TSTP Solution File: SWW473+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW473+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:09 EDT 2022
% Result : Timeout 300.03s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW473+2 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 02:41:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.45/1.72 ============================== Prover9 ===============================
% 1.45/1.72 Prover9 (32) version 2009-11A, November 2009.
% 1.45/1.72 Process 6947 was started by sandbox2 on n025.cluster.edu,
% 1.45/1.72 Mon Jun 6 02:41:04 2022
% 1.45/1.72 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6793_n025.cluster.edu".
% 1.45/1.72 ============================== end of head ===========================
% 1.45/1.72
% 1.45/1.72 ============================== INPUT =================================
% 1.45/1.72
% 1.45/1.72 % Reading from file /tmp/Prover9_6793_n025.cluster.edu
% 1.45/1.72
% 1.45/1.72 set(prolog_style_variables).
% 1.45/1.72 set(auto2).
% 1.45/1.72 % set(auto2) -> set(auto).
% 1.45/1.72 % set(auto) -> set(auto_inference).
% 1.45/1.72 % set(auto) -> set(auto_setup).
% 1.45/1.72 % set(auto_setup) -> set(predicate_elim).
% 1.45/1.72 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.45/1.72 % set(auto) -> set(auto_limits).
% 1.45/1.72 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.45/1.72 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.45/1.72 % set(auto) -> set(auto_denials).
% 1.45/1.72 % set(auto) -> set(auto_process).
% 1.45/1.72 % set(auto2) -> assign(new_constants, 1).
% 1.45/1.72 % set(auto2) -> assign(fold_denial_max, 3).
% 1.45/1.72 % set(auto2) -> assign(max_weight, "200.000").
% 1.45/1.72 % set(auto2) -> assign(max_hours, 1).
% 1.45/1.72 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.45/1.72 % set(auto2) -> assign(max_seconds, 0).
% 1.45/1.72 % set(auto2) -> assign(max_minutes, 5).
% 1.45/1.72 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.45/1.72 % set(auto2) -> set(sort_initial_sos).
% 1.45/1.72 % set(auto2) -> assign(sos_limit, -1).
% 1.45/1.72 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.45/1.72 % set(auto2) -> assign(max_megs, 400).
% 1.45/1.72 % set(auto2) -> assign(stats, some).
% 1.45/1.72 % set(auto2) -> clear(echo_input).
% 1.45/1.72 % set(auto2) -> set(quiet).
% 1.45/1.72 % set(auto2) -> clear(print_initial_clauses).
% 1.45/1.72 % set(auto2) -> clear(print_given).
% 1.45/1.72 assign(lrs_ticks,-1).
% 1.45/1.72 assign(sos_limit,10000).
% 1.45/1.72 assign(order,kbo).
% 1.45/1.72 set(lex_order_vars).
% 1.45/1.72 clear(print_given).
% 1.45/1.72
% 1.45/1.72 % formulas(sos). % not echoed (917 formulas)
% 1.45/1.72
% 1.45/1.72 ============================== end of input ==========================
% 1.45/1.72
% 1.45/1.72 % From the command line: assign(max_seconds, 300).
% 1.45/1.72
% 1.45/1.72 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.45/1.72
% 1.45/1.72 % Formulas that are not ordinary clauses:
% 1.45/1.72 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].
% 1.45/1.72 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].
% 1.45/1.72 3 (all B_1_1 all B_2_1 (is_fun949378684l_bool(B_2_1) -> is_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 4 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 5 (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].
% 1.45/1.72 6 (all B_1_1 (is_bool(B_1_1) -> is_fun_pname_bool(cOMBK_bool_pname(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 7 (all B_1_1 (is_bool(B_1_1) -> is_fun949378684l_bool(cOMBK_324466864a_bool(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 8 (all B_1_1 (is_bool(B_1_1) -> is_fun1661590463l_bool(cOMBK_1857069011e_bool(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 9 (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].
% 1.45/1.72 10 (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].
% 1.45/1.72 11 (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].
% 1.45/1.72 12 (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].
% 1.45/1.72 13 (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].
% 1.45/1.72 14 (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].
% 1.45/1.72 15 (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].
% 1.45/1.72 16 (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].
% 1.45/1.72 17 (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].
% 1.45/1.72 18 (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].
% 1.45/1.72 19 (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].
% 1.45/1.72 20 (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].
% 1.45/1.72 21 (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].
% 1.45/1.72 22 (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].
% 1.45/1.72 23 (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].
% 1.45/1.72 24 (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].
% 1.45/1.72 25 (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].
% 1.45/1.72 26 (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].
% 1.45/1.72 27 (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].
% 1.45/1.72 28 (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].
% 1.45/1.72 29 (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].
% 1.45/1.72 30 (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].
% 1.45/1.72 31 (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].
% 1.45/1.72 32 (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].
% 1.45/1.72 33 (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].
% 1.45/1.72 34 (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].
% 1.45/1.72 35 (all B_1_1 all B_2_1 (is_a(B_1_1) & is_fun_a_bool(B_2_1) -> is_fun_a_bool(insert_a(B_1_1,B_2_1)))) # label(gsy_c_Set_Oinsert_000t__a) # label(hypothesis) # label(non_clause). [assumption].
% 1.45/1.72 36 (all B_1_1 all B_2_1 (is_pname(B_1_1) & is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(insert_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oinsert_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 37 (all B_1_1 all B_2_1 (is_fun_a_bool(B_1_1) & is_fun949378684l_bool(B_2_1) -> is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 38 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_1_1) & is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 39 (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].
% 1.45/1.72 40 (all B_1_1 all B_2_1 (is_a(B_2_1) -> is_pname(hAPP_a_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000t__a_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 41 (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].
% 1.45/1.72 42 (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].
% 1.45/1.72 43 (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].
% 1.45/1.72 44 (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].
% 1.45/1.72 45 (all B_1_1 all B_2_1 (is_a(B_2_1) -> is_fun1661590463l_bool(hAPP_a217006258l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 46 (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].
% 1.45/1.72 47 (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].
% 1.45/1.72 48 (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].
% 1.45/1.72 49 (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].
% 1.45/1.72 50 (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].
% 1.45/1.72 51 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun949378684l_bool(hAPP_p1824510254l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 52 (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].
% 1.45/1.72 53 (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].
% 1.45/1.72 54 (all B_1_1 all B_2_1 is_a(hAPP_nat_a(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 55 (all B_1_1 all B_2_1 is_pname(hAPP_nat_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 56 (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].
% 1.45/1.72 57 (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].
% 1.45/1.72 58 (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].
% 1.45/1.72 59 (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].
% 1.45/1.72 60 (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].
% 1.45/1.72 61 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_pname(hAPP_f1128469712_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 62 (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].
% 1.45/1.72 63 (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(axiom) # label(non_clause). [assumption].
% 1.45/1.72 64 (all B_1_1 all B_2_1 (is_fun_a_bool(B_2_1) -> is_fun_pname_bool(hAPP_f1794073134e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opname_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.72 65 (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].
% 1.45/1.72 66 (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].
% 1.45/1.73 67 (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].
% 1.45/1.73 68 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_a_bool(hAPP_f1051908748a_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 69 (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].
% 1.45/1.73 70 (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].
% 1.45/1.73 71 (all B_1_1 all B_2_1 is_pname(hAPP_f1291551745_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 72 (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].
% 1.45/1.73 73 (all B_1_1 all B_2_1 is_fun_a_bool(hAPP_f1549043526a_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 74 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f654413245e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 75 (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].
% 1.45/1.73 76 (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].
% 1.45/1.73 77 (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].
% 1.45/1.73 78 (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].
% 1.45/1.73 79 (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].
% 1.45/1.73 80 (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].
% 1.45/1.73 81 (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].
% 1.45/1.73 82 (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].
% 1.45/1.73 83 (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].
% 1.45/1.73 84 (all B_1_1 is_a(mgt(B_1_1))) # label(gsy_v_mgt) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 85 (all B_1_1 is_bool(wt(B_1_1))) # label(gsy_v_wt) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 86 (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].
% 1.45/1.73 87 (all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A_1)))))) # label(fact_1_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 88 (all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A_1)))))) # label(fact_2_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 89 (all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A_1)))))) # label(fact_3_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 90 (all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A_1)))))) # label(fact_4_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 91 (all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A_1)))))) # label(fact_5_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 92 (all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A_1)))))) # label(fact_6_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 93 (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_7_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 94 (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_8_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 95 (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_9_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 96 (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_10_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 97 (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_11_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 98 (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_12_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 99 (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_13_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 100 (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_14_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 101 (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_15_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 102 (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_16_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 103 (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_17_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 104 (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_18_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 105 (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_19_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 106 (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_20_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 107 (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_21_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 108 (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_22_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 109 (all A_3 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1))))) # label(fact_23_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 110 (all A_3 all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1))))) # label(fact_24_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 111 (all A_3 all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1))))) # label(fact_25_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 112 (all A_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1))))) # label(fact_26_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 113 (all A_3 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1))))) # label(fact_27_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 114 (all A_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1))))) # label(fact_28_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 115 (all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))))) # label(fact_29_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 116 (all F all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))))) # label(fact_30_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 117 (all F all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> 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_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))))) # label(fact_31_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 118 (all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))))) # label(fact_32_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 119 (all F all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> 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_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))))) # label(fact_33_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 120 (all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))))) # label(fact_34_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 121 (all F all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))))) # label(fact_35_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 122 (all F all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))))) # label(fact_36_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 123 (all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))))) # label(fact_37_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 124 (all F all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))))) # label(fact_38_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 125 (all F all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))))) # label(fact_39_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 126 (all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A_1))),hAPP_f22106695ol_nat(finite_card_nat,A_1))))) # label(fact_40_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 127 (all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))))) # label(fact_41_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 128 (all A_1 all B_6 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,B_6)))))) # label(fact_42_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 129 (all A_1 all B_6 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,B_6)))))) # label(fact_43_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 130 (all A_1 all B_6 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6)))))) # label(fact_44_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 131 (all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,B_6)))))) # label(fact_45_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 132 (all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,B_6)))))) # label(fact_46_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 133 (all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,B_6)))))) # label(fact_47_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 134 (all A_1 all B_6 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B_6)),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))) -> A_1 = B_6)))) # label(fact_48_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 135 (all A_1 all B_6 (is_fun1661590463l_bool(A_1) & is_fun1661590463l_bool(B_6) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B_6)),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))) -> A_1 = B_6))))) # label(fact_49_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 136 (all A_1 all B_6 (is_fun949378684l_bool(A_1) & is_fun949378684l_bool(B_6) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))) -> A_1 = B_6))))) # label(fact_50_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 137 (all A_1 all B_6 (is_fun_pname_bool(A_1) & is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B_6)),hAPP_f921600141ol_nat(finite_card_pname,A_1))) -> A_1 = B_6))))) # label(fact_51_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.73 138 (all A_1 all B_6 (is_fun_a_bool(A_1) & is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B_6)),hAPP_fun_a_bool_nat(finite_card_a,A_1))) -> A_1 = B_6))))) # label(fact_52_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 139 (all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B_6)),hAPP_f22106695ol_nat(finite_card_nat,A_1))) -> A_1 = B_6)))) # label(fact_53_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 140 (all X_3 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)))))) # label(fact_54_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 141 (all X_3 all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)))))) # label(fact_55_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 142 (all X_3 all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)))))) # label(fact_56_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 143 (all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)))))) # label(fact_57_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 144 (all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)))))) # label(fact_58_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 145 (all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)))))) # label(fact_59_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 146 (all X_3 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) -> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_f696928925ol_nat(finite346522414t_bool,A_1)) & (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) -> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1))))) # label(fact_60_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 147 (all X_3 all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)) & (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))))) # label(fact_61_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 148 (all X_3 all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)) & (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))))) # label(fact_62_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 149 (all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_f22106695ol_nat(finite_card_nat,A_1)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1))))) # label(fact_63_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 150 (all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_f921600141ol_nat(finite_card_pname,A_1)) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1))))) # label(fact_64_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 151 (all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_fun_a_bool_nat(finite_card_a,A_1)) & (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1))))) # label(fact_65_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 152 (all X_3 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) -> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1))))) # label(fact_66_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 153 (all X_3 all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))))) # label(fact_67_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 154 (all X_3 all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))))) # label(fact_68_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 