TSTP Solution File: SWW473+1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW473+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 : Theorem 16.04s 16.36s
% Output : Refutation 16.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW473+1 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 5 02:09:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.10/1.41 ============================== Prover9 ===============================
% 1.10/1.41 Prover9 (32) version 2009-11A, November 2009.
% 1.10/1.41 Process 11453 was started by sandbox on n018.cluster.edu,
% 1.10/1.41 Sun Jun 5 02:09:34 2022
% 1.10/1.41 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11287_n018.cluster.edu".
% 1.10/1.41 ============================== end of head ===========================
% 1.10/1.41
% 1.10/1.41 ============================== INPUT =================================
% 1.10/1.41
% 1.10/1.41 % Reading from file /tmp/Prover9_11287_n018.cluster.edu
% 1.10/1.41
% 1.10/1.41 set(prolog_style_variables).
% 1.10/1.41 set(auto2).
% 1.10/1.41 % set(auto2) -> set(auto).
% 1.10/1.41 % set(auto) -> set(auto_inference).
% 1.10/1.41 % set(auto) -> set(auto_setup).
% 1.10/1.41 % set(auto_setup) -> set(predicate_elim).
% 1.10/1.41 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.10/1.41 % set(auto) -> set(auto_limits).
% 1.10/1.41 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.10/1.41 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.10/1.41 % set(auto) -> set(auto_denials).
% 1.10/1.41 % set(auto) -> set(auto_process).
% 1.10/1.41 % set(auto2) -> assign(new_constants, 1).
% 1.10/1.41 % set(auto2) -> assign(fold_denial_max, 3).
% 1.10/1.41 % set(auto2) -> assign(max_weight, "200.000").
% 1.10/1.41 % set(auto2) -> assign(max_hours, 1).
% 1.10/1.41 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.10/1.41 % set(auto2) -> assign(max_seconds, 0).
% 1.10/1.41 % set(auto2) -> assign(max_minutes, 5).
% 1.10/1.41 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.10/1.41 % set(auto2) -> set(sort_initial_sos).
% 1.10/1.41 % set(auto2) -> assign(sos_limit, -1).
% 1.10/1.41 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.10/1.41 % set(auto2) -> assign(max_megs, 400).
% 1.10/1.41 % set(auto2) -> assign(stats, some).
% 1.10/1.41 % set(auto2) -> clear(echo_input).
% 1.10/1.41 % set(auto2) -> set(quiet).
% 1.10/1.41 % set(auto2) -> clear(print_initial_clauses).
% 1.10/1.41 % set(auto2) -> clear(print_given).
% 1.10/1.41 assign(lrs_ticks,-1).
% 1.10/1.41 assign(sos_limit,10000).
% 1.10/1.41 assign(order,kbo).
% 1.10/1.41 set(lex_order_vars).
% 1.10/1.41 clear(print_given).
% 1.10/1.41
% 1.10/1.41 % formulas(sos). % not echoed (449 formulas)
% 1.10/1.41
% 1.10/1.41 ============================== end of input ==========================
% 1.10/1.41
% 1.10/1.41 % From the command line: assign(max_seconds, 300).
% 1.10/1.41
% 1.10/1.41 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.10/1.41
% 1.10/1.41 % Formulas that are not ordinary clauses:
% 1.10/1.41 1 (all B_1_1 all B_2 (is_fun_a_bool(B_2) -> is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 2 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 3 (all B_1_1 all B_2 (is_fun949378684l_bool(B_2) -> is_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 4 (all B_1_1 all B_2 (is_fun1661590463l_bool(B_2) -> is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 5 (all B_1_1 all B_2 (is_fun_a_bool(B_2) -> is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2)))) # label(gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 6 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2)))) # label(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 7 (all B_1_1 all B_2 (is_fun949378684l_bool(B_2) -> is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2)))) # label(gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 8 (all B_1_1 all B_2 (is_fun1661590463l_bool(B_2) -> is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2)))) # label(gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 9 (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].
% 1.10/1.41 10 (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].
% 1.10/1.41 11 (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].
% 1.10/1.41 12 (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].
% 1.10/1.41 13 (all B_1_1 all B_2 (is_fun_a_bool(B_2) -> is_fun_a_bool(image_a_a(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000t__a_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 14 (all B_1_1 all B_2 (is_fun_a_bool(B_2) -> is_fun_pname_bool(image_a_pname(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 15 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_a_bool(image_pname_a(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) # label(hypothesis) # label(non_clause). [assumption].
% 1.10/1.41 16 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(image_pname_pname(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 17 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 18 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 19 (all B_1_1 all B_2 is_fun_a_bool(image_nat_a(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 20 (all B_1_1 all B_2 is_fun_pname_bool(image_nat_pname(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 21 (all B_1_1 all B_2 is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 22 (all B_1_1 all B_2 is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 23 (all B_1_1 all B_2 (is_fun949378684l_bool(B_2) -> is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 24 (all B_1_1 all B_2 (is_fun949378684l_bool(B_2) -> is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 25 (all B_1_1 all B_2 (is_fun1661590463l_bool(B_2) -> is_fun_a_bool(image_876012084bool_a(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 26 (all B_1_1 all B_2 (is_fun1661590463l_bool(B_2) -> is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 27 (all B_1_1 all B_2 is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 28 (all B_1_1 all B_2 is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 29 (all B_1_1 all B_2 is_fun_a_bool(image_573985017bool_a(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 30 (all B_1_1 all B_2 is_fun_pname_bool(image_990671762_pname(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 31 (all B_1_1 all B_2 is_fun_a_bool(image_349102846bool_a(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 32 (all B_1_1 all B_2 is_fun_pname_bool(image_1705983821_pname(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 33 (all B_1_1 all B_2 is_fun_a_bool(image_526090948bool_a(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 34 (all B_1_1 all B_2 is_fun_pname_bool(image_1604018183_pname(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 35 (all B_1_1 all B_2 (is_a(B_1_1) & is_fun_a_bool(B_2) -> is_fun_a_bool(insert_a(B_1_1,B_2)))) # label(gsy_c_Set_Oinsert_000t__a) # label(hypothesis) # label(non_clause). [assumption].
