_bool(F_1) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) -> (F_1 != bot_bot_fun_a_bool -> ((all X_2 (is_a(X_2) -> hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),bot_bot_fun_a_bool))))) -> ((all X_2 all F_2 (is_a(X_2) & is_fun_a_bool(F_2) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2)) -> (F_2 != bot_bot_fun_a_bool -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),F_2)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,F_2)) -> hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),F_2))))))))) -> hBOOL(hAPP_fun_a_bool_bool(Pa,F_1)))))))) # label(fact_779_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 864 (all Pa all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> (F_1 != bot_bot_fun_int_bool -> ((all X_2 hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),bot_bot_fun_int_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) -> (F_2 != bot_bot_fun_int_bool -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,F_2)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,F_1))))))) # label(fact_780_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 865 (all Pa all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (F_1 != bot_bot_fun_nat_bool -> ((all X_2 hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (F_2 != bot_bot_fun_nat_bool -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1))))))) # label(fact_781_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 866 (all Pa all F_1 (is_fun_pname_bool(F_1) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (F_1 != bot_bo844097828e_bool -> ((all X_2 (is_pname(X_2) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool))))) -> ((all X_2 all F_2 (is_pname(X_2) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (F_2 != bot_bo844097828e_bool -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,F_2)) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))))))))) -> hBOOL(hAPP_f1664156314l_bool(Pa,F_1)))))))) # label(fact_782_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 867 (all X_3 hAPP_fun_a_bool_a(the_elem_a,X_3) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X_3),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool)))) # label(fact_783_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 868 (all X_3 hAPP_f22106695ol_nat(the_elem_nat,X_3) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_3),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool)))) # label(fact_784_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 869 (all X_3 hAPP_f1594865479ol_int(the_elem_int,X_3) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X_3),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool)))) # label(fact_785_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 870 (all A_13 all B_14 all C_10 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),B_14)),C_10) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_14),C_10))) # label(fact_786_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 871 (all A_13 all B_14 all C_10 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_14)),C_10) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),C_10))) # label(fact_787_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 872 (all A_2 all B_3 all C_6 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6) <-> B_3 = C_6)) # label(fact_788_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 873 (all A_2 all B_3 all C_6 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6) <-> B_3 = C_6)) # label(fact_789_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 874 (all B_3 all A_2 all C_6 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),A_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2) <-> B_3 = C_6)) # label(fact_790_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 875 (all B_3 all A_2 all C_6 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2) <-> B_3 = C_6)) # label(fact_791_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 876 (all A_12 all B_13 all C_9 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),B_13) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),C_9) -> B_13 = C_9)) # label(fact_792_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 877 (all A_12 all B_13 all C_9 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_9) -> B_13 = C_9)) # label(fact_793_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 878 (all A_11 all B_12 all C_8 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),B_12) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),C_8) -> B_12 = C_8)) # label(fact_794_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 879 (all A_11 all B_12 all C_8 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),C_8) -> B_12 = C_8)) # label(fact_795_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 880 (all B_11 all A_10 all C_7 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_11),A_10) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_7),A_10) -> B_11 = C_7)) # label(fact_796_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 881 (all B_11 all A_10 all C_7 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),A_10) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_10) -> B_11 = C_7)) # label(fact_797_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 882 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)) # label(fact_798_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 883 (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_799_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 884 (all M_1 all N 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_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1))) # label(fact_800_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 885 (all K all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na) <-> M = Na)) # label(fact_801_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 886 (all M all K all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K) <-> M = Na)) # label(fact_802_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 887 (all A_2 all C_6 all B_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),C_6))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)))) # label(fact_803_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 888 (all A_2 all C_6 all B_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),C_6))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3)))) # label(fact_804_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 889 (all C_6 all A_2 all B_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),B_3))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)))) # label(fact_805_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 890 (all C_6 all A_2 all B_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),B_3))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3)))) # label(fact_806_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 891 (all C_5 all A_9 all B_10 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_9),B_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_9),C_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_10),C_5))))) # label(fact_807_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 892 (all C_5 all A_9 all B_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_10)) -> 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_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_10),C_5))))) # label(fact_808_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 893 (all C_4 all A_8 all B_9 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_8),B_9)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),A_8)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),B_9))))) # label(fact_809_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 894 (all C_4 all A_8 all B_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),A_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),B_9))))) # label(fact_810_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 895 (all C_3 all D_3 all A_7 all B_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_7),B_8)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_3),D_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_7),C_3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_8),D_3)))))) # label(fact_811_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 896 (all C_3 all D_3 all A_7 all B_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),D_3)) -> 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_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_3)))))) # label(fact_812_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 897 (all A_6 all C_2 all B_7 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_6),C_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_7),C_2))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_6),B_7)))) # label(fact_813_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 898 (all A_6 all C_2 all B_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_7),C_2))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_7)))) # label(fact_814_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 899 (all C_1 all A_5 all B_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),A_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),B_6))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_5),B_6)))) # label(fact_815_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 900 (all C_1 all A_5 all B_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),A_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),B_6))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_5),B_6)))) # label(fact_816_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 901 (all A_4 all B_5 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_4),B_5)),B_5) = A_4) # label(fact_817_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 902 (all A_3 all B_4 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_3),B_4)),B_4) = A_3) # label(fact_818_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 903 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))) # label(fact_819_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 904 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))) # label(fact_820_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 905 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N))) # label(fact_821_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 906 (all N all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)))) # label(fact_822_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 907 (all N all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)))) # label(fact_823_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 908 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) <-> (exists K_2 Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2)))) # label(fact_824_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 909 (all K all M 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)),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),Na)))) # label(fact_825_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 910 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))))) # label(fact_826_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 911 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))))) # label(fact_827_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 912 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))))) # label(fact_828_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 913 (all K_1 all L_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))))) # label(fact_829_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 914 (all M_1 all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)))) # label(fact_830_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 915 (all M_1 all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)))) # label(fact_831_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 916 (all M_1 all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N))))) # label(fact_832_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 917 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),N) = M_1) # label(fact_833_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 918 (all N all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)),N) = M_1) # label(fact_834_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 919 (all I_1 all J all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) # label(fact_835_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 920 (all K_1 all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) # label(fact_836_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 921 (all M_1 all K_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) # label(fact_837_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 922 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J))) # label(fact_838_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 923 (all J_1 all K all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)),I_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K))))) # label(fact_839_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 924 (all M_1 all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)),K_1))))) # label(fact_840_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 925 (all N all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = M_1)) # label(fact_841_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 926 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1))) # label(fact_842_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 927 (all I_2 all K all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1))))) # label(fact_843_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 928 (all N all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),N) = M_1)) # label(fact_844_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 929 (all K all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2) = K <-> J_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),I_2)))) # label(fact_845_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 930 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)))) # label(fact_846_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 931 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1))) # label(fact_847_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 932 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1))) # label(fact_848_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 933 (all N hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N)) # label(fact_849_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 934 (all N hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)) # label(fact_850_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 935 (all M_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(suc,J)))) # label(fact_851_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 936 (all M_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)))) # label(fact_852_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 937 (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_853_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 938 (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_854_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 939 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N)))) # label(fact_855_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 940 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N))))) # label(fact_856_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 941 (all K hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),K))))) # label(fact_857_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 942 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_858_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 943 (all M all Na (M != Na <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M)))) # label(fact_859_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 944 (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_860_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 945 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_861_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 946 (all N all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_1)) -> M_1 != N)) # label(fact_862_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 947 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_863_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 948 (all Pa all M all Na ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M))) -> ((M = Na -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M)))))) # label(fact_864_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 949 (all M all Na (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M))))) # label(fact_865_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 950 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) | M = Na)) # label(fact_866_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 951 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_867_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 952 (all Na all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M))) <-> Na = M))) # label(fact_868_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 953 (all N all M_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M_1))) -> M_1 = N))) # label(fact_869_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 954 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N))))) # label(fact_870_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 955 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> (hAPP_nat_nat(suc,M_1) != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N))))) # label(fact_871_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 956 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1))))) # label(fact_872_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 957 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> M_1 = N))) # label(fact_873_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 958 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)))) # label(fact_874_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 959 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)))) # label(fact_875_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 960 (all I_1 all J -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),I_1))) # label(fact_876_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 961 (all J all I_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),I_1))) # label(fact_877_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 962 (all K all M 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)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_878_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 963 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))))) # label(fact_879_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 964 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))))) # label(fact_880_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 965 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))))) # label(fact_881_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 966 (all K_1 all L_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))))) # label(fact_882_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 967 (all M_1 all N all K_1 all L_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),L_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))))) # label(fact_883_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 968 (all I_1 all J 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_1),J)),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)))) # label(fact_884_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 969 (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_885_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 970 (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_886_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 971 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) & M != Na)) # label(fact_887_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 972 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) | M = Na)) # label(fact_888_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 973 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)))) # label(fact_889_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 974 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> (M_1 != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))))) # label(fact_890_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 975 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) | M_1 = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)))) # label(fact_891_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 976 (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_892_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 977 (all N all J all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N)),K_1)))) # label(fact_893_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 978 (all L_1 all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1)))))) # label(fact_894_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 979 (all N_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) <-> (exists M_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),M_2)))))) # label(fact_895_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 980 (all Na hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),Na))) = Na) # label(fact_896_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 981 (all Pa all I_2 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2)))))) # label(fact_897_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 982 (all I_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),M_1))))) # label(fact_898_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 983 (all I_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),I_1))))) # label(fact_899_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 984 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) <-> (exists K_2 Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2))))) # label(fact_900_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 985 (all Na all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M)))) # label(fact_901_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 986 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)))) # label(fact_902_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 987 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_903_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 988 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N))))) # label(fact_904_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 989 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N)))) # label(fact_905_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 990 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M))) <-> Na = M))) # label(fact_906_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 991 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)))) # label(fact_907_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 992 (all M_1 all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),hAPP_nat_nat(suc,M_1)))) # label(fact_908_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 993 (all I_2 all J_1 all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1)))) # label(fact_909_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 994 (all M_1 all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = M_1)) # label(fact_910_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 995 (all C all A_1 all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_2),C)))))) # label(fact_911_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 996 (all Na all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))))) # label(fact_912_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 997 (all X_2 hAPP_n1699378549t_bool(ord_less_nat,X_2) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_2))) # label(fact_913_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 998 (all M all K all F ((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(F,M_2)),hAPP_nat_nat(F,N_1))))) -> 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)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)))))) # label(fact_914_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 999 (all Pa all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) -> (hBOOL(hAPP_nat_bool(Pa,J_1)) -> ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I))) -> hBOOL(hAPP_nat_bool(Pa,I))))) -> hBOOL(hAPP_nat_bool(Pa,I_2)))))) # label(fact_915_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1000 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> (exists K_2 N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2))))) # label(fact_916_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1001 (all Na all N_2 ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Na)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)))) # label(fact_917_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1002 (all I_2 all J_1 all F ((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(F,I)),hAPP_nat_nat(F,J_2))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_1)))))) # label(fact_918_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1003 (all I_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)) -> (K_1 != hAPP_nat_nat(suc,I_1) -> -(all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2)) -> K_1 != hAPP_nat_nat(suc,J_2)))))) # label(fact_919_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1004 (all I_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1)) -> -(all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2)) -> K_1 != hAPP_nat_nat(suc,J_2))))) # label(fact_920_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1005 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_921_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1006 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_922_le0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1007 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N)))) # label(fact_923_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1008 (all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat)) <-> Na = zero_zero_nat)) # label(fact_924_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1009 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_925_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1010 (all M_1 all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N) = zero_zero_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M_1) = zero_zero_nat -> M_1 = N))) # label(fact_926_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1011 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),M_1) = zero_zero_nat) # label(fact_927_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1012 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),zero_zero_nat) = M_1) # label(fact_928_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1013 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N) = zero_zero_nat) # label(fact_929_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1014 (all M_1 all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = M_1 -> N = zero_zero_nat)) # label(fact_931_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1015 (all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) = zero_zero_nat <-> M = zero_zero_nat & Na = zero_zero_nat)) # label(fact_932_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1016 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),zero_zero_nat) = M_1) # label(fact_933_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1017 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N) # label(fact_934_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.06 1018 (all N (N != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_935_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1019 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) -> N != zero_zero_nat)) # label(fact_936_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1020 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_937_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1021 (all Na (Na != