TSTP Solution File: SWW474+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW474+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:11 EDT 2022
% Result : Theorem 24.86s 25.08s
% Output : Refutation 24.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW474+3 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 4 14:11:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.88/2.12 ============================== Prover9 ===============================
% 1.88/2.12 Prover9 (32) version 2009-11A, November 2009.
% 1.88/2.12 Process 25792 was started by sandbox on n025.cluster.edu,
% 1.88/2.12 Sat Jun 4 14:11:33 2022
% 1.88/2.12 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25639_n025.cluster.edu".
% 1.88/2.12 ============================== end of head ===========================
% 1.88/2.12
% 1.88/2.12 ============================== INPUT =================================
% 1.88/2.12
% 1.88/2.12 % Reading from file /tmp/Prover9_25639_n025.cluster.edu
% 1.88/2.12
% 1.88/2.12 set(prolog_style_variables).
% 1.88/2.12 set(auto2).
% 1.88/2.12 % set(auto2) -> set(auto).
% 1.88/2.12 % set(auto) -> set(auto_inference).
% 1.88/2.12 % set(auto) -> set(auto_setup).
% 1.88/2.12 % set(auto_setup) -> set(predicate_elim).
% 1.88/2.12 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.88/2.12 % set(auto) -> set(auto_limits).
% 1.88/2.12 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.88/2.12 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.88/2.12 % set(auto) -> set(auto_denials).
% 1.88/2.12 % set(auto) -> set(auto_process).
% 1.88/2.12 % set(auto2) -> assign(new_constants, 1).
% 1.88/2.12 % set(auto2) -> assign(fold_denial_max, 3).
% 1.88/2.12 % set(auto2) -> assign(max_weight, "200.000").
% 1.88/2.12 % set(auto2) -> assign(max_hours, 1).
% 1.88/2.12 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.88/2.12 % set(auto2) -> assign(max_seconds, 0).
% 1.88/2.12 % set(auto2) -> assign(max_minutes, 5).
% 1.88/2.12 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.88/2.12 % set(auto2) -> set(sort_initial_sos).
% 1.88/2.12 % set(auto2) -> assign(sos_limit, -1).
% 1.88/2.12 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.88/2.12 % set(auto2) -> assign(max_megs, 400).
% 1.88/2.12 % set(auto2) -> assign(stats, some).
% 1.88/2.12 % set(auto2) -> clear(echo_input).
% 1.88/2.12 % set(auto2) -> set(quiet).
% 1.88/2.12 % set(auto2) -> clear(print_initial_clauses).
% 1.88/2.12 % set(auto2) -> clear(print_given).
% 1.88/2.12 assign(lrs_ticks,-1).
% 1.88/2.12 assign(sos_limit,10000).
% 1.88/2.12 assign(order,kbo).
% 1.88/2.12 set(lex_order_vars).
% 1.88/2.12 clear(print_given).
% 1.88/2.12
% 1.88/2.12 % formulas(sos). % not echoed (1441 formulas)
% 1.88/2.12
% 1.88/2.12 ============================== end of input ==========================
% 1.88/2.12
% 1.88/2.12 % From the command line: assign(max_seconds, 300).
% 1.88/2.12
% 1.88/2.12 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.88/2.12
% 1.88/2.12 % Formulas that are not ordinary clauses:
% 1.88/2.12 1 (all B_1_1 is_bool(finite1653727294m_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Ocom_000tc__fun_Itc__Com__Ocom_Mt) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 2 (all B_1_1 is_bool(finite2017903282e_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Opname_000tc__fun_Itc__Com__Opnam) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 3 (all B_1_1 is_bool(finite318301748l_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 4 (all B_1_1 is_bool(finite2036162504e_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otri) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 5 (all B_1_1 is_bool(finite367769966e_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 6 (all B_1_1 is_bool(finite1765632844e_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvf) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 7 (all B_1_1 all B_2_1 is_bool(finite860057415ne_com(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Ocom) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 8 (all B_1_1 all B_2_1 is_bool(finite1282449217_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 9 (all B_1_1 all B_2_1 is_bool(finite683959609_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 10 (all B_1_1 all B_2_1 is_bool(finite1626890877e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 11 (all B_1_1 all B_2_1 is_bool(finite2009063477e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 12 (all B_1_1 all B_2_1 is_bool(finite666746948em_com(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Ocom) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 13 (all B_1_1 all B_2_1 is_bool(finite89670078_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 14 (all B_1_1 all B_2_1 is_bool(finite416071164_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 15 (all B_1_1 all B_2_1 is_bool(finite1268145088e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 16 (all B_1_1 all B_2_1 is_bool(finite688249778e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Hoare____Mirabelle____uwgp) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 17 (all B_1_1 is_fun1661590463l_bool(inj_on_pname_pname(B_1_1))) # label(gsy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 18 (all B_1_1 is_fun1661590463l_bool(inj_on621632009_state(B_1_1))) # label(gsy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 19 (all B_1_1 is_fun1661590463l_bool(inj_on737724108_pname(B_1_1))) # label(gsy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 20 (all B_1_1 is_fun_pname_bool(dom_pname_com(B_1_1))) # label(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom) # label(hypothesis) # label(non_clause). [assumption].