% 1.10/1.41 36 (all B_1_1 all B_2 (is_pname(B_1_1) & is_fun_pname_bool(B_2) -> is_fun_pname_bool(insert_pname(B_1_1,B_2)))) # label(gsy_c_Set_Oinsert_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 37 (all B_1_1 all B_2 (is_fun_a_bool(B_1_1) & is_fun949378684l_bool(B_2) -> is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2)))) # label(gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 38 (all B_1_1 all B_2 (is_fun_pname_bool(B_1_1) & is_fun1661590463l_bool(B_2) -> is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2)))) # label(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 39 (all B_1_1 all B_2 (is_fun_a_bool(B_1_1) & is_a(B_2) -> is_bool(hAPP_a_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000t__a_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 40 (all B_1_1 all B_2 (is_a(B_2) -> is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 41 (all B_1_1 all B_2 (is_a(B_2) -> is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 42 (all B_1_1 all B_2 (is_a(B_2) -> is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2)))) # 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].
% 1.10/1.41 43 (all B_1_1 all B_2 (is_pname(B_2) -> is_a(hAPP_pname_a(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000t__a) # label(hypothesis) # label(non_clause). [assumption].
% 1.10/1.41 44 (all B_1_1 all B_2 (is_fun_pname_bool(B_1_1) & is_pname(B_2) -> is_bool(hAPP_pname_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 45 (all B_1_1 all B_2 (is_pname(B_2) -> is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 46 (all B_1_1 all B_2 (is_pname(B_2) -> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 47 (all B_1_1 all B_2 (is_pname(B_2) -> is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(hypothesis) # label(non_clause). [assumption].
% 1.10/1.41 48 (all B_1_1 all B_2 (is_bool(B_2) -> is_bool(hAPP_bool_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 49 (all B_1_1 all B_2 is_bool(hAPP_nat_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 1.10/1.41 50 (all B_1_1 all B_2 is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 51 (all B_1_1 all B_2 is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 52 (all B_1_1 all B_2 (is_fun949378684l_bool(B_1_1) & is_fun_a_bool(B_2) -> is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 1.10/1.41 53 (all B_1_1 all B_2 (is_fun_a_bool(B_2) -> is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2)))) # 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].
% 1.10/1.41 54 (all B_1_1 all B_2 (is_fun_a_bool(B_2) -> is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2)))) # 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].
% 1.10/1.41 55 (all B_1_1 all B_2 (is_fun1661590463l_bool(B_1_1) & is_fun_pname_bool(B_2) -> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 1.10/1.41 56 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 57 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 58 (all B_1_1 all B_2 is_bool(hAPP_f54304608l_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 59 (all B_1_1 all B_2 (is_fun949378684l_bool(B_2) -> is_bool(hAPP_f621171935l_bool(B_1_1,B_2)))) # 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].
% 1.10/1.41 60 (all B_1_1 all B_2 (is_fun949378684l_bool(B_2) -> is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 61 (all B_1_1 all B_2 (is_fun1661590463l_bool(B_2) -> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 62 (all B_1_1 all B_2 (is_fun1661590463l_bool(B_2) -> is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 63 (all B_1_1 all B_2 is_bool(hAPP_f1637334154l_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 64 (all B_1_1 all B_2 is_bool(hAPP_f292226953l_bool(B_1_1,B_2))) # 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].
% 1.10/1.41 65 (all B_1_1 all B_2 is_bool(hAPP_f389811538l_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 66 (all B_1_1 all B_2 is_bool(hAPP_f937997336l_bool(B_1_1,B_2))) # 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].
% 1.10/1.41 67 (all B_1_1 all B_2 is_bool(hAPP_f1363661463l_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 68 (all B_1_1 all B_2 is_bool(hAPP_f595608956l_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 69 (all B_1_1 all B_2 is_bool(hAPP_f1295398978l_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 70 (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].
% 1.10/1.41 71 (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].