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)))) # label(fact_938_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1022 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_939_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1023 (all M_1 hAPP_nat_nat(suc,M_1) != zero_zero_nat) # label(fact_940_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1024 (all M_1 zero_zero_nat != hAPP_nat_nat(suc,M_1)) # label(fact_941_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1025 (all Nat_2 hAPP_nat_nat(suc,Nat_2) != zero_zero_nat) # label(fact_942_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1026 (all M_1 hAPP_nat_nat(suc,M_1) != zero_zero_nat) # label(fact_943_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1027 (all Nat_1 zero_zero_nat != hAPP_nat_nat(suc,Nat_1)) # label(fact_944_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1028 (all M_1 zero_zero_nat != hAPP_nat_nat(suc,M_1)) # label(fact_945_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1029 (all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) <-> (exists M_2 Na = hAPP_nat_nat(suc,M_2)))) # label(fact_946_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1030 (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_947_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1031 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na))) <-> M = zero_zero_nat | (exists J_2 (M = hAPP_nat_nat(suc,J_2) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na)))))) # label(fact_948_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1032 (all M all Na (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & Na = zero_zero_nat | M = zero_zero_nat & Na = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_949_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1033 (all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & Na = zero_zero_nat | M = zero_zero_nat & Na = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_950_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1034 (all M 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),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)))) # label(fact_951_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1035 (all Na all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_952_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1036 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),M_1))))) # label(fact_953_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1037 (all N all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)) = zero_zero_nat) # label(fact_954_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1038 (all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),Na) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)))) # label(fact_955_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1039 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N) = zero_zero_nat)) # label(fact_956_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1040 (all M all Na hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,Na)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),Na))) # label(fact_958_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1041 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))) = N)) # label(fact_959_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1042 (all I_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,I_1))),N)))) # label(fact_960_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1043 (all Pa all A_2 all B_3 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3)) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))) & (all D_2 (A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2) -> hBOOL(hAPP_nat_bool(Pa,D_2)))))) # label(fact_961_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1044 (all Pa all A_2 all B_3 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3))) <-> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3)) & -hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) | (exists D_2 (A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2) & -hBOOL(hAPP_nat_bool(Pa,D_2))))))) # label(fact_962_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1045 (all I_2 all M_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2))))))) # label(fact_963_card__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1046 (all I_2 all M_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2))))) != zero_zero_nat)) # label(fact_964_card__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1047 (all I_2 all M_3 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2))))))) # label(fact_965_card__less__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1048 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)) = N)) # label(fact_966_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1049 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)))) # label(fact_967_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1050 (all N all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = N) & (M_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N))))) # label(fact_968_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1051 (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 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2)) -> -hBOOL(hAPP_nat_bool(Pa,I)))) & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat)))))))) # label(fact_969_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1052 (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 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)) -> -hBOOL(hAPP_nat_bool(Pa,I)))) & hBOOL(hAPP_nat_bool(Pa,K_2))))))) # label(fact_970_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1053 (all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) & hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_2) = J)))) # label(fact_971_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1054 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (exists M_2 N = hAPP_nat_nat(suc,M_2)))) # label(fact_972_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1055 (all Y (Y != zero_zero_nat -> -(all Nat Y != hAPP_nat_nat(suc,Nat)))) # label(fact_973_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1056 (all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N_1 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(Pa,N_1)))) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))))) # label(fact_974_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1057 (all N (N != zero_zero_nat -> (exists M_2 N = hAPP_nat_nat(suc,M_2)))) # label(fact_975_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1058 (all Na all Pa (hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> ((all N_1 (hBOOL(hAPP_nat_bool(Pa,N_1)) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))))) -> hBOOL(hAPP_nat_bool(Pa,Na))))) # label(fact_976_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1059 (all V (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V))) -> number_number_of_nat(V) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(V)),one_one_nat)))) # label(fact_977_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1060 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N) = zero_zero_nat) # label(fact_978_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1061 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),zero_zero_nat) = zero_zero_nat) # label(fact_979_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1062 (all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = zero_zero_nat <-> M = zero_zero_nat | Na = zero_zero_nat)) # label(fact_980_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1063 (all K all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na) <-> M = Na | K = zero_zero_nat)) # label(fact_981_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1064 (all M all K all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K) <-> M = Na | K = zero_zero_nat)) # label(fact_982_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1065 (all K all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na) <-> M = Na)) # label(fact_983_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1066 (all M_1 all N all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1))) # label(fact_984_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1067 (all K_1 all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) # label(fact_985_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1068 (all K_1 all L_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),L_1)))))) # label(fact_986_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1069 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J))))) # label(fact_987_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1070 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1))))) # label(fact_988_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1071 (all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1))))) # label(fact_989_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1072 (all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1)))) # label(fact_990_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1073 (all M_1 all N all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1))) # label(fact_991_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1074 (all K_1 all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) # label(fact_992_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1075 (all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = one_one_nat <-> M = one_one_nat & Na = one_one_nat)) # label(fact_993_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1076 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),one_one_nat) = N) # label(fact_994_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1077 (all M all Na (one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) <-> M = one_one_nat & Na = one_one_nat)) # label(fact_995_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1078 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N) = N) # label(fact_996_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1079 (all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & Na = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_997_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1080 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J)))))) # label(fact_998_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1081 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1)))))) # label(fact_999_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1082 (all M all K all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_1000_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1083 (all K all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_1001_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1084 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)))) # label(fact_1002_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1085 (all K all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_1003_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1086 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N))) # label(fact_1004_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1087 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N))) # label(fact_1005_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1088 (all K all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)))) # label(fact_1006_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1089 (all M_1 all N (M_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) -> N = one_one_nat | M_1 = zero_zero_nat)) # label(fact_1007_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1090 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)))))) # label(fact_1008_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1091 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M_1)))))) # label(fact_1009_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1092 (all M_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)))))) # label(fact_1010_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1093 (all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na)))) # label(fact_1011_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1094 (all K all M all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))))) # label(fact_1012_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1095 (all M all K all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))))) # label(fact_1013_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1096 (all N all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = zero_zero_nat) & (M_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N))))) # label(fact_1014_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1097 (all U all M all Na all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na)))))) # label(fact_1015_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1098 (all M_1 all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M_1)) # label(fact_1016_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1099 (all M_1 all N all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1))) # label(fact_1017_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1100 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K)),number_number_of_int(L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)))) # label(fact_1018_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1101 (all Z hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),Z) = Z) # label(fact_1019_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1102 (all Z hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),one_one_int) = Z) # label(fact_1020_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1103 (all Z all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),W) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z)) # label(fact_1021_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1104 (all V all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V),W))) # label(fact_1022_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1105 (all Z1 all Z2 all Z3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),Z3))) # label(fact_1023_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1106 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K)),number_number_of_int(L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)))) # label(fact_1024_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1107 (all Z1 all Z2 all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W))) # label(fact_1025_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1108 (all W all Z1 all Z2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2))) # label(fact_1026_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1109 (all W all Z1 all Z2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2))) # label(fact_1027_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1110 (all V all W hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),W))) # label(fact_1028_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1111 (all Z1 all Z2 all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W))) # label(fact_1029_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1112 