% 1.88/2.12 21 (all B_1_1 is_fun_pname_bool(dom_pname_pname(B_1_1))) # label(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 22 (all B_1_1 is_fun_pname_bool(dom_pn480909800_state(B_1_1))) # label(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otrip) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 23 (all B_1_1 is_bool(is_none_com(B_1_1))) # label(gsy_c_Option_Ois__none_000tc__Com__Ocom) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 24 (all B_1_1 (is_option_pname(B_1_1) -> is_bool(is_none_pname(B_1_1)))) # label(gsy_c_Option_Ois__none_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 25 (all B_1_1 is_bool(is_non1379144176_state(B_1_1))) # label(gsy_c_Option_Ois__none_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 26 (all B_1_1 (is_option_pname(B_1_1) -> is_fun_pname_bool(set_pname(B_1_1)))) # label(gsy_c_Option_Oset_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 27 (all B_1_1 all B_2_1 is_fun_pname_bool(vimage1011814463_state(B_1_1,B_2_1))) # label(gsy_c_Set_Ovimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__Ot) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 28 (all B_1_1 all B_2_1 is_pname(hAPP_com_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ocom_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 29 (all B_1_1 all B_2_1 is_bool(hAPP_com_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ocom_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 30 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_c1967741679e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ocom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 31 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_pname(hAPP_pname_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 32 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_1_1) & is_pname(B_2_1) -> is_bool(hAPP_pname_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 33 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_option_pname(hAPP_p1252095976_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 34 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 35 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 36 (all B_1_1 all B_2_1 is_bool(hAPP_state_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 37 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 38 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun_pname_bool(hAPP_b76515610e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 39 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_b357632156l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 40 (all B_1_1 all B_2_1 is_pname(hAPP_H1193503499_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 41 (all B_1_1 all B_2_1 is_bool(hAPP_H242767318e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_001) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 42 (all B_1_1 all B_2_1 is_option_pname(hAPP_H1671063474_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_002) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 43 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H1776011827e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_003) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 44 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_H358531139l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_004) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 45 (all B_1_1 all B_2_1 is_bool(hAPP_option_com_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 46 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_o1092643708e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__fun_Itc__Com__Opname_M) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 47 (all B_1_1 all B_2_1 (is_option_pname(B_2_1) -> is_pname(hAPP_o593586696_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Option__Ooption_Itc__Com__Opname_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 48 (all B_1_1 all B_2_1 is_bool(hAPP_f990396704l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 49 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f1438183293e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 50 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 51 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_1_1) & is_fun_pname_bool(B_2_1) -> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 52 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 53 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 54 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f42430548e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__fun_Itc__Com__Opname_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 55 (all B_1_1 all B_2_1 is_bool(hAPP_f327114704l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 56 (all B_1_1 all B_2_1 is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 57 (all B_1_1 all B_2_1 is_pname(hAPP_f88366945_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 58 (all B_1_1 all B_2_1 is_bool(hAPP_f1378282496l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O_005) # label(hypothesis) # label(non_clause). [assumption].
% 1.88/2.12 59 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f1083669085e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O_006) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 60 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_f1709493145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O_007) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 61 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 62 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun_pname_bool(hAPP_f674760225e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_008) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 63 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_009) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 64 (all B_1_1 all B_2_1 is_bool(hAPP_f1410040974l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 65 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f306376939e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It_010) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 66 (all B_1_1 all B_2_1 is_bool(hAPP_f389811538l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 67 (all B_1_1 all B_2_1 is_bool(hAPP_f1178960312l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 68 (all G_2 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),bot_bo784226126e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 69 (all Ts all G_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),G_2)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)))) # label(fact_1_asm) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 70 (all Ts all G_2 all Ts_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),Ts_1)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))))) # label(fact_2_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 71 (all G_2 all G_3 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_3),Ts)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,G_3),G_2)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 72 (all G_2 all G_3 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_3),Ts)) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),G_3)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 73 (all Ts all G_2 all T (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),bot_bo784226126e_bool))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),Ts)))))) # label(fact_5_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 74 (all G_2 all T all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),Ts))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),bot_bo784226126e_bool))) & hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)))) # label(fact_6_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 75 (all Pn_1 all G_2 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),G_2)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1)))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),bot_bo784226126e_bool))))) # label(fact_7_MGT__BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 76 (all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,hAPP_f783502055l_bool(collec1613912337l_bool,hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,ord_le675606854l_bool),A)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 77 (all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hBOOL(hAPP_f1178960312l_bool(finite1203709595l_bool,hAPP_f347786453l_bool(collec895295961l_bool,hAPP_f1516997247l_bool(hAPP_f1901243753l_bool(cOMBC_991209188l_bool,ord_le694194916l_bool),A)))))) # label(fact_9_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 