% 1.10/1.41 72 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A)))))) # label(fact_1_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 73 (all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A)))))) # label(fact_2_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 74 (all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A)))))) # label(fact_3_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 75 (all A (hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A)) -> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),A)))))) # label(fact_4_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 76 (all A (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) -> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A)))))) # label(fact_5_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 77 (all A (hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A)) -> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),A)))))) # label(fact_6_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 78 (all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A)))))) # label(fact_7_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 79 (all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 80 (all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A)))))) # label(fact_9_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 81 (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_10_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 82 (all H all F_1 (hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(H,F_1))))) # label(fact_11_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 83 (all H all F_1 (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(H,F_1))))) # label(fact_12_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 84 (all H all F_1 (hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(H,F_1))))) # label(fact_13_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 85 (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_14_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 86 (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_15_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 87 (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_16_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 88 (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_17_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 89 (all H all F_1 (hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(H,F_1))))) # label(fact_18_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 90 (all H all F_1 (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,F_1))))) # label(fact_19_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 91 (all H all F_1 (hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(H,F_1))))) # label(fact_20_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 92 (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_21_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 93 (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_22_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 94 (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_23_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 95 (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_24_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 96 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(H,F_1))))) # label(fact_25_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 97 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(H,F_1))))) # label(fact_26_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 98 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(H,F_1))))) # label(fact_27_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 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_28_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 100 (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_29_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 101 (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_30_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 102 (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_31_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 103 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(H,F_1))))) # label(fact_32_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 104 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,F_1))))) # label(fact_33_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 105 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(H,F_1))))) # label(fact_34_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 106 (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_35_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 107 (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_36_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 108 (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_37_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 109 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,F_1))))) # label(fact_38_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 110 (all H all F_1 (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(H,F_1))))) # label(fact_39_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 111 (all H all F_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(H,F_1))))) # label(fact_40_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 112 (all H all F_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(H,F_1))))) # label(fact_41_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 113 (all H all F_1 (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(H,F_1))))) # label(fact_42_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 114 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(H,F_1))))) # label(fact_43_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 115 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(H,F_1))))) # label(fact_44_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 116 (all A_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A))))) # label(fact_45_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 117 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A))))) # label(fact_46_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 118 (all A_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A))))) # label(fact_47_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 119 (all A_1 all A (hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A)) -> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(A_1,A))))) # label(fact_48_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 120 (all A_1 all A (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_1,A))))) # label(fact_49_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 121 (all A_1 all A (hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A)) -> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(A_1,A))))) # label(fact_50_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 122 (all A_1 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A))))) # label(fact_51_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 123 (all A_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A))))) # label(fact_52_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 124 (all A_1 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A))))) # label(fact_53_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 125 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_54_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 126 (all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_55_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 127 (all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_56_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 128 (all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_57_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 129 (all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_58_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 130 (all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_59_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 131 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_60_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 132 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_61_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 133 (all F all A (hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(F,A))),hAPP_f1690079119ol_nat(finite1352710292l_bool,A))))) # label(fact_62_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 134 (all F all A (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(F,A))),hAPP_f98387925ol_nat(finite269641166l_bool,A))))) # label(fact_63_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 135 (all F all A (hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(F,A))),hAPP_f1253658590ol_nat(finite1659325229l_bool,A))))) # label(fact_64_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 136 (all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_65_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 137 (all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_66_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 138 (all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_67_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 139 (all F all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_68_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 140 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_69_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 141 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_70_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 142 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_71_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 143 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_72_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 144 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_73_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 145 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_74_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 146 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_75_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 147 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_76_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 148 (all F all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_77_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 149 (all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_78_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 150 (all F all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_79_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 151 (all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,B)))))) # label(fact_80_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 152 (all A all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,B)))))) # label(fact_81_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 153 (all A all B (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B)))))) # label(fact_82_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 154 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B)))))) # label(fact_83_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 155 (all A all B (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B)))))) # label(fact_84_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 156 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B)))))) # label(fact_85_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 157 (all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B)),hAPP_f696928925ol_nat(finite346522414t_bool,A))) -> A = B)))) # label(fact_86_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 158 (all A all B (is_fun1661590463l_bool(A) & is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B)),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) -> A = B))))) # label(fact_87_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 159 (all A all B (is_fun949378684l_bool(A) & is_fun949378684l_bool(B) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) -> A = B))))) # label(fact_88_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 160 (all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B)),hAPP_f921600141ol_nat(finite_card_pname,A))) -> A = B))))) # label(fact_89_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 161 (all A all B (is_fun_a_bool(A) & is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B)),hAPP_fun_a_bool_nat(finite_card_a,A))) -> A = B))))) # label(fact_90_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 162 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B)),hAPP_f22106695ol_nat(finite_card_nat,A))) -> A = B)))) # label(fact_91_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 163 (all X_2 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)))))) # label(fact_92_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 164 (all X_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)))))) # label(fact_93_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.41 165 (all X_2 