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),J)))))) # label(fact_1030_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1113 (all Na all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),Na) = one_one_int <-> M = one_one_int & Na = one_one_int))) # label(fact_1031_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1114 (all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z)),Z) != zero_zero_int) # label(fact_1032_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1115 (all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),zero_zero_int) = Z) # label(fact_1033_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1116 (all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),Z) = Z) # label(fact_1034_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1117 (all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)))) # label(fact_1036_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1118 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),L)),zero_zero_int)))) # label(fact_1037_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1119 (all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z))))) # label(fact_1038_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1120 (all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_2)),Z_2)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),zero_zero_int)))) # label(fact_1039_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1121 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),J))))) # label(fact_1040_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1122 (all Z1 all Z2 all Z3 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z2),Z3))) # label(fact_1041_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1123 (all X all Y all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Z))) # label(fact_1042_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1124 (all Z all W hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z)) # label(fact_1043_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1125 (all W hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),W))) # label(fact_1044_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1126 (all Z all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z)))) # label(fact_1045_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1127 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),K_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1))))) # label(fact_1046_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1128 (all Z all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z)) -> Z = W))) # label(fact_1047_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1129 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_2),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)))) # label(fact_1048_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1130 (all X all Y (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),Y)) | X = Y | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),X)))) # label(fact_1049_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1131 (all Z_2 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1)) & Z_2 != W_1)) # label(fact_1050_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1132 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_1),K_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,J),K_1))))) # label(fact_1051_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1133 (all Z_4 all Z all W_2 all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_2),W)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_4),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_2),Z_4)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z)))))) # label(fact_1052_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1134 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2)))) # label(fact_1053_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1135 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),one_one_int)),Z_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)))) # label(fact_1054_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1136 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),one_one_int)),Z)))) # label(fact_1055_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1137 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) | W_1 = Z_2)) # label(fact_1056_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1138 (all K all M all Na (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na) <-> K = zero_zero_nat | M = Na)) # label(fact_1057_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1139 (all I_1 all U_1 all J all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),U_1)),K_1)) # label(fact_1058_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1140 (all M all Na all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na) <-> M = Na))) # label(fact_1059_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1141 (all M all Na all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))))) # label(fact_1060_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1142 (all M all Na all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))))) # label(fact_1061_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1143 (all U all M all Na all J_1 all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2)) -> (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(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) <-> 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(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na))))) # label(fact_1062_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1144 (all U_1 all M_1 all N all J all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U_1)),M_1)),N))) # label(fact_1063_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1145 (all U all M all Na all J_1 all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M) = Na))) # label(fact_1064_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1146 (all U all M all Na all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) -> (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(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na)))))) # label(fact_1065_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1147 (all U_1 all M_1 all N all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U_1)),N)))) # label(fact_1066_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1148 (all U all M all Na all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na) <-> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na)))) # label(fact_1067_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1149 (all U all M all Na all J_1 all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na))))) # label(fact_1068_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1150 (all B_2 all Q_2 all R_2 all B_1 all Q_1 all R_1 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2))))))))) # label(fact_1069_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1151 (all B_2 all Q_1 all R_1 all Q_2 all R_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),R_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),R_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1))))))) # label(fact_1070_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1152 (all K_1 number_number_of_int(K_1) = K_1) # label(fact_1071_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1153 (all R_2 all Q_2 all A_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_1)) -> (A_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Q_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),A_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_2)))))) # label(fact_1073_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1154 (all R_2 all Q_2 all A_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_1)) -> (A_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Q_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),one_one_int)))))) # label(fact_1074_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1155 (all B_1 all Q_1 all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_1)))))) # label(fact_1075_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1156 (all B_1 all Q_1 all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),zero_zero_int)))))) # label(fact_1076_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1157 (all B_2 all Q_1 all R_1 all Q_2 all R_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2))))))) # label(fact_1077_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1158 (all B_2 all Q_2 all R_2 all B_1 all Q_1 all R_1 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1))))))))) # label(fact_1078_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1159 (all Pa all I_2 all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K)) -> (hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),one_one_int))) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),K)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1079_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1160 (all Pa all I_2 all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K)) -> (hBOOL(hAPP_int_bool(Pa,K)) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1080_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1161 (all Pa all K all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I_2)) -> (hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K),one_one_int))) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1081_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1162 (all Pa all K all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I_2)) -> (hBOOL(hAPP_int_bool(Pa,K)) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1082_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1163 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)))))) # label(fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1164 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1165 (all P_1 all Pa ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> (hBOOL(hAPP_int_bool(Pa,X_2)) <-> hBOOL(hAPP_int_bool(P_1,X_2))))) -> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),Pa)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),P_1)))) # label(fact_1087_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1166 (all K all Pa all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K)) -> (all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))))))))) # label(fact_1088_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1167 (all P_1 all Pa all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(Pa) <-> hBOOL(P_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(Pa) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P_1)))) # label(fact_1089_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1168 (all P_1 all Pa all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(Pa) <-> hBOOL(P_1))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(Pa)) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P_1))))) # label(fact_1090_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1169 (all K all Pa all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K)) -> (all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))))))))) # label(fact_1091_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1170 (all I_2 all Pa all K (hBOOL(hAPP_int_bool(Pa,K)) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))))) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1092_int__induct) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1171 (all Pa all P1 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 all K_2 (hBOOL(hAPP_int_bool(P1,X_2)) <-> hBOOL(hAPP_int_bool(P1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z_3)) -> (hBOOL(hAPP_int_bool(Pa,X_2)) <-> hBOOL(hAPP_int_bool(P1,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(Pa,X1)))))))) # label(fact_1093_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1172 (all Pa all P_1 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 all K_2 (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),X_2)) -> (hBOOL(hAPP_int_bool(Pa,X_2)) <-> hBOOL(hAPP_int_bool(P_1,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(Pa,X1)))))))) # label(fact_1094_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1173 (all Y all X ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = zero_zero_int))) # label(fact_1095_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1174 (all N hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N)))) # label(fact_1096_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1175 (all K_1 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K_1)),zero_zero_int))) # label(fact_1097_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1176 (all Na (hAPP_nat_int(semiri1621563631at_int,Na) = zero_zero_int <-> Na = zero_zero_nat)) # label(fact_1100_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1177 (all M all Na (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)))) # label(fact_1101_zless__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1178 (all M all Na (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)))) # label(fact_1102_zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1179 (all M_1 all N hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))) # label(fact_1103_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1180 (all M_1 all N all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,N)),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))),Z)) # label(fact_1104_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1181 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2)) <-> (exists N_1 Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,N_1))))) # label(fact_1105_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1182 (all M_1 all N hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N))) # label(fact_1106_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1183 (all M_1 all N hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N))) # label(fact_1107_int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1184 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y))) # label(fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1185 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)))) # label(fact_1109_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1186 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)))) # label(fact_1110_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1187 