78 (all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,ord_le1449778818e_bool),A)))))) # label(fact_10_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 79 (all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,ord_le313189616e_bool),A)))))) # label(fact_11_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 80 (all H_1 all Fa (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f1709493145l_bool(image_1403607267e_bool(H_1),Fa))))) # label(fact_12_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 81 (all H_1 all Fa (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f849457489l_bool(image_995511119e_bool(H_1),Fa))))) # label(fact_13_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 82 (all H_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(H_1),Fa))))) # label(fact_14_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 83 (all H_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f1492100075l_bool(image_234387449e_bool(H_1),Fa))))) # label(fact_15_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 84 (all H_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f509793681e_bool(image_845802851_state(H_1),Fa))))) # label(fact_16_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 85 (all H_1 all Fa (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f1216288071e_bool(image_1497401961_state(H_1),Fa))))) # label(fact_17_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 86 (all H_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(H_1),Fa))))) # label(fact_18_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 87 (all H_1 all Fa (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f306376939e_bool(image_1863446033_pname(H_1),Fa))))) # label(fact_19_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 88 (all H_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(H_1),Fa))))) # label(fact_20_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 89 (all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A))) # label(fact_21_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 90 (all A hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,bot_bot_fun_com_bool),A))) # label(fact_22_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 91 (all A hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A))) # label(fact_23_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 92 (all A_4 all A (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A))))) # label(fact_24_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 93 (all A_4 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A))))) # label(fact_25_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 94 (all A_4 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A))))) # label(fact_26_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.12 95 (all A_4 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A))))) # label(fact_27_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 96 (all A_4 all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A))))) # label(fact_28_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 97 (all Q_1 all P_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1))) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)))))) # label(fact_34_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 98 (all Q_1 all P_1 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1))) | hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),P_1)),Q_1)))))) # label(fact_35_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 99 (all Q_1 all P_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,P_1))) | hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,Q_1))) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),P_1)),Q_1)))))) # label(fact_36_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 100 (all Q_1 all P_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1))) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)))))) # label(fact_37_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 101 (all C all A ((A = bot_bo784226126e_bool -> hAPP_f1083669085e_bool(image_1774499931_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,C)),A) = bot_bo844097828e_bool) & (A != bot_bo784226126e_bool -> hAPP_f1083669085e_bool(image_1774499931_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool)))) # label(fact_38_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 102 (all C all A ((A = bot_bo784226126e_bool -> hAPP_f1815646051m_bool(image_741143905te_com(hAPP_c57939194te_com(cOMBK_131063602_state,C)),A) = bot_bot_fun_com_bool) & (A != bot_bo784226126e_bool -> hAPP_f1815646051m_bool(image_741143905te_com(hAPP_c57939194te_com(cOMBK_131063602_state,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool)))) # label(fact_39_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 103 (all C all A ((A = bot_bot_fun_com_bool -> hAPP_f457085749e_bool(image_2605051_state(hAPP_H275587026_state(cOMBK_869602456te_com,C)),A) = bot_bo784226126e_bool) & (A != bot_bot_fun_com_bool -> hAPP_f457085749e_bool(image_2605051_state(hAPP_H275587026_state(cOMBK_869602456te_com,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool)))) # label(fact_40_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 104 (all C all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C)),A) = bot_bo784226126e_bool) & (A != bot_bo844097828e_bool -> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool)))) # label(fact_41_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 105 (all C all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hAPP_f1083669085e_bool(image_1774499931_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool))) # label(fact_42_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 106 (all C all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hAPP_f1815646051m_bool(image_741143905te_com(hAPP_c57939194te_com(cOMBK_131063602_state,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool))) # label(fact_43_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 107 (all C all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f759274231e_bool(image_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool))) # label(fact_44_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 108 (all C all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f1206115581m_bool(image_pname_com(hAPP_c1494068046me_com(cOMBK_com_pname,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool))) # label(fact_45_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 109 (all C all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hAPP_f457085749e_bool(image_2605051_state(hAPP_H275587026_state(cOMBK_869602456te_com,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool))) # label(fact_46_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 110 (all C all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool))) # label(fact_47_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 111 (all F all X_1 all Y_2 (hAPP_com_option_com(F,X_1) = hAPP_com_option_com(some_com,Y_2) -> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),dom_com_com(F)) = dom_com_com(F))) # label(fact_48_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 112 (all F all X_1 all Y_2 (hAPP_H1671063474_pname(F,X_1) = hAPP_p1252095976_pname(some_pname,Y_2) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),dom_Ho2070278094_pname(F)) = dom_Ho2070278094_pname(F))) # label(fact_49_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 113 (all F all X_1 all Y_2 (hAPP_H1633077406_state(F,X_1) = hAPP_H1633077406_state(some_H1043067815_state,Y_2) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),dom_Ho1607160812_state(F)) = dom_Ho1607160812_state(F))) # label(fact_50_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 114 (all F all X_1 all Y_2 (hAPP_p799580910on_com(F,X_1) = hAPP_com_option_com(some_com,Y_2) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) = dom_pname_com(F))) # label(fact_51_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 115 (all B all F all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f1709493145l_bool(image_1403607267e_bool(F),A))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_52_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 116 (all B all F all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f849457489l_bool(image_995511119e_bool(F),A))) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))))) # label(fact_53_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 117 (all B all F all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_54_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 