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)))))) # label(fact_94_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 166 (all X_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)))))) # label(fact_95_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 167 (all X_2 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)))))) # label(fact_96_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 168 (all X_2 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)))))) # label(fact_97_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 169 (all X_2 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A)) -> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_f696928925ol_nat(finite346522414t_bool,A)) & (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A)) -> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_98_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 170 (all X_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A)) & (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_99_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 171 (all X_2 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A)) & (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_100_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 172 (all X_2 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_f22106695ol_nat(finite_card_nat,A)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_101_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 173 (all X_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_f921600141ol_nat(finite_card_pname,A)) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_102_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 174 (all X_2 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_fun_a_bool_nat(finite_card_a,A)) & (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_103_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 175 (all X_2 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) -> (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A)) -> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))))) # label(fact_104_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 176 (all X_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))))) # label(fact_105_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 177 (all X_2 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) -> (-hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A)) -> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))))) # label(fact_106_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 178 (all X_2 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_107_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 179 (all X_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))))) # label(fact_108_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 180 (all X_2 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A))))) # label(fact_109_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 181 (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_110_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 182 (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_111_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 183 (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_112_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 184 (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_113_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 185 (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_114_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 186 (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_115_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 187 (all N_1 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M_2),N_1)))) # label(fact_116_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 188 (all K hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K))))) # label(fact_117_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 189 (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_118_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 190 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_119_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 191 (all Nat_1 all Nat (hAPP_nat_nat(suc,Nat_1) = hAPP_nat_nat(suc,Nat) <-> Nat_1 = Nat)) # label(fact_120_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 192 (all N_1 hAPP_nat_nat(suc,N_1) != N_1) # label(fact_121_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 193 (all N_1 N_1 != hAPP_nat_nat(suc,N_1)) # label(fact_122_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 194 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)) -> M_2 = N_1))) # label(fact_123_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 195 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))))) # label(fact_124_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 196 (all M_2 all N_1 (M_2 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_125_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 197 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)))) # label(fact_126_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 198 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1))) # label(fact_127_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 199 (all I_1 all J all K_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),K_1)),J)) # label(fact_128_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 200 (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_129_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 201 (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_130_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 202 (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_131_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 203 (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_132_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 204 (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_133_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 205 (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_134_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 206 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)))) # label(fact_135_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 207 (all A_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)))) # label(fact_136_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 208 (all A_1 all A (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A))) <-> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)))) # label(fact_137_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 209 (all A_1 all A (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A))) <-> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)))) # label(fact_138_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 210 (all A_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)))) # label(fact_139_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 211 (all A_1 all A (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A))) <-> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)))) # label(fact_140_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 212 (all A all B (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))))) # label(fact_141_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 213 (all A all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))))) # label(fact_142_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 214 (all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))))) # label(fact_143_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 215 (all A all B (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))))) # label(fact_144_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 216 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_145_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 217 (all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_146_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 218 (all A all B (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))))) # label(fact_147_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 219 (all A all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))))) # label(fact_148_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 220 (all A all B (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))))) # label(fact_149_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 221 (all A all B (hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) -> (hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) -> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))))) # label(fact_150_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 222 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_151_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 223 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_152_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 224 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_153_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 225 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> M_2 = hAPP_nat_nat(suc,N_1)))) # label(fact_154_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 226 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))))) # label(fact_155_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 227 (all Na all M_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_3))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_3)))) # label(fact_156_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 228 (all M_3 all Na (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),hAPP_nat_nat(suc,Na))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) | M_3 = hAPP_nat_nat(suc,Na))) # label(fact_157_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 229 (all M_3 all Na (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_3)))) # label(fact_158_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 230 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1))) # label(fact_159_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 231 (all M_2 all N_1 all K_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),N_1)),K_1)) # label(fact_160_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 232 (all M_2 all N_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1)) # label(fact_161_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 233 (all Na all K all M_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_3),K)),hAPP_nat_nat(minus_minus_nat(Na),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)))))) # label(fact_162_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 234 (all N_1 all K_1 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),K_1)),hAPP_nat_nat(minus_minus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1)))) # label(fact_163_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 235 (all Na all K all M_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na)) -> (hAPP_nat_nat(minus_minus_nat(M_3),K) = hAPP_nat_nat(minus_minus_nat(Na),K) <-> M_3 = Na)))) # label(fact_164_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 236 (all I_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1)) -> hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(minus_minus_nat(N_1),I_1)) = I_1)) # label(fact_165_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 237 (all L all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),L)),hAPP_nat_nat(minus_minus_nat(N_1),L))))) # label(fact_166_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 238 (all L all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M_2))))) # label(fact_167_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 239 (all M_2 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),N_1)),M_2))) # label(fact_168_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 240 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A))) -> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))))) # label(fact_169_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 241 (all F all A all B (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A))) -> (exists C_2 (is_fun_pname_bool(C_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_2)) & B = image_pname_a(F,C_2))))))) # label(fact_170_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 242 (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_171_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 243 (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_172_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 244 (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_173_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 245 (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_174_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 246 (all F all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A))) -> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1))))))))))) # label(fact_175_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 247 (all A all B_1 all F all X_2 (B_1 = hAPP_pname_a(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A)))))) # label(fact_176_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 