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X),Y))) # label(fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1188 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Y))) # label(fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1189 (all A hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,A))) # label(fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1190 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,A))))) # label(fact_1114_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1191 (all Pa collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),Pa)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(Pa,semiri1621563631at_int)))) # label(fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1192 (all Z hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z)))) # label(fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1193 (all Pa ((exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) & hBOOL(hAPP_int_bool(Pa,X_2)))) <-> (exists X_2 hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_1119_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1194 (all Pa ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> hBOOL(hAPP_int_bool(Pa,X_2)))) <-> (all X_2 hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_1120_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1195 (all Na (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,Na)),zero_zero_int)) <-> Na = zero_zero_nat)) # label(fact_1121_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1196 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) <-> (exists N_1 Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1)))))) # label(fact_1123_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1197 (all M_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M_1))) # label(fact_1124_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1198 (all N all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) -> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)))) # label(fact_1125_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1199 (all Na (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)))) # label(fact_1126_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1200 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),J)))))) # label(fact_1127_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1201 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y)))))) # label(fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1202 (all Pa all X_1 all Y_1 (hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_1)))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))))) & (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) -> hBOOL(hAPP_int_bool(Pa,zero_zero_int))))) # label(fact_1129_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1203 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y))) # label(fact_1130_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1204 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) -> (exists N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) & K_1 = hAPP_nat_int(semiri1621563631at_int,N_1))))) # label(fact_1131_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1205 (all M all Na (hAPP_nat_int(semiri1621563631at_int,M) = hAPP_nat_int(semiri1621563631at_int,Na) <-> M = Na)) # label(fact_1132_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1206 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))))) # label(fact_1133_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1207 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))))) # label(fact_1134_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1208 (all A all B (A = B <-> image_nat_int(semiri1621563631at_int,A) = image_nat_int(semiri1621563631at_int,B))) # label(fact_1136_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1209 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X_1)),image_nat_int(semiri1621563631at_int,A))))) # label(fact_1137_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1210 (all X_1 all Y_1 all Pa ((hBOOL(Pa) -> hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1))) & (-hBOOL(Pa) -> hAPP_nat_int(semiri1621563631at_int,Y_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1))))) # label(fact_1138_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1211 (all X_1 all Y_1 (hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,Y_1) <-> X_1 = Y_1)) # label(fact_1139_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1212 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> -(all N_1 K_1 != hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_1140_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1213 (all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z)) -> -(all M_2 Z != hAPP_nat_int(semiri1621563631at_int,M_2)))) # label(fact_1141_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1214 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> (exists N_1 K_1 = hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_1142_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1215 (all Z -(all M_2 all N_1 Z != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_2)),hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_1143_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1216 (all X all Z all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D))),Z)))) # label(fact_1144_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1217 (all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(Z_2)),one_one_int)) <-> Z_2 = zero_zero_int)) # label(fact_1145_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1218 (all Z_1 (hBOOL(hAPP_int_bool(nat_neg,Z_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)))) # label(fact_1146_neg__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1219 (all X_1 (-hBOOL(hAPP_int_bool(nat_neg,X_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)))) # label(fact_1147_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1220 (all M_1 all N (abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N)) = one_one_int -> abs_abs_int(M_1) = one_one_int)) # label(fact_1150_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1221 (all N -hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,N)))) # label(fact_1151_not__neg__int) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1222 (all M_1 abs_abs_int(hAPP_nat_int(semiri1621563631at_int,M_1)) = hAPP_nat_int(semiri1621563631at_int,M_1)) # label(fact_1152_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.07 1223 (all V (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> number_number_of_nat(V) = zero_zero_nat)) # label(fact_1153_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1224 (all V_3 all V_2 (number_number_of_nat(V_3) = number_number_of_nat(V_2) <-> (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_2)),zero_zero_int))) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) -> (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) -> number_number_of_int(V_3) = zero_zero_int) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) -> V_3 = V_2)))) # label(fact_1154_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1225 (all V_1 all K_1 all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),K_1)) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),V_1))),K_1))))) # label(fact_1155_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1226 (all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = zero_zero_int) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = number_number_of_int(V)))) # label(fact_1156_int__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1227 (all Z all X all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D)))))) # label(fact_1157_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1228 (all K all F all Na ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na))) -> (exists I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na)) & hAPP_nat_int(F,I) = K)))))) # label(fact_1158_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1229 (all K all F all Na ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na))) -> (exists I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na)) & hAPP_nat_int(F,I) = K)))))) # label(fact_1159_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1230 (all K all F all Na all M ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,M)),K)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na))) -> (exists I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na)) & hAPP_nat_int(F,I) = K))))))) # label(fact_1160_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1231 (all N all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N)) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(V))),N)))) # label(fact_1161_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1232 (all K_1 succ(K_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),one_one_int)) # label(fact_1162_succ__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1233 (all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,number_number_of_nat(V)) = one_one_nat) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,number_number_of_nat(V)) = number_number_of_nat(succ(V))))) # label(fact_1163_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1234 (all W ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W))) -> number_number_of_nat(bit1(W)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W))) -> number_number_of_nat(bit1(W)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(W)),number_number_of_nat(W)))))) # label(fact_1164_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1235 (all V ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(V)) = one_one_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(V)) = number_number_of_nat(succ(V))))) # label(fact_1165_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1236 (all W_1 (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(W_1)))) <-> hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W_1))))) # label(fact_1167_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1237 (all N hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,N))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),N)) # label(fact_1172_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1238 (all K_1 bit1(K_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_1)),K_1)) # label(fact_1177_Bit1__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1239 (all K all L (bit1(K) = bit1(L) <-> K = L)) # label(fact_1181_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1240 (all K_1 bit1(K_1) != pls) # label(fact_1182_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1241 (all L_1 pls != bit1(L_1)) # label(fact_1183_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1242 (all K_1 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_1),pls) = K_1) # label(fact_1184_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1243 (all K_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),K_1) = K_1) # label(fact_1185_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1244 (all K_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),pls) = K_1) # label(fact_1186_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1245 (all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),W) = pls) # label(fact_1187_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1246 (all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(K))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)))) # label(fact_1190_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1247 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit1(L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)))) # label(fact_1191_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1248 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit1(K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)))) # label(fact_1192_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1249 (all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),pls)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)))) # label(fact_1194_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1250 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit1(L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)))) # label(fact_1195_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1251 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit1(K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)))) # label(fact_1196_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1252 (all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),pls)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)))) # label(fact_1197_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1253 (all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(K))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)))) # label(fact_1198_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1254 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1255 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1256 (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].
% 1.60/2.08 1257 (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].
% 1.60/2.08 1258 (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].
% 1.60/2.08 1259 (all Q all P (-hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1260 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1261 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1262 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1263 (all Q all P (hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1264 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1265 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1266 (all X all Y (is_a(X) & is_a(Y) -> -hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000t__a_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1267 (all X all Y (X != Y | hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y)))) # label(help_fequal_2_1_fequal_000t__a_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1268 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1269 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1270 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1271 (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].
% 1.60/2.08 1272 (all X all Y (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1273 (all X all Y (X != Y | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1274 (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].