118 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_55_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 119 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f1492100075l_bool(image_234387449e_bool(F),A))) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))))) # label(fact_56_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 120 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_57_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 121 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f509793681e_bool(image_845802851_state(F),A))) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))))) # label(fact_58_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 122 (all B all F all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f1216288071e_bool(image_1497401961_state(F),A))) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))))) # label(fact_59_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 123 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_60_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 124 (all B all F all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f306376939e_bool(image_1863446033_pname(F),A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_61_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 125 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A))) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))))) # label(fact_62_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 126 (all A all X_1 (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) -> A = bot_bo844097828e_bool | A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) # label(fact_63_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 127 (all A all X_1 (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))) -> A = bot_bot_fun_com_bool | A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))) # label(fact_64_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 128 (all A all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) -> A = bot_bo784226126e_bool | A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) # label(fact_65_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 129 (all C (hBOOL(hoare_1795711768gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))))))) # label(fact_66_MGF) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 130 (all A_4 -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),bot_bot_fun_com_bool))) # label(fact_67_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 131 (all A_4 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),bot_bo784226126e_bool))) # label(fact_68_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 132 (all A_4 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),bot_bo844097828e_bool))) # label(fact_69_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 133 (all B_1 all A_4 all B ((-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B)) -> A_4 = B_1) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))))) # label(fact_70_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 134 (all B_1 all A_4 all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B)) -> A_4 = B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_71_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 135 (all B_1 all A_4 all B ((-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),B)) -> A_4 = B_1) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B))))) # label(fact_72_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 136 (all A_4 all B_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),A))) -> (A_4 != B_1 -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))))) # label(fact_73_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 137 (all A_4 all B_1 all A (is_pname(A_4) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A))) -> (A_4 != B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)))))) # label(fact_74_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 138 (all A_4 all B_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A))) -> (A_4 != B_1 -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))))) # label(fact_75_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 139 (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_76_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 140 (all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)) -> A = B))) # label(fact_77_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 141 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))))) # label(fact_78_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 142 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))))) # label(fact_79_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 143 (all C 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),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_80_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 144 (all A all B_1 all F all X_1 (B_1 = hAPP_H46530577te_com(F,X_1) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1815646051m_bool(image_741143905te_com(F),A)))))) # label(fact_81_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 145 (all A all B_1 all F all X_1 (B_1 = hAPP_pname_com(F,X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A)))))) # label(fact_82_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 146 (all A all B_1 all F all X_1 (B_1 = hAPP_c1455475371_state(F,X_1) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f457085749e_bool(image_2605051_state(F),A)))))) # label(fact_83_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 147 (all A all B_1 all F all X_1 (B_1 = hAPP_com_pname(F,X_1) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A)))))) # label(fact_84_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 148 (all A all B_1 all F all X_1 (B_1 = hAPP_p1751618853_state(F,X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A)))))) # label(fact_85_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 149 (all A_4 all A (A = bot_bot_fun_com_bool -> -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)))) # label(fact_86_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 150 (all A_4 all A (A = bot_bo784226126e_bool -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)))) # label(fact_87_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 151 (all A_4 all A (A = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)))) # label(fact_88_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 152 (all P_1 (hAPP_f759274231e_bool(collect_pname,P_1) = bot_bo844097828e_bool <-> (all X_2 (is_pname(X_2) -> -hBOOL(hAPP_pname_bool(P_1,X_2)))))) # label(fact_89_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.88/2.13 153 (all P_1 (hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = bot_bo1649642514l_bool <-> (all X_2 (is_fun_pname_bool(X_2) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_2)))))) # label(fact_90_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 154 (all P_1 (hAPP_f734420447l_bool(collec1987918285e_bool,P_1) = bot_bo942947096l_bool <-> (all X_2 -hBOOL(hAPP_f1378282496l_bool(P_1,X_2))))) # label(fact_91_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 155 (all P_1 (hAPP_f1682609283m_bool(collect_com,P_1) = bot_bot_fun_com_bool <-> (all X_2 -hBOOL(hAPP_com_bool(P_1,X_2))))) # label(fact_92_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 156 (all P_1 (hAPP_f806699093e_bool(collec637225377_state,P_1) = bot_bo784226126e_bool <-> (all X_2 -hBOOL(hAPP_H242767318e_bool(P_1,X_2))))) # label(fact_93_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 157 (all C -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),bot_bot_fun_com_bool))) # label(fact_94_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 158 (all C -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),bot_bo784226126e_bool))) # label(fact_95_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 159 (all C -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool))) # label(fact_96_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 160 (all P_1 (bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,P_1) <-> (all X_2 (is_pname(X_2) -> -hBOOL(hAPP_pname_bool(P_1,X_2)))))) # label(fact_97_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 161 (all P_1 (bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,P_1) <-> (all X_2 (is_fun_pname_bool(X_2) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_2)))))) # label(fact_98_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 162 (all P_1 (bot_bo942947096l_bool = hAPP_f734420447l_bool(collec1987918285e_bool,P_1) <-> (all