248 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> A = B))) # label(fact_177_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 249 (all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) -> A = B)))) # label(fact_178_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 250 (all A all B (is_fun_a_bool(A) & is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) -> A = B)))) # label(fact_179_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 251 (all C_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B))))) # label(fact_180_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 252 (all C_1 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B))))) # label(fact_181_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 253 (all C_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B))))) # label(fact_182_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 254 (all B_1 all A_1 all B ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B)) -> A_1 = B_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B))))) # label(fact_183_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 255 (all B_1 all A_1 all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B)) -> A_1 = B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B))))) # label(fact_184_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 256 (all B_1 all A_1 all B ((-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B)) -> A_1 = B_1) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B))))) # label(fact_185_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 257 (all A_1 all B_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A))) -> (A_1 != B_1 -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))))) # label(fact_186_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 258 (all A_1 all B_1 all A (is_pname(A_1) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A))) -> (A_1 != B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)))))) # label(fact_187_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 259 (all A_1 all B_1 all A (is_a(A_1) & is_a(B_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A))) -> (A_1 != B_1 -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A)))))) # label(fact_188_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 260 (all A_1 all B hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(A_1,B)))) # label(fact_189_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 261 (all A_1 all B hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(A_1,B)))) # label(fact_190_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 262 (all A_1 all B hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(A_1,B)))) # label(fact_191_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 263 (all A_1 all B insert_nat(A_1,B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B)))) # label(fact_192_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 264 (all A_1 all B insert_pname(A_1,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B)))) # label(fact_193_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 265 (all A_1 all B insert_a(A_1,B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B)))) # label(fact_194_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 266 (all A_1 all B insert_fun_nat_bool(A_1,B) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B)))) # label(fact_195_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 267 (all A_1 all B insert1325755072e_bool(A_1,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B)))) # label(fact_196_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 268 (all A_1 all B insert_fun_a_bool(A_1,B) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B)))) # label(fact_197_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 269 (all A_1 all Pa insert_nat(A_1,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_1))),Pa))) # label(fact_198_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 270 (all A_1 all Pa insert_pname(A_1,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_1))),Pa))) # label(fact_199_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 271 (all A_1 all Pa insert_a(A_1,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_1))),Pa))) # label(fact_200_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 272 (all A_1 all Pa insert_fun_nat_bool(A_1,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_1))),Pa))) # label(fact_201_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 273 (all A_1 all Pa insert1325755072e_bool(A_1,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_1))),Pa))) # label(fact_202_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 274 (all A_1 all Pa insert_fun_a_bool(A_1,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_1))),Pa))) # label(fact_203_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 275 (all X_2 all A insert_nat(X_2,insert_nat(X_2,A)) = insert_nat(X_2,A)) # label(fact_204_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 276 (all X_2 all A insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A)) # label(fact_205_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 277 (all X_2 all A insert_a(X_2,insert_a(X_2,A)) = insert_a(X_2,A)) # label(fact_206_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 278 (all X_2 all Y_1 all A insert_nat(X_2,insert_nat(Y_1,A)) = insert_nat(Y_1,insert_nat(X_2,A))) # label(fact_207_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 279 (all X_2 all Y_1 all A insert_pname(X_2,insert_pname(Y_1,A)) = insert_pname(Y_1,insert_pname(X_2,A))) # label(fact_208_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 280 (all X_2 all Y_1 all A insert_a(X_2,insert_a(Y_1,A)) = insert_a(Y_1,insert_a(X_2,A))) # label(fact_209_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 281 (all A_1 all B_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A))) <-> A_1 = B_1 | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)))) # label(fact_210_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 282 (all A_1 all B_1 all A (is_pname(A_1) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A))) <-> A_1 = B_1 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))))) # label(fact_211_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 283 (all A_1 all B_1 all A (is_a(A_1) & is_a(B_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A))) <-> A_1 = B_1 | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))))) # label(fact_212_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 284 (all Y_1 all A all X_2 (hBOOL(hAPP_nat_bool(insert_nat(Y_1,A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_nat_bool(A,X_2)))) # label(fact_213_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 285 (all Y_1 all A all X_2 (is_pname(Y_1) & is_pname(X_2) -> (hBOOL(hAPP_pname_bool(insert_pname(Y_1,A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_pname_bool(A,X_2))))) # label(fact_214_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 286 (all Y_1 all A all X_2 (is_a(Y_1) & is_a(X_2) -> (hBOOL(hAPP_a_bool(insert_a(Y_1,A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_a_bool(A,X_2))))) # label(fact_215_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 287 (all B all X_2 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) -> (insert_nat(X_2,A) = insert_nat(X_2,B) <-> A = B)))) # label(fact_216_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 288 (all B all X_2 all A (is_fun_pname_bool(B) & is_fun_pname_bool(A) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) -> (insert_pname(X_2,A) = insert_pname(X_2,B) <-> A = B))))) # label(fact_217_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 289 (all B all X_2 all A (is_fun_a_bool(B) & is_fun_a_bool(A) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) -> (insert_a(X_2,A) = insert_a(X_2,B) <-> A = B))))) # label(fact_218_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 290 (all B_1 all A_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B))))) # label(fact_219_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 291 (all B_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B))))) # label(fact_220_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 292 (all B_1 all A_1 all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B))))) # label(fact_221_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 293 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> insert_nat(A_1,A) = A)) # label(fact_222_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 294 (all A_1 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> insert_pname(A_1,A) = A))) # label(fact_223_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 295 (all A_1 all A (is_fun_a_bool(A) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A)) -> insert_a(A_1,A) = A))) # label(fact_224_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.42 296 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A))) # label(fact_225_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 297 (all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A))) # label(fact_226_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 298 (all A hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),A))) # label(fact_227_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 299 (all A all B (A = B <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)))) # label(fact_228_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 300 (all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (A = B <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))))) # label(fact_229_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 301 (all A all B (is_fun_a_bool(A) & is_fun_a_bool(B) -> (A = B <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))))) # label(fact_230_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 302 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_231_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 303 (all A all B (A = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_232_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 304 (all A all B (A = B -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)))) # label(fact_233_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 305 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)))) # label(fact_234_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 306 (all A all B (A = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)))) # label(fact_235_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 307 (all A all B (A = B -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)))) # label(fact_236_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 308 (all X_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))))) # label(fact_237_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 309 (all X_2 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))))) # label(fact_238_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 310 (all X_2 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) # label(fact_239_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 311 (all B all X_2 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))))) # label(fact_240_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 312 (all B all X_2 all A (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))))) # label(fact_241_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 313 (all B all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) # label(fact_242_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 314 (all X_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))))) # label(fact_243_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 315 (all X_2 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))))) # label(fact_244_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 316 (all X_2 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) # label(fact_245_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 317 (all C all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C))))) # label(fact_246_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 318 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))))) # label(fact_247_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 319 (all C all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C))))) # label(fact_248_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 320 (all A all B (A = B -> -(hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))))) # label(fact_249_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 321 (all A all B (A = B -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))))) # label(fact_250_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 322 (all A all B (A = B -> -(hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))))) # label(fact_251_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 323 (all X_2 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) <-> hBOOL(hAPP_nat_bool(A,X_2)))) # label(fact_252_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 324 (all X_2 all A (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) <-> hBOOL(hAPP_a_bool(A,X_2)))) # label(fact_253_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 