% 1.60/2.08 1275 (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].
% 1.60/2.08 1276 (all X all Y (is_pname(X) & is_pname(Y) -> -hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1277 (all X all Y (X != Y | hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1278 (all P all Q (is_bool(P) -> hAPP_a_bool(cOMBK_bool_a(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1279 (all P all Q (is_a(P) -> hAPP_pname_a(cOMBK_a_pname(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1280 (all P all Q all R hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(P),Q),R) = hAPP_a_bool(hAPP_a_fun_a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1281 (all P all Q hAPP_nat_int(cOMBK_int_nat(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1282 (all P all Q (is_bool(P) -> hAPP_int_bool(cOMBK_bool_int(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1283 (all P all Q (is_bool(P) -> hAPP_nat_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].
% 1.60/2.08 1284 (all X all Y (is_fun_a_bool(X) & is_fun_a_bool(Y) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1285 (all X all Y (X != Y | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1286 (all P all Q all R hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(P),Q),R) = hAPP_a_bool(hAPP_int_fun_a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1287 (all P all Q all R hAPP_a_bool(cOMBB_bool_bool_a(P,Q),R) = hAPP_bool_bool(P,hAPP_a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1288 (all P all Q all R hAPP_a_bool(cOMBS_a_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_a_fun_bool_bool(P,R),hAPP_a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1289 (all P all Q all R hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(P),Q),R) = hAPP_a_bool(hAPP_p1534023578a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1290 (all X all Y (-hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1291 (all X all Y (X != Y | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1292 (all X all Y (-hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1293 (all X all Y (X != Y | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1294 (all X all Y (is_fun_pname_bool(X) & is_fun_pname_bool(Y) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1295 (all X all Y (X != Y | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1296 (all P all Q all R hAPP_nat_bool(cOMBB_int_bool_nat(P,Q),R) = hAPP_int_bool(P,hAPP_nat_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1297 (all P all Q all R hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(P),Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1298 (all P all Q all R hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(P),Q),R) = hAPP_int_bool(hAPP_n1082236369t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1299 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1300 (all P all Q all R hAPP_int_bool(cOMBB_bool_bool_int(P,Q),R) = hAPP_bool_bool(P,hAPP_int_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1301 (all P all Q all R hAPP_nat_bool(cOMBB_bool_bool_nat(P,Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1302 (all P all Q all R hAPP_int_bool(cOMBS_int_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1303 (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].
% 1.60/2.08 1304 (all P all Q all R hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1305 (all P all Q all R hAPP_pname_bool(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1306 (all P all Q all R hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1307 (all P all Q all R hAPP_int_fun_a_bool(cOMBB_375279840ol_int(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_int_a(Q,R))) # label(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1308 (all P all Q all R hAPP_a_bool(cOMBB_1273333599bool_a(P,Q),R) = hAPP_fun_a_bool_bool(P,hAPP_a_fun_a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1309 (all P all Q all R hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1310 (all P all Q all R hAPP_p1534023578a_bool(cOMBB_1897541054_pname(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_pname_a(Q,R))) # label(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1311 (all P all Q all R hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1312 (all P all Q all R hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1313 (all P all Q all R hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_a_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].
% 1.60/2.08 1314 (all P all Q all R hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f198738859l_bool(P,R),hAPP_fun_a_bool_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1315 (all P all Q all R hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(P,Q),R) = hAPP_i1948725293t_bool(P,hAPP_nat_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1316 (all P all Q all R hAPP_n1699378549t_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].
% 1.60/2.08 1317 (all P all Q all R hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(P),Q),R) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1318 (all P all Q all R hAPP_int_bool(cOMBB_1418110531ol_int(P,Q),R) = hAPP_f448129468l_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1319 (all P all Q all R hAPP_nat_bool(cOMBB_955900739ol_nat(P,Q),R) = hAPP_f54304608l_bool(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1320 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1321 (all P all Q all R hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1322 (all P all Q all R hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1323 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1324 (all P all Q all R hAPP_i68813070l_bool(cOMBB_1652995168ol_int(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1325 (all P all Q all R hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1326 (all P all Q all R hAPP_f448129468l_bool(cOMBS_1912792529l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1721100032l_bool(P,R),hAPP_f448129468l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1327 (all P all Q all R hAPP_f54304608l_bool(cOMBS_1187019125l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1748468828l_bool(P,R),hAPP_f54304608l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1328 (all P all Q all R hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1329 (all P all Q all R hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1330 (all P all Q all R hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_005) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1331 (all P all Q all R hAPP_f1664156314l_bool(cOMBS_350070575l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1332 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1333 (all P all Q all R hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1334 (all P all Q all R hAPP_f198738859l_bool(cOMBB_338059395a_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_fun_a_bool_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1335 (all P all Q all R hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(P,Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1336 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(P),Q),R) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1337 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(P),Q),R) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__008) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1338 (all P all Q all R hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1339 (all P all Q all R hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1340 (all P all Q all R hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f448129468l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1341 (all P all Q all R hAPP_f1748468828l_bool(cOMBB_444170502t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f54304608l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1342 (all P all Q all R hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1343 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1344 (all P all Q all R hAPP_i888906320l_bool(cOMBB_313729068ol_int(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_int_fun_a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) # label(axiom) # label(non_clause). [assumption].
% 1.60/2.08 1345 (all P all Q all R hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_nat_fun_a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.87 1346 (all P all Q all R hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(P,Q),R) = hAPP_f284875647l_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.87 1347 (all P all Q all R hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(P,Q),R) = hAPP_f284875647l_bool(P,hAPP_n1082236369t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.87 1348 (all P all Q all R hAPP_i1718399025l_bool(cOMBB_516767136ol_int(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_i418383825t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.87 1349 (all P all Q all R hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.88 1350 (all P all Q all R hAPP_i1587699435l_bool(cOMBB_607112096ol_int(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_i7355787e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.88 1351 (all P all Q all R hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_n1025906991e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.88 1352 (all P all Q all R hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.88 1353 (all P all Q all R hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(P),Q),R) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.88 1354 (all P all Q all R hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.88 1355 (all P all Q all R hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 3.60/3.88
% 3.60/3.88 ============================== end of process non-clausal formulas ===
% 3.60/3.88
% 3.60/3.88 ============================== PROCESS INITIAL CLAUSES ===============
% 3.60/3.88
% 3.60/3.88 ============================== PREDICATE ELIMINATION =================
% 3.60/3.88
% 3.60/3.88 ============================== end predicate elimination =============
% 3.60/3.88
% 3.60/3.88 Auto_denials: (non-Horn, no changes).