X_2 -hBOOL(hAPP_f1378282496l_bool(P_1,X_2))))) # label(fact_99_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 163 (all P_1 (bot_bot_fun_com_bool = hAPP_f1682609283m_bool(collect_com,P_1) <-> (all X_2 -hBOOL(hAPP_com_bool(P_1,X_2))))) # label(fact_100_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 164 (all P_1 (bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,P_1) <-> (all X_2 -hBOOL(hAPP_H242767318e_bool(P_1,X_2))))) # label(fact_101_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 165 (all A ((exists X_2 hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))) <-> A != bot_bot_fun_com_bool)) # label(fact_102_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 166 (all A ((exists X_2 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))) <-> A != bot_bo784226126e_bool)) # label(fact_103_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 167 (all A (is_fun_pname_bool(A) -> ((exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)))) <-> A != bot_bo844097828e_bool))) # label(fact_104_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 168 (all A ((all X_2 -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))) <-> A = bot_bot_fun_com_bool)) # label(fact_105_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 169 (all A ((all X_2 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))) <-> A = bot_bo784226126e_bool)) # label(fact_106_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 170 (all A (is_fun_pname_bool(A) -> ((all X_2 (is_pname(X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)))) <-> A = bot_bo844097828e_bool))) # label(fact_107_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 171 (all A_4 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) -> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) = A)) # label(fact_113_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 172 (all A_4 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) = A))) # label(fact_114_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 173 (all A_4 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) = A)) # label(fact_115_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 174 (all B_1 all A_4 all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))))) # label(fact_116_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 175 (all B_1 all A_4 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_117_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 176 (all B_1 all A_4 all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B))))) # label(fact_118_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 177 (all B all X_1 all A (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) -> (hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B) <-> A = B)))) # label(fact_119_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 178 (all B all X_1 all A (is_fun_pname_bool(B) & is_fun_pname_bool(A) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B) <-> A = B))))) # label(fact_120_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 179 (all B all X_1 all A (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) -> (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B) <-> A = B)))) # label(fact_121_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 180 (all Y_2 all A all X_1 (is_pname(Y_2) & is_pname(X_1) -> (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),A),X_1)) <-> Y_2 = X_1 | hBOOL(hAPP_pname_bool(A,X_1))))) # label(fact_122_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 181 (all Y_2 all A all X_1 (hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),A),X_1)) <-> Y_2 = X_1 | hBOOL(hAPP_com_bool(A,X_1)))) # label(fact_123_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 182 (all Y_2 all A all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),A),X_1)) <-> Y_2 = X_1 | hBOOL(hAPP_H242767318e_bool(A,X_1)))) # label(fact_124_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 183 (all A_4 all B_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),A))) <-> A_4 = B_1 | hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)))) # label(fact_125_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 184 (all A_4 all B_1 all A (is_pname(A_4) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A))) <-> A_4 = B_1 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))))) # label(fact_126_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 185 (all A_4 all B_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A))) <-> A_4 = B_1 | hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)))) # label(fact_127_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 186 (all X_1 all Y_2 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A))) # label(fact_128_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 187 (all X_1 all Y_2 all A hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),A)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A))) # label(fact_129_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 188 (all X_1 all Y_2 all A hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),A)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A))) # label(fact_130_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 189 (all X_1 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) # label(fact_131_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 190 (all X_1 all A hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) # label(fact_132_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 191 (all X_1 all A hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) # label(fact_133_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 192 (all A_4 all P_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(collect_pname,P_1)) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fimplies),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4)))),P_1))) # label(fact_134_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 193 (all A_4 all P_1 hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(collect_com,P_1)) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fimplies),hAPP_f1682609283m_bool(cOMBB_bool_bool_com(fNot),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4)))),P_1))) # label(fact_135_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 194 (all A_4 all P_1 hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fimplies),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4)))),P_1))) # label(fact_136_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 195 (all A_4 all P_1 hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),hAPP_f734420447l_bool(collec1987918285e_bool,P_1)) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fimplies),hAPP_f734420447l_bool(cOMBB_1686148692e_bool(fNot),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4)))),P_1))) # label(fact_137_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 196 (all A_4 all P_1 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(collec637225377_state,P_1)) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fimplies),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_4)))),P_1))) # label(fact_138_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 197 (all A_4 all B hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B)))) # label(fact_139_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 198 (all A_4 all B hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_140_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 199 (all A_4 all B hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B)))) # label(fact_141_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 200 (all A_4 all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_142_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 201 (all A_4 all B hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_4))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B)))) # label(fact_143_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 202 (all A_4 all B hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)))) # label(fact_144_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 203 (all A_4 all B hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)))) # label(fact_145_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 204 (all A_4 all B hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)))) # label(fact_146_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 205 (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_147_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 206 (all A all B (A = B -> -(hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A))))) # label(fact_148_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 207 (all C_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,B),C_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))))) # label(fact_149_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 208 (all C_1 all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),C_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1))))) # label(fact_150_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 209 (all X_1 all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))))) # label(fact_151_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 210 (all X_1 all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))))) # label(fact_152_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 211 (all X_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_153_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 212 (all B all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))))) # label(fact_154_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 213 (all B all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))))) # label(fact_155_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 214 (all B all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_156_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 215 (all X_1 all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))))) # label(fact_157_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 216 (all X_1 all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))))) # label(fact_158_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 217 (all X_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_159_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 218 (all A all B (A = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)))) # label(fact_160_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 219 (all A all B (A = B -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)))) # label(fact_161_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 220 (all A all B (A = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_162_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 221 (all A all B (A = B -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)))) # label(fact_163_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 222 (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_164_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 223 (all A all B (A = B <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)))) # label(fact_165_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 224 (all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A))) # label(fact_166_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 225 (all A hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),A))) # label(fact_167_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 226 (all B_1 all F all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> (B_1 = hAPP_H46530577te_com(F,X_1) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1815646051m_bool(image_741143905te_com(F),A)))))) # label(fact_168_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 227 (all B_1 all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (B_1 = hAPP_pname_com(F,X_1) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A)))))) # label(fact_169_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 228 (all B_1 all F all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> (B_1 = hAPP_c1455475371_state(F,X_1) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f457085749e_bool(image_2605051_state(F),A)))))) # label(fact_170_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 229 (all B_1 all F all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> (B_1 = hAPP_com_pname(F,X_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A)))))) # label(fact_171_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 230 (all B_1 all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (B_1 = hAPP_p1751618853_state(F,X_1) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A)))))) # label(fact_172_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 231 (all F all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_H46530577te_com(F,X_1)),hAPP_f1815646051m_bool(image_741143905te_com(F),A))))) # label(fact_173_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 232 (all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_pname_com(F,X_1)),hAPP_f1206115581m_bool(image_pname_com(F),A))))) # label(fact_174_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 233 (all F all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_c1455475371_state(F,X_1)),hAPP_f457085749e_bool(image_2605051_state(F),A))))) # label(fact_175_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 234 (all F all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_com_pname(F,X_1)),hAPP_f1438183293e_bool(image_com_pname(F),A))))) # label(fact_176_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 235 (all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_1)),hAPP_f360545851e_bool(image_185131637_state(F),A))))) # label(fact_177_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 236 (all Z all F all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Z),hAPP_f360545851e_bool(image_185131637_state(F),A))) <-> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & Z = hAPP_p1751618853_state(F,X_2))))) # label(fact_178_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 237 (all P_1 all Q_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1))) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))) # label(fact_179_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 238 (all P_1 all Q_1 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1))) & hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))))) # label(fact_180_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 239 (all P_1 all Q_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,P_1))) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,Q_1))))) # label(fact_181_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 240 (all P_1 all Q_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1))) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))))) # label(fact_182_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 241 (all X_2 all Xa hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),Xa) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),X_2))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),Xa)))) # label(fact_183_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 242 (all X_2 all Xa hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),Xa) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),X_2))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),Xa)))) # label(fact_184_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 243 (all X_2 all Xa hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),Xa) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),X_2))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),Xa)))) # label(fact_185_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 244 (all X_2 all Xa hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),Xa) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),X_2))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),Xa)))) # label(fact_186_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 245 (all X_2 all Xa hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),Xa) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),X_2))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),Xa)))) # label(fact_187_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 246 (all A_4 all B_1 (is_pname(A_4) & is_pname(B_1) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool) -> A_4 = B_1))) # label(fact_188_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 247 (all A_4 all B_1 (hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool) -> A_4 = B_1)) # label(fact_189_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 248 (all A_4 all B_1 (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool) -> A_4 = B_1)) # label(fact_190_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 249 (all B_1 all A_4 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) -> B_1 = A_4)) # label(fact_191_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 250 (all B_1 all A_4 (is_pname(B_1) & is_pname(A_4) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) -> B_1 = A_4))) # label(fact_192_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 251 (all B_1 