155 (all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1))))) # label(fact_69_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 156 (all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1))))) # label(fact_70_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 157 (all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1))))) # label(fact_71_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 158 (all Q_1 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_1))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_1)))))) # label(fact_72_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 159 (all Q_1 all Pa (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1))) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_1)))))) # label(fact_73_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 160 (all Q_1 all Pa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_1)))))) # label(fact_74_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 161 (all Q_1 all Pa (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1))) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_1)))))) # label(fact_75_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 162 (all Q_1 all Pa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_1)))))) # label(fact_76_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 163 (all Q_1 all Pa (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_1)))))) # label(fact_77_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 164 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M),N)))) # label(fact_78_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 165 (all K_2 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K_2))))) # label(fact_79_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 166 (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_80_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 167 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_81_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 168 (all Nat_3 all Nat_2 (hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_2) <-> Nat_3 = Nat_2)) # label(fact_82_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 169 (all N hAPP_nat_nat(suc,N) != N) # label(fact_83_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 170 (all N N != hAPP_nat_nat(suc,N)) # label(fact_84_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 171 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> M = N))) # label(fact_85_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 172 (all K all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K))))) # label(fact_86_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 173 (all M all N (M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_87_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 174 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)))) # label(fact_88_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 175 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N))) # label(fact_89_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 176 (all I all J_2 all K hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),K)),J_2)) # label(fact_90_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 177 (all Pa all Q_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1)))) <-> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1))))) # label(fact_91_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 178 (all Pa all Q_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1)))) <-> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1))))) # label(fact_92_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 179 (all Pa all Q_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1)))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))))) # label(fact_93_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 180 (all Pa all Q_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1)))) <-> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1))))) # label(fact_94_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 181 (all Pa all Q_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))))) # label(fact_95_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 182 (all Pa all Q_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))))) # label(fact_96_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 183 (all A_3 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1))) <-> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)))) # label(fact_97_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 184 (all A_3 all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)))) # label(fact_98_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 185 (all A_3 all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1))) <-> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)))) # label(fact_99_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 186 (all A_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)))) # label(fact_100_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 187 (all A_3 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)))) # label(fact_101_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 188 (all A_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1))) <-> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)))) # label(fact_102_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 189 (all A_1 all B_6 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))))) # label(fact_103_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 190 (all A_1 all B_6 (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))))) # label(fact_104_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 191 (all A_1 all B_6 (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))))) # label(fact_105_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 192 (all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))))) # label(fact_106_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 193 (all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))))) # label(fact_107_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 194 (all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))))) # label(fact_108_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 195 (all A_1 all B_6 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))))) # label(fact_109_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 196 (all A_1 all B_6 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))))) # label(fact_110_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 197 (all A_1 all B_6 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))))) # label(fact_111_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 198 (all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))))) # label(fact_112_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 199 (all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))))) # label(fact_113_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 200 (all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))))) # label(fact_114_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 201 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_115_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 202 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> M = hAPP_nat_nat(suc,N)))) # label(fact_116_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 203 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_117_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 204 (all Na all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)))) # label(fact_118_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 205 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) | M_1 = hAPP_nat_nat(suc,Na))) # label(fact_119_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 206 (all M_1 all Na (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)))) # label(fact_120_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 207 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N))) # label(fact_121_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 208 (all M all N all K hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N)),hAPP_nat_nat(suc,K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),K)) # label(fact_122_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 209 (all M all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(M),N)) # label(fact_123_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 210 (all Na all K_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)))))) # label(fact_124_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 211 (all N all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K)),hAPP_nat_nat(minus_minus_nat(N),K)) = hAPP_nat_nat(minus_minus_nat(M),N)))) # label(fact_125_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 212 (all Na all K_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) -> (hAPP_nat_nat(minus_minus_nat(M_1),K_2) = hAPP_nat_nat(minus_minus_nat(Na),K_2) <-> M_1 = Na)))) # label(fact_126_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 213 (all I all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) -> hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(minus_minus_nat(N),I)) = I)) # label(fact_127_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 214 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N),L))))) # label(fact_128_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 215 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))))) # label(fact_129_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 216 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M))) # label(fact_130_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 217 (all B_6 all F all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))))) # label(fact_131_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 218 (all B_6 all F all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))))) # label(fact_132_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 219 (all B_6 all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))))) # label(fact_133_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 220 (all B_6 all F all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))))) # label(fact_134_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 221 (all B_6 all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1))) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))))) # label(fact_135_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 222 (all B_6 all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))))) # label(fact_136_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 223 (all B_6 all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1))) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))))) # label(fact_137_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 224 (all B_6 all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))))) # label(fact_138_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 225 (all B_6 all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))))) # label(fact_139_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 226 (all B_6 all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))))) # label(fact_140_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 227 (all B_6 all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1))) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))))) # label(fact_141_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 228 (all B_6 all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))))) # label(fact_142_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 229 (all B_6 all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1))) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))))) # label(fact_143_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 230 (all B_6 all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))))) # label(fact_144_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 231 (all B_6 all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))))) # label(fact_145_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 232 (all B_6 all F all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))))) # label(fact_146_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 233 (all B_6 all F all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))))) # label(fact_147_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 234 (all B_6 all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))))) # label(fact_148_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 235 (all B_6 all F all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))))) # label(fact_149_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 236 (all B_6 all F all A_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))))) # label(fact_150_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 237 (all B_6 all F all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))))) # label(fact_151_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 238 (all B_6 all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))))) # label(fact_152_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 239 (all B_6 all F all A_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))))) # label(fact_153_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 240 (all B_6 all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))))) # label(fact_154_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 241 (all F all A_1 all B_6 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7)) & B_6 = image_fun_nat_bool_a(F,C_7))))))) # label(fact_155_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 242 (all F all A_1 all B_6 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1))) -> (exists C_7 (is_fun1661590463l_bool(C_7) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7)) & B_6 = image_876012084bool_a(F,C_7))))))) # label(fact_156_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 243 (all F all A_1 all B_6 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1))) -> (exists C_7 (is_fun949378684l_bool(C_7) & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1)) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7)) & B_6 = image_fun_a_bool_a(F,C_7))))))) # label(fact_157_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 244 (all F all A_1 all B_6 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1))) -> (exists C_7 (is_fun_a_bool(C_7) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) & B_6 = image_a_a(F,C_7))))))) # label(fact_158_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 245 (all F all A_1 all B_6 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_a_fun_nat_bool(F,A_1))) -> (exists C_7 (is_fun_a_bool(C_7) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) & B_6 = image_a_fun_nat_bool(F,C_7)))))) # label(fact_159_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 246 (all F all A_1 all B_6 (is_fun1661590463l_bool(B_6) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_819518260e_bool(F,A_1))) -> (exists C_7 (is_fun_a_bool(C_7) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) & B_6 = image_819518260e_bool(F,C_7))))))) # label(fact_160_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 247 (all F all A_1 all B_6 (is_fun949378684l_bool(B_6) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_a_fun_a_bool(F,A_1))) -> (exists C_7 (is_fun_a_bool(C_7) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) & B_6 = image_a_fun_a_bool(F,C_7))))))) # label(fact_161_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 248 (all F all A_1 all B_6 (is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1))) -> (exists C_7 (is_fun_a_bool(C_7) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) & B_6 = image_a_pname(F,C_7))))))) # label(fact_162_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 249 (all F all A_1 all B_6 (is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7)) & B_6 = image_1921560913_pname(F,C_7))))))) # label(fact_163_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 250 (all F all A_1 all B_6 (is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1))) -> (exists C_7 (is_fun1661590463l_bool(C_7) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7)) & B_6 = image_1283814551_pname(F,C_7))))))) # label(fact_164_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 251 (all F all A_1 all B_6 (is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1))) -> (exists C_7 (is_fun949378684l_bool(C_7) & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1)) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7)) & B_6 = image_1854862208_pname(F,C_7))))))) # label(fact_165_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 252 (all F all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1))) -> (exists C_7 (is_fun_a_bool(C_7) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1)) & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7)) & B_6 = image_a_nat(F,C_7)))))) # label(fact_166_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 253 (all F all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7)) & B_6 = image_496248727ol_nat(F,C_7)))))) # label(fact_167_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 254 (all F all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1))) -> (exists C_7 (is_fun1661590463l_bool(C_7) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7)) & B_6 = image_1551609309ol_nat(F,C_7)))))) # label(fact_168_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 255 (all F all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1))) -> (exists C_7 (is_fun949378684l_bool(C_7) & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1)) & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7)) & B_6 = image_fun_a_bool_nat(F,C_7)))))) # label(fact_169_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 256 (all F all A_1 all B_6 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1))) -> (exists C_7 (is_fun_pname_bool(C_7) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) & B_6 = image_2129980159t_bool(F,C_7)))))) # label(fact_170_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 257 (all F all A_1 all B_6 (is_fun1661590463l_bool(B_6) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1))) -> (exists C_7 (is_fun_pname_bool(C_7) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) & B_6 = image_47868345e_bool(F,C_7))))))) # label(fact_171_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 258 (all F all A_1 all B_6 (is_fun949378684l_bool(B_6) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1))) -> (exists C_7 (is_fun_pname_bool(C_7) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) & B_6 = image_112932426a_bool(F,C_7))))))) # label(fact_172_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 259 (all F all A_1 all B_6 (is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1))) -> (exists C_7 (is_fun_pname_bool(C_7) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) & B_6 = image_pname_pname(F,C_7))))))) # label(fact_173_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 260 (all F all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1))) -> (exists C_7 (is_fun_pname_bool(C_7) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) & B_6 = image_pname_nat(F,C_7)))))) # label(fact_174_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 261 (all F all A_1 all B_6 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) & B_6 = image_nat_a(F,C_7))))))) # label(fact_175_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 262 (all F all A_1 all B_6 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) & B_6 = image_26036933t_bool(F,C_7)))))) # label(fact_176_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 263 (all F all A_1 all B_6 (is_fun1661590463l_bool(B_6) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) & B_6 = image_1655916159e_bool(F,C_7))))))) # label(fact_177_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 264 (all F all A_1 all B_6 (is_fun949378684l_bool(B_6) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) & B_6 = image_nat_fun_a_bool(F,C_7))))))) # label(fact_178_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 265 (all F all A_1 all B_6 (is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) & B_6 = image_nat_pname(F,C_7))))))) # label(fact_179_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 266 (all F all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1))) -> (exists C_7 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7)) & B_6 = image_nat_nat(F,C_7)))))) # label(fact_180_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 267 (all F all A_1 all B_6 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1))) -> (exists C_7 (is_fun_pname_bool(C_7) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7)) & B_6 = image_pname_a(F,C_7))))))) # label(fact_181_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 268 (all Na all N_3 all F ((all N_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,N_2)),hAPP_nat_bool(F,hAPP_nat_nat(suc,N_2))))) -> (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_182_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 