325 (all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) <-> hBOOL(hAPP_pname_bool(A,X_2)))) # label(fact_254_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 326 (all Pa (is_fun_pname_bool(Pa) -> collect_pname(Pa) = Pa)) # label(fact_255_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 327 (all Pa collect_fun_nat_bool(Pa) = Pa) # label(fact_256_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 328 (all Pa (is_fun1661590463l_bool(Pa) -> collec1974731493e_bool(Pa) = Pa)) # label(fact_257_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 329 (all Pa (is_fun949378684l_bool(Pa) -> collect_fun_a_bool(Pa) = Pa)) # label(fact_258_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 330 (all Pa collect_nat(Pa) = Pa) # label(fact_259_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 331 (all Z all F all A (is_a(Z) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z),image_pname_a(F,A))) <-> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) & Z = hAPP_pname_a(F,X_1)))))) # label(fact_260_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 332 (all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_2)),image_pname_a(F,A))))) # label(fact_261_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 333 (all B_1 all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (B_1 = hAPP_pname_a(F,X_2) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A)))))) # label(fact_262_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 334 (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_263_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 335 (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_264_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 336 (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_265_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 337 (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_266_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 338 (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_267_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 339 (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_268_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 340 (all B all A_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),insert_nat(A_1,B)))) # label(fact_269_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 341 (all B all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_1,B)))) # label(fact_270_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 342 (all B all A_1 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),insert_a(A_1,B)))) # label(fact_271_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 343 (all X_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_2,A)),B)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_272_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 344 (all X_2 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_273_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 345 (all X_2 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2,A)),B)) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)))) # label(fact_274_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 346 (all B all X_2 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(X_2,B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))))) # label(fact_275_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 347 (all B all X_2 all A (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))))) # label(fact_276_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 348 (all B all X_2 all A (-hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(X_2,B))) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))))) # label(fact_277_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 349 (all B_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(B_1,B))))) # label(fact_278_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 350 (all B_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(B_1,B))))) # label(fact_279_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 351 (all B_1 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(B_1,B))))) # label(fact_280_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 352 (all A_1 all C all D (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),D)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_1,C)),insert_nat(A_1,D))))) # label(fact_281_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 353 (all A_1 all C all D (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_1,C)),insert_pname(A_1,D))))) # label(fact_282_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 354 (all A_1 all C all D (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C),D)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_1,C)),insert_a(A_1,D))))) # label(fact_283_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 355 (all F all A_1 all B image_pname_a(F,insert_pname(A_1,B)) = insert_a(hAPP_pname_a(F,A_1),image_pname_a(F,B))) # label(fact_284_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 356 (all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> insert_a(hAPP_pname_a(F,X_2),image_pname_a(F,A)) = image_pname_a(F,A))) # label(fact_285_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 357 (all B all F all A (is_fun_a_bool(B) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A))) <-> (exists AA (is_fun_pname_bool(AA) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A)) & B = image_pname_a(F,AA)))))) # label(fact_286_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 358 (all F all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),image_pname_a(F,B))))) # label(fact_287_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 359 (all B_1 all F all A (is_a(B_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A))) -> -(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)))))))) # label(fact_288_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 360 (all B all A ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_289_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 361 (all B all A ((all X_1 (is_a(X_1) -> (hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)))) # label(fact_290_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 362 (all B all A ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_291_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 363 (all I all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((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),I)))))) # label(fact_292_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 364 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1)) -> (exists M M_1 = hAPP_nat_nat(suc,M)))) # label(fact_293_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 365 (all F all B all A ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B))))) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),B)))) # label(fact_294_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 366 (all X_2 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2))) # label(fact_295_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 367 (all X_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_2),X_2))) # label(fact_296_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 368 (all X_3 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),X_3))) # label(fact_297_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 369 (all X_2 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_2),X_2))) # label(fact_298_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 370 (all N (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N)) <-> (exists M all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)))))) # label(fact_299_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 371 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 372 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 373 (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].
% 1.10/1.43 374 (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].
% 1.10/1.43 375 (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].
% 1.10/1.43 376 (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].
% 1.10/1.43 377 (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].
% 1.10/1.43 378 (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].
% 1.10/1.43 379 (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].
% 1.10/1.43 380 (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].
% 1.10/1.43 381 (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].
% 1.10/1.43 382 (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].
% 1.10/1.43 383 (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].
% 1.10/1.43 384 (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].
% 1.10/1.43 385 (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].
% 1.10/1.43 386 (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].
% 1.10/1.43 387 (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].
% 1.10/1.43 388 (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].
% 1.10/1.43 389 (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].
% 1.10/1.43 390 (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].
% 1.10/1.43 391 (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].
% 1.10/1.43 392 (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].
% 1.10/1.43 393 (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].
% 1.10/1.43 394 (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].
% 1.10/1.43 395 (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].
% 1.10/1.43 396 (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].
% 1.10/1.43 397 (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].
% 1.10/1.43 398 (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].
% 1.10/1.43 399 (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].
% 1.10/1.43 400 (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].
% 1.10/1.43 401 (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].
% 1.10/1.43 402 (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].
% 1.10/1.43 403 (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].
% 1.10/1.43 404 (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].
% 1.10/1.43 405 (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].
% 1.10/1.43 406 (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].
% 1.10/1.43 407 (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].
% 1.10/1.43 408 (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].
% 1.10/1.43 409 (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].
% 1.10/1.43 410 (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].
% 1.10/1.43 411 (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_006) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 412 (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].
% 1.10/1.43 413 (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].
% 1.10/1.43 414 (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].
% 1.10/1.43 415 (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].
% 1.10/1.43 416 (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].
% 1.10/1.43 417 (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].
% 1.10/1.43 418 (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_008) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 419 (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].
% 1.10/1.43 420 (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_009) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 421 (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_010) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 422 (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].
% 1.10/1.62 423 (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].
% 1.10/1.62 424 (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__011) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.62 425 (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_012) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.62 426 (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].
% 1.10/1.62 427 (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].
% 1.10/1.62 428 (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].
% 1.10/1.62 429 (all P all Q all R hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(P),Q),R) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.62 430 (all P all Q all R hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(P),Q),R) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.62 431 (all P all Q all R hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(P),Q),R) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.62
% 1.10/1.62 ============================== end of process non-clausal formulas ===
% 1.10/1.62
% 1.10/1.62 ============================== PROCESS INITIAL CLAUSES ===============
% 1.10/1.62
% 1.10/1.62 ============================== PREDICATE ELIMINATION =================
% 1.10/1.62
% 1.10/1.62 ============================== end predicate elimination =============
% 1.10/1.62
% 1.10/1.62 Auto_denials: (non-Horn, no changes).