% 3.60/3.88
% 3.60/3.88 Term ordering decisions:
% 3.60/3.88 Function symbol KB weights: ord_less_eq_nat=1. ord_less_nat=1. plus_plus_nat=1. suc=1. ord_less_eq_int=1. zero_zero_nat=1. finite_finite_pname=1. times_times_nat=1. finite_finite_nat=1. minus_minus_nat=1. ord_le1311769555a_bool=1. finite_finite_a=1. finite_finite_int=1. bot_bot_fun_a_bool=1. insert_a=1. ord_le951220754t_bool=1. ord_le1568362934t_bool=1. insert_int=1. insert_nat=1. bot_bot_fun_int_bool=1. bot_bot_fun_nat_bool=1. ord_less_int=1. semiri1621563631at_int=1. plus_plus_int=1. member_nat=1. zero_zero_int=1. member_int=1. member_pname=1. member_a=1. bot_bo844097828e_bool=1. ord_le313189616e_bool=1. insert_pname=1. finite1395289673t_bool=1. finite2012431853t_bool=1. finite347923420a_bool=1. finite595471783e_bool=1. times_times_int=1. one_one_int=1. one_one_nat=1. minus_1449998731t_bool=1. minus_2067140911t_bool=1. minus_minus_int=1. fconj=1. minus_1762468890a_bool=1. finite_card_nat=1. finite_card_a=1. finite_card_int=1. minus_1015773161e_bool=1. finite_card_pname=1. pls=1. fdisj=1. nat_neg=1. ord_le1375614389l_bool=1. ord_le1454342156l_bool=1. ord_le1848167016l_bool=1. ord_le675606854l_bool=1. ord_less_eq_bool=1. finite1306199131a_bool=1. finite1340463720e_bool=1. finite1876863882t_bool=1. finite346522414t_bool=1. bot_bot_bool=1. fequal_a=1. fequal_int=1. fequal_nat=1. fFalse=1. bot_bot_nat=1. fNot=1. u=1. insert1325755072e_bool=1. insert_fun_a_bool=1. insert_fun_int_bool=1. insert_fun_nat_bool=1. bool=1. fimplies=1. mgt_call=1. fequal_fun_a_bool=1. fequal_fun_int_bool=1. fequal_fun_nat_bool=1. nat_tsub=1. fTrue=1. fequal533582459e_bool=1. fequal_pname=1. g=1. member799430823e_bool=1. member_fun_a_bool=1. member_fun_int_bool=1. member_fun_nat_bool=1. pname=1. x_a=1. cOMBI_nat=1. na=1. ord_le1912455174t_bool=1. ord_le382113706t_bool=1. pn=1. the_elem_a=1. the_elem_int=1. the_elem_nat=1. finite1381704300l_bool=1. finite1701474069l_bool=1. finite2095298929l_bool=1. finite786885583l_bool=1. the_a=1. the_int=1. the_nat=1. hAPP_nat_nat=1. hAPP_nat_bool=1. hAPP_n1699378549t_bool=1. hAPP_nat_fun_nat_nat=1. hAPP_int_bool=1. hAPP_fun_a_bool_bool=1. hAPP_f54304608l_bool=1. hAPP_f448129468l_bool=1. hAPP_f1664156314l_bool=1. hAPP_i1948725293t_bool=1. hAPP_int_fun_int_int=1. hAPP_int_int=1. hAPP_f2050579477a_bool=1. hAPP_f800510211t_bool=1. hAPP_f1805168059t_bool=1. hAPP_f1631501043l_bool=1. hAPP_nat_int=1. hAPP_f284875647l_bool=1. hAPP_a1206381875a_bool=1. hAPP_f103356543l_bool=1. hAPP_f759274231e_bool=1. hAPP_i1529485324t_bool=1. hAPP_n1512601776t_bool=1. hAPP_n215258509l_bool=1. hAPP_i2112223885l_bool=1. hAPP_p338031245l_bool=1. hAPP_a85458249l_bool=1. hAPP_f434788991l_bool=1. hAPP_f1637334154l_bool=1. hAPP_f1935102916l_bool=1. hAPP_f215623910l_bool=1. hAPP_f621171935l_bool=1. hAPP_p905327722e_bool=1. hAPP_f22106695ol_nat=1. hAPP_f1223193598t_bool=1. hAPP_f1730770594t_bool=1. image_nat_int=1. hAPP_f1791771145a_bool=1. image_pname_a=1. hAPP_fun_a_bool_nat=1. hAPP_f1388330588e_bool=1. hAPP_f957591787ol_nat=1. hAPP_f921600141ol_nat=1. hAPP_a_bool=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. hAPP_f1434722111l_bool=1. hAPP_f1772781669l_bool=1. hAPP_f317860125l_bool=1. hAPP_f510955609l_bool=1. cOMBB_1652995168ol_int=1. cOMBS_int_bool_bool=1. cOMBB_1015721476ol_nat=1. cOMBS_nat_bool_bool=1. hAPP_fun_a_bool_a=1. hAPP_a_fun_a_bool=1. hAPP_f1594865479ol_int=1. hAPP_f1297739591_pname=1. hAPP_pname_a=1. cOMBS_a_bool_bool=1. hAPP_f2009550088ol_nat=1. hAPP_f521865025ol_nat=1. hAPP_f55526627ol_nat=1. hAPP_f696928925ol_nat=1. cOMBB_1972296269bool_a=1. hAPP_pname_bool=1. cOMBS_568398431l_bool=1. cOMBB_675860798_pname=1. finite_folding_one_a=1. finite1282449217_pname=1. image_1655916159e_bool=1. image_637364955e_bool=1. image_a_pname=1. image_int_a=1. image_int_fun_a_bool=1. image_nat_fun_a_bool=1. finite1626084323ne_int=1. finite988810631ne_nat=1. hAPP_f2117159681l_bool=1. hAPP_f559147733l_bool=1. hAPP_n1082236369t_bool=1. image_112932426a_bool=1. image_1283814551_pname=1. image_1551609309ol_nat=1. image_1556378401t_bool=1. image_1854862208_pname=1. image_26036933t_bool=1. image_275383677t_bool=1. image_41399353ol_int=1. image_47868345e_bool=1. image_876012084bool_a=1. image_892525857t_bool=1. image_a_a=1. image_a_int=1. image_a_nat=1. image_fun_a_bool_a=1. image_fun_a_bool_int=1. image_fun_a_bool_nat=1. image_pname_pname=1. cOMBS_1035972772l_bool=1. cOMBS_350070575l_bool=1. hAPP_a_a=1. hAPP_f1246832597l_bool=1. hAPP_f1320879424l_bool=1. hAPP_f1531278575l_bool=1. hAPP_f1948010709l_bool=1. hAPP_f587666