269 (all Na all N_3 all F ((all N_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_2)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_2))))) -> (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_183_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 270 (all Na all N_3 all F ((all N_2 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_2)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_2))))) -> (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_184_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 271 (all Na all N_3 all F ((all N_2 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_2)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_2))))) -> (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_185_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 272 (all Na all N_3 all F ((all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2))))) -> (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_186_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 273 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) & -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_1)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,F)),hAPP_nat_pname(F,X_1))))))))))) # label(fact_187_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 274 (all F all A_1 (-hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(F,A_1))) -> (exists X_1 (is_a(X_1) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) & -hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,F)),hAPP_a_pname(F,X_1))))))))))) # label(fact_188_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 275 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(F,A_1))) -> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & -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_1)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,F)),hAPP_pname_pname(F,X_1))))))))))) # label(fact_189_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 276 (all F all A_1 (-hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) & -hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,F)),hAPP_f1291551745_pname(F,X_1))))))))))) # label(fact_190_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 277 (all F all A_1 (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(F,A_1))) -> (exists X_1 (is_fun_pname_bool(X_1) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) & -hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,F)),hAPP_f1297739591_pname(F,X_1))))))))))) # label(fact_191_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 278 (all F all A_1 (-hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(F,A_1))) -> (exists X_1 (is_fun_a_bool(X_1) & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1)) & -hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,F)),hAPP_f1128469712_pname(F,X_1))))))))))) # label(fact_192_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 279 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) & -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_1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,F)),hAPP_nat_nat(F,X_1))))))))))) # label(fact_193_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 280 (all F all A_1 (-hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(F,A_1))) -> (exists X_1 (is_a(X_1) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) & -hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,F)),hAPP_a_nat(F,X_1))))))))))) # label(fact_194_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 281 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(F,A_1))) -> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & -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_1)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,F)),hAPP_pname_nat(F,X_1))))))))))) # label(fact_195_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 282 (all F all A_1 (-hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) & -hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,F)),hAPP_f22106695ol_nat(F,X_1))))))))))) # label(fact_196_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 283 (all F all A_1 (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(F,A_1))) -> (exists X_1 (is_fun_pname_bool(X_1) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) & -hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,F)),hAPP_f921600141ol_nat(F,X_1))))))))))) # label(fact_197_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.73 284 (all F all A_1 (-hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(F,A_1))) -> (exists X_1 (is_fun_a_bool(X_1) & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1)) & -hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,F)),hAPP_fun_a_bool_nat(F,X_1))))))))))) # label(fact_198_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 285 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) & -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_1)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,F)),hAPP_nat_a(F,X_1))))))))))) # label(fact_199_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 286 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) & -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_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,F)),hAPP_n1699378549t_bool(F,X_1))))))))))) # label(fact_200_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 287 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) & -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_1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,F)),hAPP_n1025906991e_bool(F,X_1))))))))))) # label(fact_201_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 288 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(F,A_1))) -> (exists X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) & -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_1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,F)),hAPP_nat_fun_a_bool(F,X_1))))))))))) # label(fact_202_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 289 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(F,A_1))) -> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & -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_1)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,F)),hAPP_p1499970991t_bool(F,X_1))))))))))) # label(fact_203_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 290 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(F,A_1))) -> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & -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_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,F)),hAPP_p61793385e_bool(F,X_1))))))))))) # label(fact_204_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 291 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(F,A_1))) -> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & -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_1)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,F)),hAPP_p1534023578a_bool(F,X_1))))))))))) # label(fact_205_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 292 (all F all A_1 (-hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(F,A_1))) -> (exists X_1 (is_a(X_1) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) & -hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,F)),hAPP_a_a(F,X_1))))))))))) # label(fact_206_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 293 (all F all A_1 (-hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(F,A_1))) -> (exists X_1 (is_a(X_1) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) & -hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,F)),hAPP_a_fun_nat_bool(F,X_1))))))))))) # label(fact_207_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 294 (all F all A_1 (-hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(F,A_1))) -> (exists X_1 (is_a(X_1) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) & -hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,F)),hAPP_a93125764e_bool(F,X_1))))))))))) # label(fact_208_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 295 (all F all A_1 (-hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(F,A_1))) -> (exists X_1 (is_a(X_1) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) & -hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,F)),hAPP_a_fun_a_bool(F,X_1))))))))))) # label(fact_209_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 296 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A_1))) -> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & -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_1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1))))))))))) # label(fact_210_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 297 (all A_1 all B_1 all F all X_3 (B_1 = hAPP_pname_nat(F,X_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1)))))) # label(fact_211_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 298 (all A_1 all B_1 all F all X_3 (B_1 = hAPP_a_nat(F,X_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1)))))) # label(fact_212_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 299 (all A_1 all B_1 all F all X_3 (B_1 = hAPP_nat_pname(F,X_3) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1)))))) # label(fact_213_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 300 (all A_1 all B_1 all F all X_3 (B_1 = hAPP_nat_a(F,X_3) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1)))))) # label(fact_214_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 301 (all A_1 all B_1 all F all X_3 (B_1 = hAPP_pname_a(F,X_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))))) # label(fact_215_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 302 (all A_1 all B_6 (is_fun_pname_bool(A_1) & is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)) -> A_1 = B_6)))) # label(fact_216_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 303 (all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)) -> A_1 = B_6))) # label(fact_217_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 304 (all A_1 all B_6 (is_fun_a_bool(A_1) & is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)) -> A_1 = B_6)))) # label(fact_218_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 305 (all C_1 all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B_6))))) # label(fact_219_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 306 (all C_1 all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B_6))))) # label(fact_220_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 307 (all C_1 all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B_6))))) # label(fact_221_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 308 (all B_1 all A_3 all B_6 ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6)) -> A_3 = B_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6))))) # label(fact_222_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 309 (all B_1 all A_3 all B_6 ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6)) -> A_3 = B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6))))) # label(fact_223_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 310 (all B_1 all A_3 all B_6 ((-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6)) -> A_3 = B_1) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6))))) # label(fact_224_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 311 (all A_3 all B_1 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1))) -> (A_3 != B_1 -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1))))) # label(fact_225_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 312 (all A_3 all B_1 all A_1 (is_pname(A_3) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1))) -> (A_3 != B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)))))) # label(fact_226_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 313 (all A_3 all B_1 all A_1 (is_a(A_3) & is_a(B_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1))) -> (A_3 != B_1 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)))))) # label(fact_227_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 314 (all I_1 all Pa all K_2 (hBOOL(hAPP_nat_bool(Pa,K_2)) -> ((all N_2 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))) -> hBOOL(hAPP_nat_bool(Pa,N_2)))) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K_2),I_1)))))) # label(fact_228_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 315 (all N all M_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3)) -> (exists M_2 M_3 = hAPP_nat_nat(suc,M_2)))) # label(fact_229_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 316 (all A_3 all B_6 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(A_3,B_6)))) # label(fact_230_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 317 (all A_3 all B_6 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(A_3,B_6)))) # label(fact_231_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 318 (all A_3 all B_6 hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(A_3,B_6)))) # label(fact_232_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 319 (all A_3 all B_6 insert_fun_nat_bool(A_3,B_6) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B_6)))) # label(fact_233_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 320 (all A_3 all B_6 insert1325755072e_bool(A_3,B_6) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B_6)))) # label(fact_234_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 321 (all A_3 all B_6 insert_fun_a_bool(A_3,B_6) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B_6)))) # label(fact_235_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 322 (all A_3 all B_6 insert_nat(A_3,B_6) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_6)))) # label(fact_236_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 323 (all A_3 all B_6 insert_pname(A_3,B_6) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B_6)))) # label(fact_237_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 324 (all A_3 all B_6 insert_a(A_3,B_6) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B_6)))) # label(fact_238_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 325 (all A_3 all Pa insert_pname(A_3,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3))),Pa))) # label(fact_239_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 326 (all A_3 all Pa insert_fun_nat_bool(A_3,collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3))),Pa))) # label(fact_240_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 327 (all A_3 all Pa insert1325755072e_bool(A_3,collec1974731493e_bool(Pa)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3))),Pa))) # label(fact_241_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 328 (all A_3 all Pa insert_fun_a_bool(A_3,collect_fun_a_bool(Pa)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3))),Pa))) # label(fact_242_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 329 (all A_3 all Pa insert_nat(A_3,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_3))),Pa))) # label(fact_243_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 330 (all A_3 all Pa insert_a(A_3,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_3))),Pa))) # label(fact_244_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 331 (all X_3 all A_1 insert_pname(X_3,insert_pname(X_3,A_1)) = insert_pname(X_3,A_1)) # label(fact_245_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 332 (all X_3 all A_1 insert_nat(X_3,insert_nat(X_3,A_1)) = insert_nat(X_3,A_1)) # label(fact_246_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 333 (all X_3 all A_1 insert_a(X_3,insert_a(X_3,A_1)) = insert_a(X_3,A_1)) # label(fact_247_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 334 (all X_3 all Y_2 all A_1 insert_pname(X_3,insert_pname(Y_2,A_1)) = insert_pname(Y_2,insert_pname(X_3,A_1))) # label(fact_248_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 335 (all X_3 all Y_2 all A_1 insert_nat(X_3,insert_nat(Y_2,A_1)) = insert_nat(Y_2,insert_nat(X_3,A_1))) # label(fact_249_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 336 (all X_3 all Y_2 all A_1 insert_a(X_3,insert_a(Y_2,A_1)) = insert_a(Y_2,insert_a(X_3,A_1))) # label(fact_250_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 337 (all A_3 all B_1 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1))) <-> A_3 = B_1 | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)))) # label(fact_251_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 338 (all A_3 all B_1 all A_1 (is_pname(A_3) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1))) <-> A_3 = B_1 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))))) # label(fact_252_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 339 (all A_3 all B_1 all A_1 (is_a(A_3) & is_a(B_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1))) <-> A_3 = B_1 | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))))) # label(fact_253_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 340 (all Y_2 all A_1 all X_3 (is_pname(Y_2) & is_pname(X_3) -> (hBOOL(hAPP_pname_bool(insert_pname(Y_2,A_1),X_3)) <-> Y_2 = X_3 | hBOOL(hAPP_pname_bool(A_1,X_3))))) # label(fact_254_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 341 (all Y_2 all A_1 all X_3 (hBOOL(hAPP_nat_bool(insert_nat(Y_2,A_1),X_3)) <-> Y_2 = X_3 | hBOOL(hAPP_nat_bool(A_1,X_3)))) # label(fact_255_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 342 (all Y_2 all A_1 all X_3 (is_a(Y_2) & is_a(X_3) -> (hBOOL(hAPP_a_bool(insert_a(Y_2,A_1),X_3)) <-> Y_2 = X_3 | hBOOL(hAPP_a_bool(A_1,X_3))))) # label(fact_256_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 343 (all B_6 all X_3 all A_1 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) -> (insert_nat(X_3,A_1) = insert_nat(X_3,B_6) <-> A_1 = B_6)))) # label(fact_257_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 344 (all B_6 all X_3 all A_1 (is_fun_pname_bool(B_6) & is_fun_pname_bool(A_1) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) -> (insert_pname(X_3,A_1) = insert_pname(X_3,B_6) <-> A_1 = B_6))))) # label(fact_258_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 345 (all B_6 all X_3 all A_1 (is_fun_a_bool(B_6) & is_fun_a_bool(A_1) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) -> (insert_a(X_3,A_1) = insert_a(X_3,B_6) <-> A_1 = B_6))))) # label(fact_259_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 346 (all B_1 all A_3 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6))))) # label(fact_260_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 347 (all B_1 all A_3 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6))))) # label(fact_261_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 348 (all B_1 all A_3 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6))))) # label(fact_262_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 349 (all A_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) -> insert_nat(A_3,A_1) = A_1)) # label(fact_263_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 350 (all A_3 all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) -> insert_pname(A_3,A_1) = A_1))) # label(fact_264_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 351 (all A_3 all A_1 (is_fun_a_bool(A_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) -> insert_a(A_3,A_1) = A_1))) # label(fact_265_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 352 (all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1))) # label(fact_266_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 353 (all A_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),A_1))) # label(fact_267_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 354 (all A_1 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),A_1))) # label(fact_268_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 355 (all A_1 all B_6 (is_fun_pname_bool(A_1) & is_fun_pname_bool(B_6) -> (A_1 = B_6 <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))))) # label(fact_269_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 356 (all A_1 all B_6 (A_1 = B_6 <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)))) # label(fact_270_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 357 (all A_1 all B_6 (is_fun_a_bool(A_1) & is_fun_a_bool(B_6) -> (A_1 = B_6 <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))))) # label(fact_271_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 358 (all A_1 all B_6 (A_1 = B_6 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)))) # label(fact_272_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 359 (all A_1 all B_6 (A_1 = B_6 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)))) # label(fact_273_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 360 (all A_1 all B_6 (A_1 = B_6 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)))) # label(fact_274_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 361 (all A_1 all B_6 (A_1 = B_6 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)))) # label(fact_275_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 362 (all A_1 all B_6 (A_1 = B_6 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)))) # label(fact_276_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 363 (all A_1 all B_6 (A_1 = B_6 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)))) # label(fact_277_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 