% 1.10/1.62
% 1.10/1.62 Term ordering decisions:
% 1.10/1.62 Function symbol KB weights: ord_less_eq_nat=1. finite_finite_pname=1. ord_le1311769555a_bool=1. finite_finite_nat=1. member_a=1. member_pname=1. finite_finite_a=1. suc=1. ord_le313189616e_bool=1. ord_le1568362934t_bool=1. member_nat=1. finite2012431853t_bool=1. finite347923420a_bool=1. finite595471783e_bool=1. fdisj=1. finite_card_a=1. finite_card_pname=1. finite_card_nat=1. finite1306199131a_bool=1. finite1340463720e_bool=1. finite346522414t_bool=1. fconj=1. fimplies=1. finite1381704300l_bool=1. finite1701474069l_bool=1. finite786885583l_bool=1. fNot=1. bool=1. fequal_a=1. u=1. fequal533582459e_bool=1. fequal_fun_a_bool=1. fequal_fun_nat_bool=1. fequal_nat=1. fequal_pname=1. member799430823e_bool=1. member_fun_a_bool=1. member_fun_nat_bool=1. ord_le1375614389l_bool=1. ord_le1454342156l_bool=1. ord_le675606854l_bool=1. g=1. mgt_call=1. pname=1. x_a=1. na=1. pn=1. finite1343359508l_bool=1. finite1352710292l_bool=1. finite1491191519l_bool=1. finite1659325229l_bool=1. finite269641166l_bool=1. finite719726885l_bool=1. ord_le1375671464l_bool=1. ord_le65145710l_bool=1. ord_le967226251l_bool=1. hAPP_fun_a_bool_bool=1. hAPP_f1664156314l_bool=1. hAPP_f54304608l_bool=1. hAPP_nat_bool=1. hAPP_n1699378549t_bool=1. hAPP_nat_nat=1. hAPP_f1631501043l_bool=1. hAPP_f434788991l_bool=1. hAPP_a85458249l_bool=1. hAPP_f103356543l_bool=1. hAPP_p338031245l_bool=1. hAPP_f1637334154l_bool=1. hAPP_f1935102916l_bool=1. hAPP_f621171935l_bool=1. insert_a=1. insert_pname=1. insert_nat=1. hAPP_n215258509l_bool=1. image_pname_a=1. hAPP_fun_a_bool_nat=1. hAPP_f921600141ol_nat=1. hAPP_bool_bool=1. hAPP_f22106695ol_nat=1. hAPP_a_bool=1. hAPP_pname_bool=1. hAPP_f2009550088ol_nat=1. hAPP_f55526627ol_nat=1. hAPP_f696928925ol_nat=1. hAPP_b589554111l_bool=1. hAPP_f292226953l_bool=1. hAPP_f389811538l_bool=1. hAPP_f937997336l_bool=1. hAPP_pname_a=1. cOMBS_568398431l_bool=1. insert1325755072e_bool=1. insert_fun_a_bool=1. cOMBB_675860798_pname=1. cOMBS_1035972772l_bool=1. cOMBS_350070575l_bool=1. cOMBS_a_bool_bool=1. insert_fun_nat_bool=1. cOMBB_1015721476ol_nat=1. cOMBB_1972296269bool_a=1. cOMBB_2095475776e_bool=1. cOMBB_338059395a_bool=1. cOMBB_444170502t_bool=1. cOMBS_1187019125l_bool=1. cOMBS_nat_bool_bool=1. hAPP_a_fun_a_bool=1. hAPP_p61793385e_bool=1. hAPP_f1434722111l_bool=1. hAPP_f1772781669l_bool=1. hAPP_f510955609l_bool=1. fun=1. hAPP_f759274231e_bool=1. hAPP_n1025906991e_bool=1. hAPP_nat_fun_a_bool=1. hAPP_f1951378235l_bool=1. hAPP_f2050579477a_bool=1. hAPP_f2117159681l_bool=1. hAPP_f285962445l_bool=1. hAPP_f556039215l_bool=1. hAPP_f559147733l_bool=1. cOMBB_2140588453a_bool=1. cOMBB_307249310e_bool=1. cOMBB_647938656_pname=1. cOMBB_bool_bool_a=1. hAPP_a93125764e_bool=1. hAPP_f1050622307l_bool=1. hAPP_f1246832597l_bool=1. hAPP_f1759205631l_bool=1. hAPP_f760187903l_bool=1. hAPP_f800510211t_bool=1. hAPP_p1534023578a_bool=1. image_112932426a_bool=1. image_1283814551_pname=1. image_1655916159e_bool=1. image_1854862208_pname=1. image_1921560913_pname=1. image_47868345e_bool=1. image_876012084bool_a=1. image_a_a=1. image_a_pname=1. image_fun_a_bool_a=1. image_fun_nat_bool_a=1. image_nat_a=1. image_nat_fun_a_bool=1. image_nat_pname=1. image_pname_pname=1. cOMBB_1897541054_pname=1. cOMBB_238756964t_bool=1. cOMBB_bool_bool_nat=1. hAPP_a_fun_bool_bool=1. hAPP_f1295398978l_bool=1. hAPP_f1363661463l_bool=1. hAPP_f1476298914l_bool=1. hAPP_f1748468828l_bool=1. hAPP_f198738859l_bool=1. hAPP_f595608956l_bool=1. hAPP_n1006566506l_bool=1. hAPP_p393069232l_bool=1. image_1551609309ol_nat=1. image_1604018183_pname=1. image_1705983821_pname=1. image_2129980159t_bool=1. image_26036933t_bool=1. image_349102846bool_a=1. image_496248727ol_nat=1. image_526090948bool_a=1. image_573985017bool_a=1. image_990671762_pname=1. image_a_nat=1. image_fun_a_bool_nat=1. image_pname_nat=1. hAPP_f1253658590ol_nat=1. hAPP_f1690079119ol_nat=1. hAPP_f98387925ol_nat=1. image_1079571347ol_nat=1. image_1154884483l_bool=1. image_1208015684l_bool=1. image_1420695166l_bool=1. image_1607900221l_bool=1. image_1642285373l_bool=1. image_1802975832ol_nat=1. image_1874789623l_bool=1. image_2089570637ol_nat=1. insert1117693814l_bool=1. insert1457093509l_bool=1. insert2003652156l_bool=1. f6=1. f10=1. f11=1. f12=1. f14=1. f17=1. minus_minus_nat=1. collec1974731493e_bool=1. collect_fun_a_bool=1. collect_nat=1. collect_pname=1. collect_fun_nat_bool=1. collect_a=1. cOMBC_nat_nat_bool=1. cOMBC_1284144636l_bool=1. cOMBC_1693257480l_bool=1. cOMBC_1732670874l_bool=1. cOMBC_1058051404l_bool=1. cOMBC_1149511130e_bool=1. cOMBC_a_a_bool=1. cOMBC_1245412066l_bool=1. cOMBC_1355376034l_bool=1. cOMBC_1880041174l_bool=1. cOMBC_1988546018l_bool=1. cOMBC_226598744l_bool=1. cOMBC_1269652216l_bool=1. cOMBC_331553030l_bool=1. cOMBC_336095980l_bool=1. cOMBC_595898202l_bool=1. cOMBC_636888218l_bool=1. cOMBC_7971162l_bool=1. cOMBC_pname_a_bool=1. p=1. collec1015864663l_bool=1. collec1613912337l_bool=1. collec1635217238l_bool=1. collec1874991203l_bool=1. collec707592106l_bool=1. collec792590109l_bool=1. undefi1699038445l_bool=1. undefi17486888e_bool=1. undefi64961550l_bool=1. undefined_a=1. undefined_fun_a_bool=1. undefined_pname=1. f16=1. f1=1. f2=1. f3=1. f4=1. f5=1. f7=1. f8=1. f9=1. f13=1. f15=1.