all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))) -> B_1 = A_4)) # label(fact_193_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 252 (all A_4 all B_1 all C all D_1 (is_pname(A_4) & is_pname(B_1) & is_pname(C) & is_pname(D_1) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D_1),bot_bo844097828e_bool)) <-> A_4 = C & B_1 = D_1 | A_4 = D_1 & B_1 = C))) # label(fact_194_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 253 (all A_4 all B_1 all C all D_1 (hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,D_1),bot_bot_fun_com_bool)) <-> A_4 = C & B_1 = D_1 | A_4 = D_1 & B_1 = C)) # label(fact_195_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 254 (all A_4 all B_1 all C all D_1 (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,D_1),bot_bo784226126e_bool)) <-> A_4 = C & B_1 = D_1 | A_4 = D_1 & B_1 = C)) # label(fact_196_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 255 (all B_1 all A_4 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) <-> B_1 = A_4)) # label(fact_197_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 256 (all B_1 all A_4 (is_pname(B_1) & is_pname(A_4) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) <-> B_1 = A_4))) # label(fact_198_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 257 (all B_1 all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))) <-> B_1 = A_4)) # label(fact_199_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 258 (all A_4 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) != bot_bo844097828e_bool) # label(fact_200_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 259 (all A_4 all A hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) != bot_bot_fun_com_bool) # label(fact_201_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 260 (all A_4 all A hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) != bot_bo784226126e_bool) # label(fact_202_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 261 (all A_4 all A bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)) # label(fact_203_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 262 (all A_4 all A bot_bot_fun_com_bool != hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)) # label(fact_204_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 263 (all A_4 all A bot_bo784226126e_bool != hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A)) # label(fact_205_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 264 (all A_4 all A (hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A))) <-> hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)))) # label(fact_206_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 265 (all A_4 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)))) # label(fact_207_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 266 (all A_4 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A))) <-> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)))) # label(fact_208_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 267 (all A_4 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)))) # label(fact_209_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 268 (all A_4 all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)))) # label(fact_210_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 269 (all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool)) <-> A = bot_bo844097828e_bool))) # label(fact_211_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 270 (all A (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),bot_bot_fun_com_bool)) <-> A = bot_bot_fun_com_bool)) # label(fact_212_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 271 (all A (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),bot_bo784226126e_bool)) <-> A = bot_bo784226126e_bool)) # label(fact_213_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 272 (all F all A (hAPP_f457085749e_bool(image_2605051_state(F),A) = bot_bo784226126e_bool <-> A = bot_bot_fun_com_bool)) # label(fact_214_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 273 (all F all A (hAPP_f1083669085e_bool(image_1774499931_pname(F),A) = bot_bo844097828e_bool <-> A = bot_bo784226126e_bool)) # label(fact_215_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 274 (all F all A (hAPP_f1815646051m_bool(image_741143905te_com(F),A) = bot_bot_fun_com_bool <-> A = bot_bo784226126e_bool)) # label(fact_216_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 275 (all F all A (is_fun_pname_bool(A) -> (hAPP_f360545851e_bool(image_185131637_state(F),A) = bot_bo784226126e_bool <-> A = bot_bo844097828e_bool))) # label(fact_217_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 276 (all F hAPP_f1083669085e_bool(image_1774499931_pname(F),bot_bo784226126e_bool) = bot_bo844097828e_bool) # label(fact_218_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 277 (all F hAPP_f1815646051m_bool(image_741143905te_com(F),bot_bo784226126e_bool) = bot_bot_fun_com_bool) # label(fact_219_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 278 (all F hAPP_f457085749e_bool(image_2605051_state(F),bot_bot_fun_com_bool) = bot_bo784226126e_bool) # label(fact_220_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 279 (all F hAPP_f360545851e_bool(image_185131637_state(F),bot_bo844097828e_bool) = bot_bo784226126e_bool) # label(fact_221_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 280 (all F all A (bot_bo784226126e_bool = hAPP_f457085749e_bool(image_2605051_state(F),A) <-> A = bot_bot_fun_com_bool)) # label(fact_222_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 281 (all F all A (bot_bo844097828e_bool = hAPP_f1083669085e_bool(image_1774499931_pname(F),A) <-> A = bot_bo784226126e_bool)) # label(fact_223_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 282 (all F all A (bot_bot_fun_com_bool = hAPP_f1815646051m_bool(image_741143905te_com(F),A) <-> A = bot_bo784226126e_bool)) # label(fact_224_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 283 (all F all A (is_fun_pname_bool(A) -> (bot_bo784226126e_bool = hAPP_f360545851e_bool(image_185131637_state(F),A) <-> A = bot_bo844097828e_bool))) # label(fact_225_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 284 (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_226_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 285 (all A all B (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),B)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))))) # label(fact_227_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 286 (all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))))) # label(fact_228_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 287 (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_229_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 288 (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_230_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 289 (all A all B (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),B)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))))) # label(fact_231_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 290 (all A all B (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))))) # label(fact_232_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 291 (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_233_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 292 (all A_4 all C_1 all D (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),C_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),D))))) # label(fact_234_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 293 (all A_4 all C_1 all D (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,C_1),D)) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),C_1)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),D))))) # label(fact_235_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 294 (all A_4 all C_1 all D (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),D)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),C_1)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),D))))) # label(fact_236_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 295 (all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) <-> hBOOL(hAPP_com_bool(A,X_1)))) # label(fact_237_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 296 (all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) <-> hBOOL(hAPP_H242767318e_bool(A,X_1)))) # label(fact_238_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 297 (all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) <-> hBOOL(hAPP_pname_bool(A,X_1)))) # label(fact_239_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 298 (all P_1 