364 (all X_3 all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))))) # label(fact_278_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 365 (all X_3 all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))))) # label(fact_279_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 366 (all X_3 all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))))) # label(fact_280_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 367 (all B_6 all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))))) # label(fact_281_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 368 (all B_6 all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))))) # label(fact_282_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 369 (all B_6 all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))))) # label(fact_283_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 370 (all X_3 all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))))) # label(fact_284_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 371 (all X_3 all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))))) # label(fact_285_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 372 (all X_3 all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))))) # label(fact_286_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 373 (all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) <-> hBOOL(hAPP_nat_bool(A_1,X_3)))) # label(fact_287_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 374 (all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) <-> hBOOL(hAPP_pname_bool(A_1,X_3)))) # label(fact_288_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 375 (all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) <-> hBOOL(hAPP_a_bool(A_1,X_3)))) # label(fact_289_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 376 (all Pa (is_fun_a_bool(Pa) -> collect_a(Pa) = Pa)) # label(fact_290_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 377 (all Pa (is_fun_pname_bool(Pa) -> collect_pname(Pa) = Pa)) # label(fact_291_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 378 (all Pa collect_fun_nat_bool(Pa) = Pa) # label(fact_292_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 379 (all Pa (is_fun1661590463l_bool(Pa) -> collec1974731493e_bool(Pa) = Pa)) # label(fact_293_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 380 (all Pa (is_fun949378684l_bool(Pa) -> collect_fun_a_bool(Pa) = Pa)) # label(fact_294_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 381 (all Pa collect_nat(Pa) = Pa) # label(fact_295_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 382 (all C_6 all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),C_6)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_6))))) # label(fact_296_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 383 (all C_6 all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),C_6)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),C_6))))) # label(fact_297_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 384 (all C_6 all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6))))) # label(fact_298_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 385 (all A_1 all B_6 (A_1 = B_6 -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))))) # label(fact_299_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 386 (all A_1 all B_6 (A_1 = B_6 -> -(hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))))) # label(fact_300_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 387 (all A_1 all B_6 (A_1 = B_6 -> -(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))))) # label(fact_301_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 388 (all Z_1 all F all A_1 (is_a(Z_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_1),image_pname_a(F,A_1))) <-> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & Z_1 = hAPP_pname_a(F,X_1)))))) # label(fact_302_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 389 (all F all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_3)),image_pname_nat(F,A_1))))) # label(fact_303_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 390 (all F all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_3)),image_a_nat(F,A_1))))) # label(fact_304_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 391 (all F all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_3)),image_nat_pname(F,A_1))))) # label(fact_305_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 392 (all F all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_3)),image_nat_a(F,A_1))))) # label(fact_306_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 393 (all F all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_3)),image_pname_a(F,A_1))))) # label(fact_307_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 394 (all B_1 all F all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> (B_1 = hAPP_pname_nat(F,X_3) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1)))))) # label(fact_308_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 395 (all B_1 all F all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> (B_1 = hAPP_a_nat(F,X_3) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1)))))) # label(fact_309_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 396 (all B_1 all F all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> (B_1 = hAPP_nat_pname(F,X_3) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1)))))) # label(fact_310_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 397 (all B_1 all F all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> (B_1 = hAPP_nat_a(F,X_3) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1)))))) # label(fact_311_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 398 (all B_1 all F all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> (B_1 = hAPP_pname_a(F,X_3) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))))) # label(fact_312_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 399 (all X_1 all Xa insert_fun_nat_bool(X_1,Xa) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),Xa)))) # label(fact_313_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 400 (all X_1 all Xa insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa)))) # label(fact_314_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 401 (all X_1 all Xa insert_fun_a_bool(X_1,Xa) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),Xa)))) # label(fact_315_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 402 (all X_1 all Xa insert_nat(X_1,Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa)))) # label(fact_316_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 403 (all X_1 all Xa insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa)))) # label(fact_317_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 404 (all X_1 all Xa insert_a(X_1,Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa)))) # label(fact_318_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 405 (all B_6 all A_3 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),insert_pname(A_3,B_6)))) # label(fact_319_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 406 (all B_6 all A_3 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),insert_nat(A_3,B_6)))) # label(fact_320_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 407 (all B_6 all A_3 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),insert_a(A_3,B_6)))) # label(fact_321_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 408 (all X_3 all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_3,A_1)),B_6)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)))) # label(fact_322_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 409 (all X_3 all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_3,A_1)),B_6)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)))) # label(fact_323_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 410 (all X_3 all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6)) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)))) # label(fact_324_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 411 (all B_6 all X_3 all A_1 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,B_6))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))))) # label(fact_325_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 412 (all B_6 all X_3 all A_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,B_6))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))))) # label(fact_326_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 413 (all B_6 all X_3 all A_1 (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,B_6))) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))))) # label(fact_327_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 414 (all B_1 all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(B_1,B_6))))) # label(fact_328_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 415 (all B_1 all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(B_1,B_6))))) # label(fact_329_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 416 (all B_1 all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(B_1,B_6))))) # label(fact_330_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 417 (all A_3 all C_6 all D_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_6),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_3,C_6)),insert_pname(A_3,D_1))))) # label(fact_331_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 418 (all A_3 all C_6 all D_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),D_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_3,C_6)),insert_nat(A_3,D_1))))) # label(fact_332_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 419 (all A_3 all C_6 all D_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1))))) # label(fact_333_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 420 (all F all A_3 all B_6 image_a_pname(F,insert_a(A_3,B_6)) = insert_pname(hAPP_a_pname(F,A_3),image_a_pname(F,B_6))) # label(fact_334_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 421 (all F all A_3 all B_6 image_a_nat(F,insert_a(A_3,B_6)) = insert_nat(hAPP_a_nat(F,A_3),image_a_nat(F,B_6))) # label(fact_335_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 422 (all F all A_3 all B_6 image_nat_a(F,insert_nat(A_3,B_6)) = insert_a(hAPP_nat_a(F,A_3),image_nat_a(F,B_6))) # label(fact_336_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 423 (all F all A_3 all B_6 image_pname_a(F,insert_pname(A_3,B_6)) = insert_a(hAPP_pname_a(F,A_3),image_pname_a(F,B_6))) # label(fact_337_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 424 (all F all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> insert_pname(hAPP_pname_pname(F,X_3),image_pname_pname(F,A_1)) = image_pname_pname(F,A_1))) # label(fact_338_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 425 (all F all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> insert_nat(hAPP_pname_nat(F,X_3),image_pname_nat(F,A_1)) = image_pname_nat(F,A_1))) # label(fact_339_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 426 (all F all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> insert_pname(hAPP_a_pname(F,X_3),image_a_pname(F,A_1)) = image_a_pname(F,A_1))) # label(fact_340_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 427 (all F all X_3 all A_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) -> insert_nat(hAPP_a_nat(F,X_3),image_a_nat(F,A_1)) = image_a_nat(F,A_1))) # label(fact_341_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 428 (all F all X_3 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) -> insert_a(hAPP_nat_a(F,X_3),image_nat_a(F,A_1)) = image_nat_a(F,A_1))) # label(fact_342_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 429 (all F all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1))) # label(fact_343_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 430 (all B_6 all F all A_1 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1))) <-> (exists AA (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A_1)) & B_6 = image_nat_a(F,AA)))))) # label(fact_344_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 431 (all B_6 all F all A_1 (is_fun_pname_bool(B_6) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1))) <-> (exists AA (is_fun_a_bool(AA) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1)) & B_6 = image_a_pname(F,AA)))))) # label(fact_345_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 432 (all B_6 all F all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1))) <-> (exists AA (is_fun_a_bool(AA) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1)) & B_6 = image_a_nat(F,AA))))) # label(fact_346_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 433 (all B_6 all F all A_1 (is_fun_a_bool(B_6) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1))) <-> (exists AA (is_fun_pname_bool(AA) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1)) & B_6 = image_pname_a(F,AA)))))) # label(fact_347_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 434 (all F all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),image_a_pname(F,B_6))))) # label(fact_348_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 435 (all F all A_1 all B_6 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),image_a_nat(F,B_6))))) # label(fact_349_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 436 (all F all A_1 all B_6 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),image_nat_a(F,B_6))))) # label(fact_350_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 437 (all F all A_1 all B_6 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),image_pname_a(F,B_6))))) # label(fact_351_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 438 (all B_1 all F all A_1 (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1))) -> -(all X_1 (B_1 = hAPP_nat_pname(F,X_1) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))))))) # label(fact_352_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 439 (all B_1 all F all A_1 (is_a(B_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1))) -> -(all X_1 (B_1 = hAPP_nat_a(F,X_1) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))))))) # label(fact_353_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 440 (all B_1 all F all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1))) -> -(all X_1 (is_pname(X_1) -> (B_1 = hAPP_pname_nat(F,X_1) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))))))) # label(fact_354_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 441 (all B_1 all F all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1))) -> -(all X_1 (is_a(X_1) -> (B_1 = hAPP_a_nat(F,X_1) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))))))) # label(fact_355_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 442 (all B_1 all F all A_1 (is_a(B_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) -> -(all X_1 (is_pname(X_1) -> (B_1 = hAPP_pname_a(F,X_1) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)))))))) # label(fact_356_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 443 (all B_6 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_6)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)))) # label(fact_357_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 444 (all B_6 all A_1 ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_6))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)))) # label(fact_358_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 445 (all B_6 all A_1 ((all X_1 (is_a(X_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)))) # label(fact_359_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 446 (all F all B_6 all A_1 ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_1)),B_6))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(F,A_1)),B_6)))) # label(fact_360_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 447 (all F all B_6 all A_1 ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(F,X_1)),B_6))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(F,A_1)),B_6)))) # label(fact_361_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 448 (all F all B_6 all A_1 ((all X_1 (is_a(X_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_1)),B_6))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),B_6)))) # label(fact_362_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 449 (all F all B_6 all A_1 ((all X_1 (is_a(X_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(F,X_1)),B_6))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),B_6)))) # label(fact_363_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 450 (all F all B_6 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_1)),B_6)))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(F,A_1)),B_6)))) # label(fact_364_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 451 (all F all B_6 all A_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_1)),B_6)))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),B_6)))) # label(fact_365_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 452 (all F all B_6 all A_1 ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B_6))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),B_6)))) # label(fact_366_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 453 (all X_3 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),X_3))) # label(fact_367_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 454 (all X_3 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),X_3))) # label(fact_368_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 455 (all X_3 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),X_3))) # label(fact_369_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 456 (all X_3 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),X_3))) # label(fact_370_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 457 (all X_10 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),X_10))) # label(fact_371_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 458 (all N_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) <-> (exists M_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M_2)))))) # label(fact_372_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 459 (all G all C_1 (hBOOL(wt(C_1)) -> ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),u)) -> hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,X_1),bot_bot_fun_a_bool)))))) -> hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(mgt(C_1),bot_bot_fun_a_bool)))))) # label(fact_373_assms_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 460 (all F all G_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) <-> (all X_1 (is_pname(X_1) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G_1,X_1))))))) # label(fact_374_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 461 (all F all G_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) <-> (all X_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_375_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 462 (all F all G_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) <-> (all X_1 (is_a(X_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_376_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 463 (all X_3 all F all G_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3))))) # label(fact_377_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 464 (all X_3 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_3)),hAPP_nat_bool(G_1,X_3))))) # label(fact_378_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 465 (all X_3 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_3)),hAPP_a_bool(G_1,X_3))))) # label(fact_379_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 466 (all X_3 all F all G_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3))))) # label(fact_380_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.50/1.74 467 (all X_3 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_3)),hAPP_nat_bool(G_1,X_3))))) # label(fact_381_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 468 (all X_3 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_3)),hAPP_a_bool(G_1,X_3))))) # label(fact_382_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 469 (all A_3 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),bot_bot_fun_nat_bool))) # label(fact_383_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 470 (all A_3 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),bot_bo844097828e_bool))) # label(fact_384_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 471 (all A_3 -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),bot_bot_fun_a_bool))) # label(fact_385_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 472 (all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1))) # label(fact_392_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 473 (all A_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_1))) # label(fact_393_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 474 (all A_1 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_1))) # label(fact_394_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 475 (all A_3 all A_1 (A_1 = bot_bot_fun_nat_bool -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)))) # label(fact_395_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 