% 16.04/16.36
% 16.04/16.36 ============================== end of process initial clauses ========
% 16.04/16.36
% 16.04/16.36 ============================== CLAUSES FOR SEARCH ====================
% 16.04/16.36
% 16.04/16.36 ============================== end of clauses for search =============
% 16.04/16.36
% 16.04/16.36 ============================== SEARCH ================================
% 16.04/16.36
% 16.04/16.36 % Starting search at 0.27 seconds.
% 16.04/16.36
% 16.04/16.36 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 27 (0.00 of 0.65 sec).
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=54.000, iters=3351
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=49.000, iters=3335
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=46.000, iters=3335
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=41.000, iters=3339
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=39.000, iters=3360
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=37.000, iters=3333
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=36.000, iters=3361
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=35.000, iters=3340
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=34.000, iters=3340
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=33.000, iters=3372
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=32.000, iters=3340
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=31.000, iters=3348
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=29.000, iters=3336
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=28.000, iters=3343
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=25.000, iters=3336
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=23.000, iters=3352
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=22.000, iters=3346
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=21.000, iters=3334
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=18.000, iters=5250
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=13.000, iters=4762
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=10.000, iters=4041
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=9.000, iters=3587
% 16.04/16.36
% 16.04/16.36 Low Water (keep): wt=8.000, iters=3339
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=2320, wt=113.000
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=2318, wt=105.000
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=2133, wt=71.000
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=11689, wt=70.000
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=10351, wt=67.000
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=11912, wt=66.000
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=10848, wt=63.000
% 16.04/16.36
% 16.04/16.36 Low Water (displace): id=12295, wt=8.000
% 16.04/16.36
% 16.04/16.36 ============================== PROOF =================================
% 16.04/16.36 % SZS status Theorem
% 16.04/16.36 % SZS output start Refutation
% 16.04/16.36
% 16.04/16.36 % Proof 1 at 14.82 (+ 0.20) seconds.
% 16.04/16.36 % Length of proof is 14.
% 16.04/16.36 % Level of proof is 4.
% 16.04/16.36 % Maximum clause weight is 29.000.
% 16.04/16.36 % Given clauses 7044.
% 16.04/16.36
% 16.04/16.36 265 (all A_1 all B insert_a(A_1,B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B)))) # label(fact_194_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 16.04/16.36 332 (all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_2)),image_pname_a(F,A))))) # label(fact_261_imageI) # label(axiom) # label(non_clause). [assumption].
% 16.04/16.36 345 (all X_2 all A all B (hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2,A)),B)) <-> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)))) # label(fact_274_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 16.04/16.36 732 insert_a(A,B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B))) # label(fact_194_insert__compr) # label(axiom). [clausify(265)].
% 16.04/16.36 849 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B)) | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(C,A)),image_pname_a(C,B))) # label(fact_261_imageI) # label(axiom). [clausify(332)].
% 16.04/16.36 878 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A,B)),C)) | -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A),C)) | -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C)) # label(fact_274_insert__subset) # label(axiom). [clausify(345)].
% 16.04/16.36 879 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B)))),C)) | -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A),C)) | -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C)). [copy(878),rewrite([732(2)])].
% 16.04/16.36 1011 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) # label(conj_1) # label(hypothesis). [assumption].
% 16.04/16.36 1015 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) # label(conj_4) # label(hypothesis). [assumption].
% 16.04/16.36 1017 -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))) # label(conj_6) # label(negated_conjecture). [assumption].
% 16.04/16.36 1018 -hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))). [copy(1017),rewrite([732(6)])].
% 16.04/16.36 2076 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))) | -hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A),image_pname_a(mgt_call,u))). [resolve(1011,a,879,c)].
% 16.04/16.36 2121 hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(A,pn)),image_pname_a(A,u))). [resolve(1015,a,849,a)].
% 16.04/16.36 56203 $F. [resolve(2121,a,2076,b),unit_del(a,1018)].
% 16.04/16.36
% 16.04/16.36 % SZS output end Refutation
% 16.04/16.36 ============================== end of proof ==========================
% 16.04/16.36
% 16.04/16.36 ============================== STATISTICS ============================
% 16.04/16.36
% 16.04/16.36 Given=7044. Generated=301474. Kept=55677. proofs=1.
% 16.04/16.36 Usable=7043. Sos=9997. Demods=375. Limbo=0, Disabled=39185. Hints=0.
% 16.04/16.36 Megabytes=112.98.
% 16.04/16.36 User_CPU=14.82, System_CPU=0.20, Wall_clock=15.
% 16.04/16.36
% 16.04/16.36 ============================== end of statistics =====================
% 16.04/16.36
% 16.04/16.36 ============================== end of search =========================
% 16.04/16.36
% 16.04/16.36 THEOREM PROVED
% 16.04/16.36 % SZS status Theorem
% 16.04/16.36
% 16.04/16.36 Exiting with 1 proof.
% 16.04/16.36
% 16.04/16.36 Process 11453 exit (max_proofs) Sun Jun 5 02:09:49 2022
% 16.04/16.36 Prover9 interrupted
%------------------------------------------------------------------------------