462l_bool=1. hAPP_f633452666l_bool=1. hAPP_n1025906991e_bool=1. hAPP_nat_fun_a_bool=1. hAPP_p61793385e_bool=1. hAPP_pname_pname=1. image_1133522419ol_int=1. image_1431733819ol_nat=1. image_1512837979t_bool=1. image_1921560913_pname=1. image_2069007511ol_int=1. image_2129980159t_bool=1. image_496248727ol_nat=1. image_62782965_pname=1. image_fun_int_bool_a=1. image_fun_nat_bool_a=1. image_int_pname=1. image_nat_a=1. image_nat_pname=1. cOMBB_1974511970t_bool=1. cOMBB_2095475776e_bool=1. cOMBB_338059395a_bool=1. cOMBB_444170502t_bool=1. cOMBS_1187019125l_bool=1. cOMBS_1912792529l_bool=1. fun=1. hAPP_a_fun_a_a=1. hAPP_p1170154830_pname=1. image_819518260e_bool=1. image_a_fun_a_bool=1. image_pname_int=1. image_pname_nat=1. hAPP_int_fun_a_bool=1. image_a_fun_int_bool=1. image_a_fun_nat_bool=1. cOMBB_bool_bool_a=1. hAPP_i418383825t_bool=1. nat_case_bool=1. cOMBB_1146692694ol_nat=1. cOMBB_1273333599bool_a=1. cOMBB_647938656_pname=1. cOMBB_bool_bool_int=1. cOMBB_bool_bool_nat=1. finite1432773856em_int=1. finite1819937229idem_a=1. finite795500164em_nat=1. finite89670078_pname=1. hAPP_a93125764e_bool=1. hAPP_f1951378235l_bool=1. hAPP_f285962445l_bool=1. hAPP_f556039215l_bool=1. hAPP_f628503027l_bool=1. hAPP_i1587699435l_bool=1. hAPP_i7355787e_bool=1. hAPP_i888906320l_bool=1. hAPP_int_a=1. hAPP_n1414589940l_bool=1. hAPP_n850744903l_bool=1. hAPP_p1534023578a_bool=1. cOMBB_1123824708ol_nat=1. cOMBB_1418110531ol_int=1. cOMBB_1628441366ol_nat=1. cOMBB_1761098400ol_int=1. cOMBB_1823939024ol_nat=1. cOMBB_1897541054_pname=1. cOMBB_2026977092ol_nat=1. cOMBB_2117322052ol_nat=1. cOMBB_313729068ol_int=1. cOMBB_375279840ol_int=1. cOMBB_516767136ol_int=1. cOMBB_607112096ol_int=1. cOMBB_800536526ol_nat=1. cOMBB_955900739ol_nat=1. cOMBB_int_bool_nat=1. hAPP_a_fun_bool_bool=1. hAPP_a_fun_int_bool=1. hAPP_f1038053735a_bool=1. hAPP_f1048215610t_bool=1. hAPP_f1066163005t_bool=1. hAPP_f1476298914l_bool=1. hAPP_f1570313510t_bool=1. hAPP_f1593524852l_bool=1. hAPP_f1721100032l_bool=1. hAPP_f1748468828l_bool=1. hAPP_f1812805200t_bool=1. hAPP_f183368031t_bool=1. hAPP_f198738859l_bool=1. hAPP_f274826591t_bool=1. hAPP_f282463732t_bool=1. hAPP_f292226953l_bool=1. hAPP_f389811538l_bool=1. hAPP_f449020825t_bool=1. hAPP_f937997336l_bool=1. hAPP_i1718399025l_bool=1. hAPP_i68813070l_bool=1. hAPP_n1006566506l_bool=1. hAPP_n609083369l_bool=1. hAPP_p393069232l_bool=1. nat_case_nat=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f65=1. f68=1. f69=1. f70=1. f75=1. f76=1. f77=1. f78=1. f81=1. f82=1. f83=1. f85=1. f86=1. f109=1. f110=1. f111=1. f112=1. f113=1. f114=1. f115=1. f116=1. f117=1. f118=1. f119=1. f120=1. f121=1. f122=1. f123=1. f124=1. f133=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f156=1. f157=1. f158=1. f159=1. f160=1. f161=1. f162=1. f164=1. f165=1. f169=1. f170=1. f173=1. f174=1. f176=1. f179=1. f180=1. f181=1. f184=1. f186=1. f191=1. f204=1. f209=1. number_number_of_int=1. number_number_of_nat=1. bit1=1. collect_nat=1. collect_int=1. collect_a=1. cOMBC_nat_nat_bool=1. collect_pname=1. cOMBC_226598744l_bool=1. abs_abs_int=1. collec1974731493e_bool=1. collect_fun_a_bool=1. collect_fun_int_bool=1. collect_fun_nat_bool=1. cOMBC_94739984l_bool=1. p=1. cOMBC_a_a_bool=1. cOMBC_int_int_bool=1. cOMBC_1058051404l_bool=1. cOMBC_1355376034l_bool=1. mgt=1. succ=1. wt=1. cOMBK_a_pname=1. cOMBK_int_nat=1. if_nat=1. cOMBC_1149511130e_bool=1. cOMBK_bool_a=1. body=1. cOMBC_1284144636l_bool=1. cOMBC_1683390479t_bool=1. cOMBC_1693257480l_bool=1. cOMBC_1732670874l_bool=1. cOMBC_1753430397l_bool=1. cOMBC_178881787t_bool=1. cOMBC_1848398772l_bool=1. cOMBC_1928494297l_bool=1. cOMBC_316919022l_bool=1. cOMBC_331553030l_bool=1. cOMBC_348868698l_bool=1. cOMBC_386238098l_bool=1. cOMBC_394484100a_bool=1. cOMBC_595898202l_bool=1. cOMBC_605892544l_bool=1. cOMBC_620423604l_bool=1. cOMBC_7971162l_bool=1. cOMBC_int_a_bool=1. cOMBC_nat_int_bool=1. cOMBC_pname_a_bool=1. cOMBK_bool_int=1. cOMBK_bool_nat=1. the_com=1. collec1015864663l_bool=1. collec1409689523l_bool=1. collec1613912337l_bool=1. collec707592106l_bool=1. undefi1699038445l_bool=1. undefi17486888e_bool=1. undefi64961550l_bool=1. undefined_a=1. undefined_fun_a_bool=1. undefined_pname=1. f84=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. f100=1. f125=1. f126=1. f127=1. f128=1. f129=1. f130=1. f131=1. f132=1. f134=1. f135=1. f136=1. f137=1. f138=1. f139=1. f140=1. f141=1. f163=1. f175=1. f182=1. f183=1. f185=1. f205=1. f206=1. f207=1. f208=1. f210=1. f211=1. f212=1. f213=1. f214=1. fCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------