476 (all A_3 all A_1 (A_1 = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)))) # label(fact_396_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 477 (all A_3 all A_1 (A_1 = bot_bot_fun_a_bool -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)))) # label(fact_397_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 478 (all Pa (collect_pname(Pa) = bot_bo844097828e_bool <-> (all X_1 (is_pname(X_1) -> -hBOOL(hAPP_pname_bool(Pa,X_1)))))) # label(fact_398_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 479 (all Pa (collect_fun_nat_bool(Pa) = bot_bo1701429464l_bool <-> (all X_1 -hBOOL(hAPP_f54304608l_bool(Pa,X_1))))) # label(fact_399_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 480 (all Pa (collec1974731493e_bool(Pa) = bot_bo1649642514l_bool <-> (all X_1 (is_fun_pname_bool(X_1) -> -hBOOL(hAPP_f1664156314l_bool(Pa,X_1)))))) # label(fact_400_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 481 (all Pa (collect_fun_a_bool(Pa) = bot_bo1389914601l_bool <-> (all X_1 (is_fun_a_bool(X_1) -> -hBOOL(hAPP_fun_a_bool_bool(Pa,X_1)))))) # label(fact_401_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 482 (all Pa (collect_a(Pa) = bot_bot_fun_a_bool <-> (all X_1 (is_a(X_1) -> -hBOOL(hAPP_a_bool(Pa,X_1)))))) # label(fact_402_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 483 (all Pa (collect_nat(Pa) = bot_bot_fun_nat_bool <-> (all X_1 -hBOOL(hAPP_nat_bool(Pa,X_1))))) # label(fact_403_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 484 (all C_1 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),bot_bot_fun_nat_bool))) # label(fact_404_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 485 (all C_1 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool))) # label(fact_405_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 486 (all C_1 -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),bot_bot_fun_a_bool))) # label(fact_406_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 487 (all Pa (bot_bo844097828e_bool = collect_pname(Pa) <-> (all X_1 (is_pname(X_1) -> -hBOOL(hAPP_pname_bool(Pa,X_1)))))) # label(fact_407_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 488 (all Pa (bot_bo1701429464l_bool = collect_fun_nat_bool(Pa) <-> (all X_1 -hBOOL(hAPP_f54304608l_bool(Pa,X_1))))) # label(fact_408_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 489 (all Pa (bot_bo1649642514l_bool = collec1974731493e_bool(Pa) <-> (all X_1 (is_fun_pname_bool(X_1) -> -hBOOL(hAPP_f1664156314l_bool(Pa,X_1)))))) # label(fact_409_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 490 (all Pa (bot_bo1389914601l_bool = collect_fun_a_bool(Pa) <-> (all X_1 (is_fun_a_bool(X_1) -> -hBOOL(hAPP_fun_a_bool_bool(Pa,X_1)))))) # label(fact_410_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 491 (all Pa (bot_bot_fun_a_bool = collect_a(Pa) <-> (all X_1 (is_a(X_1) -> -hBOOL(hAPP_a_bool(Pa,X_1)))))) # label(fact_411_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 492 (all Pa (bot_bot_fun_nat_bool = collect_nat(Pa) <-> (all X_1 -hBOOL(hAPP_nat_bool(Pa,X_1))))) # label(fact_412_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 493 (all A_1 ((exists X_1 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))) <-> A_1 != bot_bot_fun_nat_bool)) # label(fact_413_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 494 (all A_1 (is_fun_pname_bool(A_1) -> ((exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)))) <-> A_1 != bot_bo844097828e_bool))) # label(fact_414_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 495 (all A_1 (is_fun_a_bool(A_1) -> ((exists X_1 (is_a(X_1) & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)))) <-> A_1 != bot_bot_fun_a_bool))) # label(fact_415_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 496 (all A_1 ((all X_1 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))) <-> A_1 = bot_bot_fun_nat_bool)) # label(fact_416_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 497 (all A_1 (is_fun_pname_bool(A_1) -> ((all X_1 (is_pname(X_1) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)))) <-> A_1 = bot_bo844097828e_bool))) # label(fact_417_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 498 (all A_1 (is_fun_a_bool(A_1) -> ((all X_1 (is_a(X_1) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)))) <-> A_1 = bot_bot_fun_a_bool))) # label(fact_418_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 499 (all X_1 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_425_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 500 (all X_1 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_426_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 501 (all X_1 (hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_427_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 502 (all X_3 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_3)) <-> hBOOL(bot_bot_bool))) # label(fact_428_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 503 (all X_3 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_3)) <-> hBOOL(bot_bot_bool))) # label(fact_429_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 504 (all X_3 (hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_3)) <-> hBOOL(bot_bot_bool))) # label(fact_430_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 505 (all A_3 (is_fun_pname_bool(A_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool)) -> A_3 = bot_bo844097828e_bool))) # label(fact_431_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.74 506 (all A_3 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool)) -> (hBOOL(A_3) <-> hBOOL(bot_bot_bool)))) # label(fact_432_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 507 (all A_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool)) -> A_3 = bot_bot_fun_nat_bool)) # label(fact_433_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 508 (all A_3 (is_fun_a_bool(A_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool)) -> A_3 = bot_bot_fun_a_bool))) # label(fact_434_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 509 (all A_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),bot_bot_nat)) -> A_9 = bot_bot_nat)) # label(fact_435_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 510 (all A_3 (is_fun_pname_bool(A_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool)) <-> A_3 = bot_bo844097828e_bool))) # label(fact_436_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 511 (all A_3 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool)) <-> (hBOOL(A_3) <-> hBOOL(bot_bot_bool)))) # label(fact_437_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 512 (all A_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool)) <-> A_3 = bot_bot_fun_nat_bool)) # label(fact_438_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 513 (all A_3 (is_fun_a_bool(A_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool)) <-> A_3 = bot_bot_fun_a_bool))) # label(fact_439_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 514 (all A_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_3),bot_bot_nat)) <-> A_3 = bot_bot_nat)) # label(fact_440_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 515 (all A_3 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_3))) # label(fact_441_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 516 (all A_3 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_3))) # label(fact_442_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 517 (all A_3 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_3))) # label(fact_443_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 518 (all A_3 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_3))) # label(fact_444_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 519 (all A_8 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_8))) # label(fact_445_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 520 (all A_3 all B_1 (is_pname(A_3) & is_pname(B_1) -> (insert_pname(A_3,bot_bo844097828e_bool) = insert_pname(B_1,bot_bo844097828e_bool) -> A_3 = B_1))) # label(fact_446_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 521 (all A_3 all B_1 (insert_nat(A_3,bot_bot_fun_nat_bool) = insert_nat(B_1,bot_bot_fun_nat_bool) -> A_3 = B_1)) # label(fact_447_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 522 (all A_3 all B_1 (is_a(A_3) & is_a(B_1) -> (insert_a(A_3,bot_bot_fun_a_bool) = insert_a(B_1,bot_bot_fun_a_bool) -> A_3 = B_1))) # label(fact_448_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 523 (all B_1 all A_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool))) -> B_1 = A_3)) # label(fact_449_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 524 (all B_1 all A_3 (is_pname(B_1) & is_pname(A_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool))) -> B_1 = A_3))) # label(fact_450_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 525 (all B_1 all A_3 (is_a(B_1) & is_a(A_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool))) -> B_1 = A_3))) # label(fact_451_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 526 (all A_3 all B_1 all C_1 all D (is_pname(A_3) & is_pname(B_1) & is_pname(C_1) & is_pname(D) -> (insert_pname(A_3,insert_pname(B_1,bot_bo844097828e_bool)) = insert_pname(C_1,insert_pname(D,bot_bo844097828e_bool)) <-> A_3 = C_1 & B_1 = D | A_3 = D & B_1 = C_1))) # label(fact_452_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 527 (all A_3 all B_1 all C_1 all D (insert_nat(A_3,insert_nat(B_1,bot_bot_fun_nat_bool)) = insert_nat(C_1,insert_nat(D,bot_bot_fun_nat_bool)) <-> A_3 = C_1 & B_1 = D | A_3 = D & B_1 = C_1)) # label(fact_453_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 528 (all A_3 all B_1 all C_1 all D (is_a(A_3) & is_a(B_1) & is_a(C_1) & is_a(D) -> (insert_a(A_3,insert_a(B_1,bot_bot_fun_a_bool)) = insert_a(C_1,insert_a(D,bot_bot_fun_a_bool)) <-> A_3 = C_1 & B_1 = D | A_3 = D & B_1 = C_1))) # label(fact_454_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 529 (all B_1 all A_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool))) <-> B_1 = A_3)) # label(fact_455_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 530 (all B_1 all A_3 (is_pname(B_1) & is_pname(A_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool))) <-> B_1 = A_3))) # label(fact_456_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 531 (all B_1 all A_3 (is_a(B_1) & is_a(A_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool))) <-> B_1 = A_3))) # label(fact_457_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 532 (all A_3 all A_1 insert_pname(A_3,A_1) != bot_bo844097828e_bool) # label(fact_458_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 533 (all A_3 all A_1 insert_nat(A_3,A_1) != bot_bot_fun_nat_bool) # label(fact_459_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 534 (all A_3 all A_1 insert_a(A_3,A_1) != bot_bot_fun_a_bool) # label(fact_460_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 535 (all A_3 all A_1 bot_bo844097828e_bool != insert_pname(A_3,A_1)) # label(fact_461_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 536 (all A_3 all A_1 bot_bot_fun_nat_bool != insert_nat(A_3,A_1)) # label(fact_462_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 537 (all A_3 all A_1 bot_bot_fun_a_bool != insert_a(A_3,A_1)) # label(fact_463_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 538 (all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool)) <-> A_1 = bot_bot_fun_nat_bool)) # label(fact_464_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 539 (all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool)) <-> A_1 = bot_bo844097828e_bool))) # label(fact_465_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 540 (all A_1 (is_fun_a_bool(A_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),bot_bot_fun_a_bool)) <-> A_1 = bot_bot_fun_a_bool))) # label(fact_466_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 541 (all F all A_1 (is_fun_pname_bool(A_1) -> (image_pname_a(F,A_1) = bot_bot_fun_a_bool <-> A_1 = bot_bo844097828e_bool))) # label(fact_467_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 542 (all F image_pname_a(F,bot_bo844097828e_bool) = bot_bot_fun_a_bool) # label(fact_468_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 543 (all F all A_1 (is_fun_pname_bool(A_1) -> (bot_bot_fun_a_bool = image_pname_a(F,A_1) <-> A_1 = bot_bo844097828e_bool))) # label(fact_469_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 544 (all Pa all A_3 ((hBOOL(hAPP_nat_bool(Pa,A_3)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) = insert_nat(A_3,bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_3)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) = bot_bot_fun_nat_bool))) # label(fact_470_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 545 (all Pa all A_3 ((hBOOL(hAPP_pname_bool(Pa,A_3)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) = insert_pname(A_3,bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_3)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) = bot_bo844097828e_bool))) # label(fact_471_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 546 (all Pa all A_3 ((hBOOL(hAPP_a_bool(Pa,A_3)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) = insert_a(A_3,bot_bot_fun_a_bool)) & (-hBOOL(hAPP_a_bool(Pa,A_3)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) = bot_bot_fun_a_bool))) # label(fact_472_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 547 (all Pa all A_3 ((hBOOL(hAPP_f54304608l_bool(Pa,A_3)) -> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool)) & (-hBOOL(hAPP_f54304608l_bool(Pa,A_3)) -> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) = bot_bo1701429464l_bool))) # label(fact_473_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 548 (all Pa all A_3 ((hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = bot_bo1649642514l_bool))) # label(fact_474_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 549 (all Pa all A_3 ((hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) -> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool)) & (-hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) -> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) = bot_bo1389914601l_bool))) # label(fact_475_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 550 (all Pa all A_3 ((hBOOL(hAPP_nat_bool(Pa,A_3)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) = insert_nat(A_3,bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_3)) -> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) = bot_bot_fun_nat_bool))) # label(fact_476_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 551 (all Pa all A_3 ((hBOOL(hAPP_pname_bool(Pa,A_3)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) = insert_pname(A_3,bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_3)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) = bot_bo844097828e_bool))) # label(fact_477_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 552 (all Pa all A_3 ((hBOOL(hAPP_a_bool(Pa,A_3)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = insert_a(A_3,bot_bot_fun_a_bool)) & (-hBOOL(hAPP_a_bool(Pa,A_3)) -> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = bot_bot_fun_a_bool))) # label(fact_478_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 553 (all Pa all A_3 ((hBOOL(hAPP_f54304608l_bool(Pa,A_3)) -> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool)) & (-hBOOL(hAPP_f54304608l_bool(Pa,A_3)) -> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) = bot_bo1701429464l_bool))) # label(fact_479_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 554 (all Pa all A_3 ((hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) = bot_bo1649642514l_bool))) # label(fact_480_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 555 (all Pa all A_3 ((hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) -> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool)) & (-hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) -> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) = bot_bo1389914601l_bool))) # label(fact_481_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 556 (all A_3 collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)) = insert_nat(A_3,bot_bot_fun_nat_bool)) # label(fact_482_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 557 (all A_3 collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)) = insert_pname(A_3,bot_bo844097828e_bool)) # label(fact_483_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 558 (all A_3 collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)) = insert_a(A_3,bot_bot_fun_a_bool)) # label(fact_484_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 559 (all A_3 collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool)) # label(fact_485_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 560 (all A_3 collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool)) # label(fact_486_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 561 (all A_3 collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool)) # label(fact_487_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 562 (all A_3 collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_3)) = insert_nat(A_3,bot_bot_fun_nat_bool)) # label(fact_488_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 563 (all A_3 collect_pname(hAPP_p61793385e_bool(fequal_pname,A_3)) = insert_pname(A_3,bot_bo844097828e_bool)) # label(fact_489_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 564 (all A_3 collect_a(hAPP_a_fun_a_bool(fequal_a,A_3)) = insert_a(A_3,bot_bot_fun_a_bool)) # label(fact_490_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 565 (all A_3 collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool)) # label(fact_491_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 566 (all A_3 collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_3)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool)) # label(fact_492_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 567 (all A_3 collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool)) # label(fact_493_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 568 (all A_1 all X_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,bot_bot_fun_nat_bool))) -> A_1 = bot_bot_fun_nat_bool | A_1 = insert_nat(X_3,bot_bot_fun_nat_bool))) # label(fact_494_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 569 (all A_1 all X_3 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,bot_bo844097828e_bool))) -> A_1 = bot_bo844097828e_bool | A_1 = insert_pname(X_3,bot_bo844097828e_bool)))) # label(fact_495_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 570 (all A_1 all X_3 (is_fun_a_bool(A_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,bot_bot_fun_a_bool))) -> A_1 = bot_bot_fun_a_bool | A_1 = insert_a(X_3,bot_bot_fun_a_bool)))) # label(fact_496_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 571 (all C_1 all X_3 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) -> image_pname_a(cOMBK_a_pname(C_1),A_1) = insert_a(C_1,bot_bot_fun_a_bool))) # label(fact_497_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 572 (all C_1 all A_1 (is_fun_pname_bool(A_1) -> (A_1 = bot_bo844097828e_bool -> image_pname_a(cOMBK_a_pname(C_1),A_1) = bot_bot_fun_a_bool) & (A_1 != bot_bo844097828e_bool -> image_pname_a(cOMBK_a_pname(C_1),A_1) = insert_a(C_1,bot_bot_fun_a_bool)))) # label(fact_498_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 573 (all X_9 all Y_8 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_8),X_9)))) # label(fact_499_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 574 (all Z_1 all Y_2 all X_3 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_3))))) # label(fact_500_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 575 (all Z_1 all Y_2 all X_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_3))))) # label(fact_501_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 576 (all Z_1 all Y_2 all X_3 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),Y_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),X_3))))) # label(fact_502_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 577 (all Z_3 all Y_7 all X_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_3),Y_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_3),X_8))))) # label(fact_503_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 578 (all Z_1 all Y_2 all X_3 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),Y_2)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),X_3))))) # label(fact_504_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 579 (all Y_2 all X_3 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) -> (hBOOL(X_3) <-> hBOOL(Y_2))))) # label(fact_505_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 580 (all Y_2 all X_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) -> X_3 = Y_2))) # label(fact_506_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 581 (all Y_2 all X_3 (is_fun_pname_bool(Y_2) & is_fun_pname_bool(X_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) -> X_3 = Y_2)))) # label(fact_507_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 582 (all Y_6 all X_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),X_7)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6)) -> X_7 = Y_6))) # label(fact_508_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 583 (all Y_2 all X_3 (is_fun_a_bool(Y_2) & is_fun_a_bool(X_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) -> X_3 = Y_2)))) # label(fact_509_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 584 (all Z_1 all X_3 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Z_1))))) # label(fact_510_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 585 (all Z_1 all X_3 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Z_1))))) # label(fact_511_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 586 (all Z_1 all X_3 all Y_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Z_1))))) # label(fact_512_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 587 (all Z_2 all X_6 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),Z_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Z_2))))) # label(fact_513_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 588 (all Z_1 all X_3 all Y_2 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),Z_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Z_1))))) # label(fact_514_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 589 (all X_3 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) -> (hBOOL(X_3) <-> hBOOL(Y_2))))) # label(fact_515_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 590 (all X_3 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) -> X_3 = Y_2))) # label(fact_516_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 591 (all X_3 all Y_2 (is_fun_pname_bool(X_3) & is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) -> X_3 = Y_2)))) # label(fact_517_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 592 (all X_5 all Y_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_5),Y_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5)) -> X_5 = Y_4))) # label(fact_518_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 593 (all X_3 all Y_2 (is_fun_a_bool(X_3) & is_fun_a_bool(Y_2) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) -> X_3 = Y_2)))) # label(fact_519_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 594 (all C_1 all B_1 all A_3 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_3)) -> ((hBOOL(B_1) <-> hBOOL(C_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3))))) # label(fact_520_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 595 (all C_1 all B_1 all A_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),A_3)) -> (B_1 = C_1 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3))))) # label(fact_521_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 596 (all C_1 all B_1 all A_3 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_3)) -> (B_1 = C_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3))))) # label(fact_522_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 597 (all C_5 all B_5 all A_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),A_7)) -> (B_5 = C_5 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_5),A_7))))) # label(fact_523_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 598 (all C_1 all B_1 all A_3 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),A_3)) -> (B_1 = C_1 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3))))) # label(fact_524_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 599 (all C_1 all A_3 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),B_1)) -> ((hBOOL(B_1) <-> hBOOL(C_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1))))) # label(fact_525_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 600 (all C_1 all A_3 all B_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1))))) # label(fact_526_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 601 (all C_1 all A_3 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1))))) # label(fact_527_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 602 (all C_4 all A_6 all B_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_4)) -> (B_4 = C_4 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),C_4))))) # label(fact_528_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 603 (all C_1 all A_3 all B_1 (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1))))) # label(fact_529_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 604 (all C_1 all B_1 all A_3 ((hBOOL(A_3) <-> hBOOL(B_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),B_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3))))) # label(fact_530_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 605 (all C_1 all A_3 all B_1 (A_3 = B_1 -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),B_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3))))) # label(fact_531_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 606 (all C_1 all A_3 all B_1 (A_3 = B_1 -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3))))) # label(fact_532_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 607 (all C_3 all A_5 all B_3 (A_5 = B_3 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),B_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),A_5))))) # label(fact_533_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 608 (all C_1 all A_3 all B_1 (A_3 = B_1 -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),B_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3))))) # label(fact_534_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 609 (all C_1 all B_1 all A_3 ((hBOOL(A_3) <-> hBOOL(B_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),C_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1))))) # label(fact_535_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 610 (all C_1 all A_3 all B_1 (A_3 = B_1 -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),C_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1))))) # label(fact_536_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 611 (all C_1 all A_3 all B_1 (A_3 = B_1 -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1))))) # label(fact_537_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 612 (all C_2 all A_4 all B_2 (A_4 = B_2 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),C_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),C_2))))) # label(fact_538_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 613 (all C_1 all A_3 all B_1 (A_3 = B_1 -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),C_1)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1))))) # label(fact_539_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 614 (all Y_2 all X_3 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) <-> (hBOOL(X_3) <-> hBOOL(Y_2))))) # label(fact_540_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 615 (all Y_2 all X_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) <-> X_3 = Y_2))) # label(fact_541_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 616 (all Y_2 all X_3 (is_fun_pname_bool(Y_2) & is_fun_pname_bool(X_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) <-> X_3 = Y_2)))) # label(fact_542_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 617 (all Y_2 all X_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) <-> X_3 = Y_2))) # label(fact_543_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 618 (all Y_2 all X_3 (is_fun_a_bool(Y_2) & is_fun_a_bool(X_3) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) <-> X_3 = Y_2)))) # label(fact_544_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 619 (all Y_2 all X_3 ((hBOOL(X_3) <-> hBOOL(Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)))) # label(fact_545_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 620 (all X_3 all Y_2 (X_3 = Y_2 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)))) # label(fact_546_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 621 (all X_3 all Y_2 (X_3 = Y_2 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)))) # label(fact_547_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 622 (all X_4 all Y_3 (X_4 = Y_3 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3)))) # label(fact_548_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 623 (all X_3 all Y_2 (X_3 = Y_2 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)))) # label(fact_549_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 624 (all Y_2 all X_3 ((hBOOL(X_3) <-> hBOOL(Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)))) # label(fact_550_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 625 (all X_3 all Y_2 (X_3 = Y_2 <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)))) # label(fact_551_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 626 (all X_3 all Y_2 (is_fun_pname_bool(X_3) & is_fun_pname_bool(Y_2) -> (X_3 = Y_2 <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))))) # label(fact_552_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 627 (all X_3 all Y_2 (X_3 = Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3)))) # label(fact_553_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 628 (all X_3 all Y_2 (is_fun_a_bool(X_3) & is_fun_a_bool(Y_2) -> (X_3 = Y_2 <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))))) # label(fact_554_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 629 (all X_2 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_2)))) # label(fact_555_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 630 (all Pa all A_1 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_1)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all A_2 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,insert_nat(A_2,F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1))))))) # label(fact_556_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 631 (all Pa all A_1 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_1)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool)) -> ((all A_2 all F_2 (is_pname(A_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,A_2),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,F_2)) -> hBOOL(hAPP_f1664156314l_bool(Pa,insert_pname(A_2,F_2))))))))) -> hBOOL(hAPP_f1664156314l_bool(Pa,F_1))))))) # label(fact_557_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 632 (all Pa all A_1 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_1)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool)) -> ((all A_2 all F_2 (is_a(A_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,A_2),A_1)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),F_2)) -> (hBOOL(hAPP_fun_a_bool_bool(Pa,F_2)) -> hBOOL(hAPP_fun_a_bool_bool(Pa,insert_a(A_2,F_2))))))))) -> hBOOL(hAPP_fun_a_bool_bool(Pa,F_1))))))) # label(fact_558_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 633 (all Pa all A_1 all F_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,F_1),A_1)) -> (hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool)) -> ((all A_2 all F_2 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),A_1)) -> (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),F_2)) -> (hBOOL(hAPP_f1637334154l_bool(Pa,F_2)) -> hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(A_2,F_2)))))))) -> hBOOL(hAPP_f1637334154l_bool(Pa,F_1))))))) # label(fact_559_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 634 (all Pa all A_1 all F_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,F_1),A_1)) -> (hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool)) -> ((all A_2 all F_2 (is_fun_pname_bool(A_2) & is_fun1661590463l_bool(F_2) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),F_2)) -> (hBOOL(hAPP_f1935102916l_bool(Pa,F_2)) -> hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(A_2,F_2))))))))) -> hBOOL(hAPP_f1935102916l_bool(Pa,F_1))))))) # label(fact_560_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 635 (all Pa all A_1 all F_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,F_1),A_1)) -> (hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool)) -> ((all A_2 all F_2 (is_fun_a_bool(A_2) & is_fun949378684l_bool(F_2) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),A_1)) -> (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),F_2)) -> (hBOOL(hAPP_f621171935l_bool(Pa,F_2)) -> hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(A_2,F_2))))))))) -> hBOOL(hAPP_f621171935l_bool(Pa,F_1))))))) # label(fact_561_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 636 (all Pn all G (hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,Pn),G)),insert_a(mgt(the_com(body(Pn))),bot_bot_fun_a_bool))) -> hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,Pn),bot_bot_fun_a_bool))))) # label(fact_562_assms_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 637 (all Pa all F_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) -> (hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool)) -> ((all X_1 all F_2 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2)) -> (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),F_2)) -> (hBOOL(hAPP_f1637334154l_bool(Pa,F_2)) -> hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(X_1,F_2))))))) -> hBOOL(hAPP_f1637334154l_bool(Pa,F_1)))))) # label(fact_563_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 638 (all Pa all F_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool)) -> ((all X_1 all F_2 (is_fun_pname_bool(X_1) & is_fun1661590463l_bool(F_2) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),F_2)) -> (hBOOL(hAPP_f1935102916l_bool(Pa,F_2)) -> hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(X_1,F_2)))))))) -> hBOOL(hAPP_f1935102916l_bool(Pa,F_1)))))) # label(fact_564_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 639 (all Pa all F_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) -> (hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool)) -> ((all X_1 all F_2 (is_fun_a_bool(X_1) & is_fun949378684l_bool(F_2) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2)) -> (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),F_2)) -> (hBOOL(hAPP_f621171935l_bool(Pa,F_2)) -> hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(X_1,F_2)))))))) -> hBOOL(hAPP_f621171935l_bool(Pa,F_1)))))) # label(fact_565_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 640 (all U all F ((all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(F,N_2)))) -> 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_566_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 641 (all Pn (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn),u)) -> hBOOL(wt(the_com(body(Pn)))))) # label(fact_567_assms_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 642 (all M all N hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N)) # label(fact_568_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 643 (all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,N)),one_one_nat) = N) # label(fact_569_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 644 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) <-> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)))) # label(fact_570_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 645 (all M all N hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N))) # label(fact_571_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 646 (all M all N hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N))) # label(fact_572_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 647 (all M all N hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N))) # label(fact_573_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 648 (all M_1 all K_2 all Na (hAPP_nat_nat(plus_plus_nat(M_1),K_2) = hAPP_nat_nat(plus_plus_nat(Na),K_2) <-> M_1 = Na)) # label(fact_574_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 649 (all K_2 all M_1 all Na (hAPP_nat_nat(plus_plus_nat(K_2),M_1) = hAPP_nat_nat(plus_plus_nat(K_2),Na) <-> M_1 = Na)) # label(fact_575_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 650 (all M all N all K hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),K) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N),K))) # label(fact_576_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 651 (all X all Y all Z hAPP_nat_nat(plus_plus_nat(X),hAPP_nat_nat(plus_plus_nat(Y),Z)) = hAPP_nat_nat(plus_plus_nat(Y),hAPP_nat_nat(plus_plus_nat(X),Z))) # label(fact_577_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 652 (all M all N hAPP_nat_nat(plus_plus_nat(M),N) = hAPP_nat_nat(plus_plus_nat(N),M)) # label(fact_578_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 653 (all M all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),N) = M) # label(fact_579_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 654 (all N all M hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),N) = M) # label(fact_580_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 655 (all I all J_2 all K hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) = hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(plus_plus_nat(J_2),K))) # label(fact_581_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 656 (all K all M all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K),M)),hAPP_nat_nat(plus_plus_nat(K),N)) = hAPP_nat_nat(minus_minus_nat(M),N)) # label(fact_582_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 657 (all M all K all N hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(plus_plus_nat(N),K)) = hAPP_nat_nat(minus_minus_nat(M),N)) # label(fact_583_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 658 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(M),N)))) # label(fact_584_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 659 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(N),M)))) # label(fact_585_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 660 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) <-> (exists K_1 Na = hAPP_nat_nat(plus_plus_nat(M_1),K_1)))) # label(fact_586_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 661 (all K_2 all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)))) # label(fact_587_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 662 (all M all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(J_2),M))))) # label(fact_588_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 663 (all M all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(M),J_2))))) # label(fact_589_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 664 (all K all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K))))) # label(fact_590_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 665 (all K all L all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L)))))) # label(fact_591_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 666 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)))) # label(fact_592_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 667 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_593_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 668 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))))) # label(fact_594_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 669 (all I all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I))) # label(fact_595_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 670 (all I all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K))) # label(fact_596_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 671 (all I all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K) = hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)))) # label(fact_597_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 672 (all K_2 all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hAPP_nat_nat(minus_minus_nat(J_1),I_1) = K_2 <-> J_1 = hAPP_nat_nat(plus_plus_nat(K_2),I_1)))) # label(fact_598_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 673 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),N) = M)) # label(fact_599_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 674 (all I_1 all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1))))) # label(fact_600_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 675 (all I all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K))) # label(fact_601_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 676 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M)) # label(fact_602_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 677 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),K))))) # label(fact_603_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 678 (all J_1 all K_2 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_1),K_2)),I_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(plus_plus_nat(I_1),K_2))))) # label(fact_604_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 679 (all I all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),K)),J_2))) # label(fact_605_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 680 (all N hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(N),one_one_nat)) # label(fact_606_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 681 (all N hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(one_one_nat),N)) # label(fact_607_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 682 (all M all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))),M) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,J_2)),hAPP_nat_nat(plus_plus_nat(K),M)))) # label(fact_608_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 683 (all M all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(suc,J_2)))) # label(fact_609_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 684 (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(plus_plus_nat(Y),Z))))) # label(fact_610_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 685 (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(plus_plus_nat(Y),Z))))) # label(fact_611_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 686 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N)))) # label(fact_612_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 687 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))))) # label(fact_613_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 688 (all K_2 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),K_2))))) # label(fact_614_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 689 (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(plus_plus_nat(Y),Z))))) # label(fact_615_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 690 (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(plus_plus_nat(Y),Z))))) # label(fact_616_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 691 (all I all J_2 all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)))) # label(fact_617_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 692 (all M all N all K all L (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) -> (hAPP_nat_nat(plus_plus_nat(M),L) = hAPP_nat_nat(plus_plus_nat(K),N) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_618_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 693 (all K all L all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L)))))) # label(fact_619_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 694 (all K 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(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K))))) # label(fact_620_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 695 (all M all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(plus_plus_nat(M),J_2))))) # label(fact_621_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 696 (all M all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(plus_plus_nat(J_2),M))))) # label(fact_622_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 697 (all K_2 all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)))) # label(fact_623_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 698 (all J_2 all I -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J_2),I)),I))) # label(fact_624_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 699 (all I all J_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),I))) # label(fact_625_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 700 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_626_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 701 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_627_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 702 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> M = N))) # label(fact_628_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 703 (all K all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K))))) # label(fact_629_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 704 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hAPP_nat_nat(suc,M) != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N))))) # label(fact_630_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 705 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_631_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 706 (all N all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) -> M = N))) # label(fact_632_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 707 (all Na all M_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) <-> Na = M_1))) # label(fact_633_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 708 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)))) # label(fact_634_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 709 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) | M_1 = Na)) # label(fact_635_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 710 (all M_1 all Na (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))))) # label(fact_636_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 711 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_637_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 712 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (M != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_638_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 713 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_639_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 714 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) | M_1 = Na)) # label(fact_640_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 715 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) & M_1 != Na)) # label(fact_641_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 716 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M)))))) # label(fact_642_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 717 (all N all J_2 all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J_2),N)),K)))) # label(fact_643_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 718 (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_644_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 719 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_645_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 720 (all M_1 all Na (M_1 != Na <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)))) # label(fact_646_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 721 (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_647_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 722 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_648_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 723 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> M != N)) # label(fact_649_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 724 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_650_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 725 (all Pa all M_1 all Na ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))) -> ((M_1 = Na -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)))))) # label(fact_651_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 726 (all N_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) <-> (exists M_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M_2)))))) # label(fact_652_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 727 (all Na hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),Na))) = Na) # label(fact_653_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 728 (all Pa all I_1 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_1)))))) # label(fact_654_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 729 (all I all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(I),M))))) # label(fact_655_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 730 (all I all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),I))))) # label(fact_656_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 731 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) <-> (exists K_1 Na = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_1),K_1))))) # label(fact_657_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 732 (all Na all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)))) # label(fact_658_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 733 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)))) # label(fact_659_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 734 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)))) # label(fact_660_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 735 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_661_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 736 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)))) # label(fact_662_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 737 (all M_1 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) <-> Na = M_1))) # label(fact_663_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 738 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_664_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 739 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),hAPP_nat_nat(suc,M)))) # label(fact_665_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 740 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M)) # label(fact_666_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 741 (all I_1 all J_1 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1)))) # label(fact_667_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 742 (all C all A all B (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C)))))) # label(fact_668_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 743 (all Na all K_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)))))) # label(fact_669_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 744 (all X_1 hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1))) # label(fact_670_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 745 (all M_1 all K_2 all F ((all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F,M_1)),K_2)),hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(M_1),K_2)))))) # label(fact_671_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 746 (all Pa all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hBOOL(hAPP_nat_bool(Pa,J_1)) -> ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) -> (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2))) -> hBOOL(hAPP_nat_bool(Pa,I_2))))) -> hBOOL(hAPP_nat_bool(Pa,I_1)))))) # label(fact_672_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 747 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (exists K_1 N = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),K_1))))) # label(fact_673_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 748 (all Na all N_1 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)))) # label(fact_674_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 749 (all I_1 all J_1 all F ((all I_2 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1)))))) # label(fact_675_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 750 (all I all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K)) -> -(all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> K != hAPP_nat_nat(suc,J))))) # label(fact_676_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 751 (all I all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)) -> (K != hAPP_nat_nat(suc,I) -> -(all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> K != hAPP_nat_nat(suc,J)))))) # label(fact_677_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 752 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_678_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 753 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_679_le0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 754 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N)))) # label(fact_680_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 755 (all M_1 all Na (hAPP_nat_nat(plus_plus_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat) <-> M_1 = hAPP_nat_nat(suc,zero_zero_nat) & Na = zero_zero_nat | M_1 = zero_zero_nat & Na = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_681_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 756 (all M_1 all Na (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(M_1),Na) <-> M_1 = hAPP_nat_nat(suc,zero_zero_nat) & Na = zero_zero_nat | M_1 = zero_zero_nat & Na = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_682_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 757 (all N all M hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(plus_plus_nat(N),M)) = zero_zero_nat) # label(fact_683_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 758 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat)) # label(fact_684_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 759 (all M_1 all Na (hAPP_nat_nat(minus_minus_nat(M_1),Na) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)))) # label(fact_685_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 760 (all M all N (hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat -> (hAPP_nat_nat(minus_minus_nat(N),M) = zero_zero_nat -> M = N))) # label(fact_687_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 761 (all M hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat) # label(fact_688_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 762 (all M hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M) # label(fact_689_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 763 (all N hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N) = zero_zero_nat) # label(fact_690_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 764 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_691_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 765 (all M zero_zero_nat != hAPP_nat_nat(suc,M)) # label(fact_692_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 766 (all Nat_1 hAPP_nat_nat(suc,Nat_1) != zero_zero_nat) # label(fact_693_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 767 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_694_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 768 (all Nat zero_zero_nat != hAPP_nat_nat(suc,Nat)) # label(fact_695_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 769 (all M zero_zero_nat != hAPP_nat_nat(suc,M)) # label(fact_696_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 770 (all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat)) <-> Na = zero_zero_nat)) # label(fact_698_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 771 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_699_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 772 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 773 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 774 (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].
% 1.52/1.76 775 (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].
% 1.52/1.76 776 (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].
% 1.52/1.76 777 (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].
% 1.52/1.76 778 (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].
% 1.52/1.76 779 (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].
% 1.52/1.76 780 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 781 (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].
% 1.52/1.76 782 (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].
% 1.52/1.76 783 (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].
% 1.52/1.76 784 (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].
% 1.52/1.76 785 (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].
% 1.52/1.76 786 (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].
% 1.52/1.76 787 (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].
% 1.52/1.76 788 (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].
% 1.52/1.76 789 (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].
% 1.52/1.76 790 (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].
% 1.52/1.76 791 (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].
% 1.52/1.76 792 (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].
% 1.52/1.76 793 (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].
% 1.52/1.76 794 (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].
% 1.52/1.76 795 (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].
% 1.52/1.76 796 (all P all Q (is_bool(P) -> hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 797 (all P all Q all R hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_a_fun_nat_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 798 (all P all Q all R hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(P),Q),R) = hAPP_a_bool(hAPP_nat_fun_a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 799 (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].
% 1.52/1.76 800 (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].
% 1.52/1.76 801 (all P all Q all R hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(P),Q),R) = hAPP_pname_bool(hAPP_a93125764e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 802 (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].
% 1.52/1.76 803 (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].
% 1.52/1.76 804 (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].
% 1.52/1.76 805 (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].
% 1.52/1.76 806 (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].
% 1.52/1.76 807 (all P all Q all R hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_a_a(Q,R))) # label(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 808 (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].
% 1.52/1.76 809 (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].
% 1.52/1.76 810 (all P all Q (is_bool(P) -> hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 811 (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].
% 1.52/1.76 812 (all P all Q all R hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_p1499970991t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 813 (all P all Q all R hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(P),Q),R) = hAPP_pname_bool(hAPP_n1025906991e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 814 (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].
% 1.52/1.76 815 (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].
% 1.52/1.76 816 (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].
% 1.52/1.76 817 (all P all Q all R hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_nat_a(Q,R))) # label(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 818 (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].
% 1.52/1.76 819 (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].
% 1.52/1.76 820 (all P all Q (is_bool(P) -> hAPP_f54304608l_bool(cOMBK_1994329625t_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 821 (all P all Q (is_bool(P) -> hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 822 (all P all Q all R hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_a_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].
% 1.52/1.76 823 (all P all Q all R hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 824 (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].
% 1.52/1.76 825 (all P all Q all R hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f282463732t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 826 (all P all Q all R hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_fun_a_bool_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 827 (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].
% 1.52/1.76 828 (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].
% 1.52/1.76 829 (all P all Q all R hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 830 (all P all Q all R hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 831 (all P all Q all R hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f1794073134e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 832 (all P all Q all R hAPP_a93125764e_bool(cOMBB_610033911bool_a(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_a_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 833 (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__003) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 834 (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].
% 1.52/1.76 835 (all P all Q all R hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f800510211t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 836 (all P all Q all R hAPP_f54304608l_bool(cOMBB_238756964t_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f54304608l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 837 (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].
% 1.52/1.76 838 (all P all Q all R hAPP_p1499970991t_bool(cOMBB_523834888_pname(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_pname_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 839 (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].
% 1.52/1.76 840 (all P all Q all R hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 841 (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].
% 1.52/1.76 842 (all P all Q all R hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f1066163005t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 843 (all P all Q all R hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f654413245e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 844 (all P all Q all R hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_nat_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 845 (all P all Q all R hAPP_f1664156314l_bool(cOMBB_307249310e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 846 (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_007) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 847 (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].
% 1.52/1.76 848 (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].
% 1.52/1.76 849 (all P all Q all R hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 850 (all P all Q all R hAPP_p61793385e_bool(cOMBB_542850580_pname(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 851 (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].
% 1.52/1.76 852 (all P all Q all R hAPP_f282463732t_bool(cOMBB_164527437a_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_fun_a_bool_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 853 (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_010) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 854 (all P all Q all R hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1128469712_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 855 (all P all Q all R hAPP_f800510211t_bool(cOMBB_1250273980t_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_f22106695ol_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 856 (all P all Q all R hAPP_a85458249l_bool(cOMBB_472261505bool_a(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_a_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].
% 1.52/1.76 857 (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].
% 1.52/1.76 858 (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_013) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 859 (all P all Q all R hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_f921600141ol_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 860 (all P all Q all R hAPP_f654413245e_bool(cOMBB_141086128t_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1291551745_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 861 (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_016) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 862 (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].
% 1.52/1.76 863 (all P all Q all R hAPP_f759274231e_bool(cOMBB_598082538e_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 864 (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___018) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 865 (all P all Q all R hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 866 (all P all Q all R hAPP_p1824510254l_bool(cOMBB_392435466_pname(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_p1534023578a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 867 (all P all Q all R hAPP_a1392362872l_bool(cOMBB_743407885bool_a(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_a_fun_nat_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].
% 1.52/1.76 868 (all P all Q all R hAPP_a217006258l_bool(cOMBB_1137537805bool_a(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_a93125764e_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].
% 1.52/1.76 869 (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__020) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 870 (all P all Q all R hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 871 (all P all Q all R hAPP_p130839763l_bool(cOMBB_928955006_pname(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_p1499970991t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 872 (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_023) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 873 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 874 (all P all Q all R hAPP_p338031245l_bool(cOMBB_408569982_pname(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.76 875 (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].
% 1.52/1.76 876 (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].
% 2.10/2.42 877 (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].
% 2.10/2.42
% 2.10/2.42 ============================== end of process non-clausal formulas ===
% 2.10/2.42
% 2.10/2.42 ============================== PROCESS INITIAL CLAUSES ===============
% 2.10/2.42
% 2.10/2.42 ============================== PREDICATE ELIMINATION =================
% 2.10/2.42
% 2.10/2.42 ============================== end predicate elimination =============
% 2.10/2.42
% 2.10/2.42 Auto_denials: (non-Horn, no changes).
% 2.10/2.42
% 2.10/2.42 Term ordering decisions:
% 2.10/2.42 Function symbol KB weights: ord_less_eq_nat=1. ord_le1311769555a_bool=1. ord_le313189616e_bool=1. suc=1. ord_le1568362934t_bool=1. finite_finite_nat=1. finite_finite_pname=1. ord_less_nat=1. finite_finite_a=1. member_nat=1. finite347923420a_bool=1. finite595471783e_bool=1. member_pname=1. member_a=1. finite2012431853t_bool=1. bot_bot_fun_a_bool=1. ord_less_eq_bool=1. bot_bo844097828e_bool=1. fconj=1. zero_zero_nat=1. bot_bot_fun_nat_bool=1. fdisj=1. ord_le1375614389l_bool=1. ord_le675606854l_bool=1. bot_bo1389914601l_bool=1. bot_bo1649642514l_bool=1. bot_bot_bool=1. ord_le1454342156l_bool=1. finite_card_a=1. finite_card_nat=1. bot_bo1701429464l_bool=1. finite_card_pname=1. fequal_nat=1. fequal_pname=1. fequal533582459e_bool=1. fequal_a=1. fequal_fun_a_bool=1. fequal_fun_nat_bool=1. finite1306199131a_bool=1. finite1340463720e_bool=1. finite346522414t_bool=1. member799430823e_bool=1. member_fun_a_bool=1. member_fun_nat_bool=1. fFalse=1. fimplies=1. bot_bot_nat=1. u=1. fNot=1. bool=1. mgt_call=1. one_one_nat=1. g=1. pname=1. x_a=1. fTrue=1. na=1. pn=1. finite1381704300l_bool=1. finite1701474069l_bool=1. finite786885583l_bool=1. hAPP_nat_bool=1. hAPP_f1664156314l_bool=1. hAPP_fun_a_bool_bool=1. hAPP_f54304608l_bool=1. hAPP_n1699378549t_bool=1. hAPP_nat_nat=1. hAPP_f1631501043l_bool=1. hAPP_f434788991l_bool=1. hAPP_f1935102916l_bool=1. hAPP_f621171935l_bool=1. hAPP_f103356543l_bool=1. hAPP_f1637334154l_bool=1. insert_a=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. hAPP_n215258509l_bool=1. hAPP_p338031245l_bool=1. insert_pname=1. insert_nat=1. hAPP_a85458249l_bool=1. image_pname_a=1. hAPP_pname_bool=1. hAPP_a_bool=1. image_a_nat=1. hAPP_f1434722111l_bool=1. hAPP_f510955609l_bool=1. hAPP_f1772781669l_bool=1. image_a_pname=1. image_nat_a=1. hAPP_fun_a_bool_nat=1. hAPP_p61793385e_bool=1. hAPP_f22106695ol_nat=1. hAPP_a_fun_a_bool=1. image_pname_nat=1. cOMBB_1015721476ol_nat=1. cOMBS_568398431l_bool=1. cOMBS_a_bool_bool=1. cOMBS_nat_bool_bool=1. hAPP_f921600141ol_nat=1. cOMBB_1972296269bool_a=1. cOMBB_675860798_pname=1. insert1325755072e_bool=1. insert_fun_a_bool=1. cOMBS_1035972772l_bool=1. cOMBS_350070575l_bool=1. hAPP_pname_a=1. image_nat_pname=1. image_pname_pname=1. insert_fun_nat_bool=1. cOMBB_2095475776e_bool=1. cOMBB_338059395a_bool=1. cOMBB_444170502t_bool=1. cOMBS_1187019125l_bool=1. hAPP_f2009550088ol_nat=1. hAPP_f55526627ol_nat=1. hAPP_f696928925ol_nat=1. hAPP_f759274231e_bool=1. hAPP_f800510211t_bool=1. hAPP_f2050579477a_bool=1. hAPP_n1025906991e_bool=1. hAPP_nat_fun_a_bool=1. image_112932426a_bool=1. image_1283814551_pname=1. image_1551609309ol_nat=1. image_1854862208_pname=1. image_47868345e_bool=1. image_a_a=1. image_fun_a_bool_nat=1. hAPP_nat_a=1. image_2129980159t_bool=1. hAPP_a_nat=1. hAPP_f1951378235l_bool=1. hAPP_f285962445l_bool=1. hAPP_f556039215l_bool=1. image_1655916159e_bool=1. image_1921560913_pname=1. image_496248727ol_nat=1. image_819518260e_bool=1. image_a_fun_a_bool=1. image_nat_fun_a_bool=1. hAPP_nat_pname=1. hAPP_pname_nat=1. image_26036933t_bool=1. image_876012084bool_a=1. image_a_fun_nat_bool=1. image_fun_a_bool_a=1. hAPP_a93125764e_bool=1. hAPP_p1534023578a_bool=1. image_fun_nat_bool_a=1. image_nat_nat=1. fun=1. hAPP_a_fun_nat_bool=1. hAPP_a_pname=1. hAPP_f2117159681l_bool=1. hAPP_f559147733l_bool=1. hAPP_p1499970991t_bool=1. hAPP_f1246832597l_bool=1. hAPP_f1794073134e_bool=1. hAPP_f654413245e_bool=1. hAPP_n1414589940l_bool=1. hAPP_n850744903l_bool=1. hAPP_p1824510254l_bool=1. hAPP_pname_pname=1. hAPP_f1066163005t_bool=1. hAPP_f282463732t_bool=1. hAPP_p130839763l_bool=1. cOMBB_2140588453a_bool=1. cOMBB_307249310e_bool=1. cOMBB_647938656_pname=1. cOMBB_800536526ol_nat=1. cOMBB_bool_bool_a=1. hAPP_a217006258l_bool=1. hAPP_a_a=1. hAPP_f1051908748a_bool=1. hAPP_f1128469712_pname=1. hAPP_f1291551745_pname=1. hAPP_f1297739591_pname=1. hAPP_f1549043526a_bool=1. cOMBB_1137537805bool_a=1. cOMBB_1212655066ol_nat=1. cOMBB_1250273980t_bool=1. cOMBB_1321347587bool_a=1. cOMBB_141086128t_bool=1. cOMBB_164527437a_bool=1. cOMBB_1693087065a_bool=1. cOMBB_1823939024ol_nat=1. cOMBB_1885489796ol_nat=1. cOMBB_1896684278e_bool=1. cOMBB_1897541054_pname=1. cOMBB_2026977092ol_nat=1. cOMBB_2117322052ol_nat=1. cOMBB_238756964t_bool=1. cOMBB_392435466_pname=1. cOMBB_408569982_pname=1. cOMBB_472261505bool_a=1. cOMBB_523834888_pname=1. cOMBB_542850580_pname=1. cOMBB_598082538e_bool=1. cOMBB_610033911bool_a=1. cOMBB_743407885bool_a=1. cOMBB_928955006_pname=1. cOMBB_a_fun_a_bool_a=1. cOMBB_bool_bool_nat=1. hAPP_a1392362872l_bool=1. hAPP_a_fun_bool_bool=1. hAPP_f1476298914l_bool=1. hAPP_f1748468828l_bool=1. hAPP_f198738859l_bool=1. hAPP_f292226953l_bool=1. hAPP_f389811538l_bool=1. hAPP_f937997336l_bool=1. hAPP_n1006566506l_bool=1. hAPP_p393069232l_bool=1. nat_case_bool=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f58=1. f69=1. f70=1. f71=1. f80=1. f81=1. f82=1. f83=1. f84=1. f115=1. f116=1. f117=1. f118=1. f119=1. f120=1. f121=1. f122=1. f124=1. f125=1. f129=1. f130=1. f133=1. f134=1. plus_plus_nat=1. minus_minus_nat=1. collect_nat=1. collect_a=1. collect_pname=1. collec1974731493e_bool=1. collect_fun_a_bool=1. collect_fun_nat_bool=1. cOMBC_nat_nat_bool=1. cOMBC_1058051404l_bool=1. cOMBC_1355376034l_bool=1. cOMBC_226598744l_bool=1. cOMBC_1149511130e_bool=1. cOMBC_1284144636l_bool=1. cOMBC_1693257480l_bool=1. cOMBC_1732670874l_bool=1. cOMBC_a_a_bool=1. p=1. cOMBC_1245412066l_bool=1. cOMBC_1880041174l_bool=1. cOMBC_1988546018l_bool=1. mgt=1. wt=1. cOMBK_a_pname=1. cOMBK_1857069011e_bool=1. cOMBK_324466864a_bool=1. cOMBK_bool_a=1. cOMBK_bool_pname=1. body=1. cOMBC_1004116266e_bool=1. cOMBC_1666426608t_bool=1. cOMBC_1738168533e_bool=1. cOMBC_1834145417l_bool=1. cOMBC_1928494297l_bool=1. cOMBC_267053842l_bool=1. cOMBC_331553030l_bool=1. cOMBC_385542954t_bool=1. cOMBC_386238098l_bool=1. cOMBC_445755039l_bool=1. cOMBC_595898202l_bool=1. cOMBC_615407716e_bool=1. cOMBC_619334683t_bool=1. cOMBC_777206479l_bool=1. cOMBC_7971162l_bool=1. cOMBC_a_nat_bool=1. cOMBC_a_pname_bool=1. cOMBC_nat_a_bool=1. cOMBC_nat_pname_bool=1. cOMBC_pname_a_bool=1. cOMBC_pname_nat_bool=1. cOMBK_1994329625t_bool=1. cOMBK_bool_nat=1. the_com=1. collec1015864663l_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. f79=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. f100=1. f101=1. f102=1. f123=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f57=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f110=1. f111=1. f112=1. f113=1. f114=1. f126=1. f127=1. f128=1. f131=1. f132=1.
% 2.10/2.42
% 2.10/2.42 ============================== end of process initial clauses ========
% 2.10/2.42
% 2.10/2.42 ============================== CLAUSES FOR SEARCH ====================
% 2.10/2.42
% 2.10/2.42 ============================== end of clauses for search =============
% 2.10/2.42
% 2.10/2.42 ============================== SEARCH =====================Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------