hAPP_f806699093e_bool(collec637225377_state,P_1) = P_1) # label(fact_240_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 299 (all P_1 (is_fun_pname_bool(P_1) -> hAPP_f759274231e_bool(collect_pname,P_1) = P_1)) # label(fact_241_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 300 (all P_1 (is_fun1661590463l_bool(P_1) -> hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = P_1)) # label(fact_242_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 301 (all P_1 hAPP_f734420447l_bool(collec1987918285e_bool,P_1) = P_1) # label(fact_243_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 302 (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),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_244_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 303 (all B_1 all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))))) # label(fact_245_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 304 (all B_1 all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B))))) # label(fact_246_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 305 (all B all X_1 all A (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B))) <-> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))))) # label(fact_247_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 306 (all B all X_1 all A (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))))) # label(fact_248_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 307 (all B all X_1 all A (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))))) # label(fact_249_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 308 (all X_1 all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B)) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) & hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)))) # label(fact_250_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 309 (all X_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_251_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 310 (all X_1 all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)))) # label(fact_252_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 311 (all B all A_4 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)))) # label(fact_253_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 312 (all B all A_4 hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,B),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)))) # label(fact_254_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 313 (all B all A_4 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)))) # label(fact_255_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 314 (all F all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1193503499_pname(F,X_1)),hAPP_f1083669085e_bool(image_1774499931_pname(F),A)) = hAPP_f1083669085e_bool(image_1774499931_pname(F),A))) # label(fact_256_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 315 (all F all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_H46530577te_com(F,X_1)),hAPP_f1815646051m_bool(image_741143905te_com(F),A)) = hAPP_f1815646051m_bool(image_741143905te_com(F),A))) # label(fact_257_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 316 (all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_pname_pname(F,X_1)),hAPP_f759274231e_bool(image_pname_pname(F),A)) = hAPP_f759274231e_bool(image_pname_pname(F),A))) # label(fact_258_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 317 (all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_pname_com(F,X_1)),hAPP_f1206115581m_bool(image_pname_com(F),A)) = hAPP_f1206115581m_bool(image_pname_com(F),A))) # label(fact_259_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 318 (all F all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(F,X_1)),hAPP_f457085749e_bool(image_2605051_state(F),A)) = hAPP_f457085749e_bool(image_2605051_state(F),A))) # label(fact_260_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.13 319 (all F all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,X_1)),hAPP_f360545851e_bool(image_185131637_state(F),A)) = hAPP_f360545851e_bool(image_185131637_state(F),A))) # label(fact_261_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 320 (all F all A_4 all B hAPP_f1083669085e_bool(image_1774499931_pname(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1193503499_pname(F,A_4)),hAPP_f1083669085e_bool(image_1774499931_pname(F),B))) # label(fact_262_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 321 (all F all A_4 all B hAPP_f1815646051m_bool(image_741143905te_com(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_H46530577te_com(F,A_4)),hAPP_f1815646051m_bool(image_741143905te_com(F),B))) # label(fact_263_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 322 (all F all A_4 all B hAPP_f457085749e_bool(image_2605051_state(F),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(F,A_4)),hAPP_f457085749e_bool(image_2605051_state(F),B))) # label(fact_264_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 323 (all F all A_4 all B hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,A_4)),hAPP_f360545851e_bool(image_185131637_state(F),B))) # label(fact_265_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 324 (all F all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F),A)),hAPP_f1083669085e_bool(image_1774499931_pname(F),B))))) # label(fact_266_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 325 (all F all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B))))) # label(fact_267_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 326 (all B all F all A (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A))) <-> (exists AA (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,AA),A)) & B = hAPP_f1083669085e_bool(image_1774499931_pname(F),AA)))))) # label(fact_268_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 327 (all B all F all A (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A))) <-> (exists AA (is_fun_pname_bool(AA) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A)) & B = hAPP_f360545851e_bool(image_185131637_state(F),AA))))) # label(fact_269_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 328 (all M all A_4 all B_1 (hAPP_com_option_com(M,A_4) = hAPP_com_option_com(some_com,B_1) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),dom_com_com(M))))) # label(fact_270_domI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 329 (all M all A_4 all B_1 (hAPP_H1671063474_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_1) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho2070278094_pname(M))))) # label(fact_271_domI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 330 (all M all A_4 all B_1 (hAPP_H1633077406_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_1) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho1607160812_state(M))))) # label(fact_272_domI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 331 (all M all A_4 all B_1 (hAPP_p1252095976_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_pname(M))))) # label(fact_273_domI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 332 (all M all A_4 all B_1 (hAPP_p485182952_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pn480909800_state(M))))) # label(fact_274_domI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 333 (all M all A_4 all B_1 (hAPP_p799580910on_com(M,A_4) = hAPP_com_option_com(some_com,B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M))))) # label(fact_275_domI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 334 (all P_1 all A_4 ((hBOOL(hAPP_pname_bool(P_1,A_4)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(P_1,A_4)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4))),P_1)) = bot_bo844097828e_bool))) # label(fact_276_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 335 (all P_1 all A_4 ((hBOOL(hAPP_com_bool(P_1,A_4)) -> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),P_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)) & (-hBOOL(hAPP_com_bool(P_1,A_4)) -> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),P_1)) = bot_bot_fun_com_bool))) # label(fact_277_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 336 (all P_1 all A_4 ((hBOOL(hAPP_f1664156314l_bool(P_1,A_4)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(P_1,A_4)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),P_1)) = bot_bo1649642514l_bool))) # label(fact_278_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 337 (all P_1 all A_4 ((hBOOL(hAPP_f1378282496l_bool(P_1,A_4)) -> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),P_1)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool)) & (-hBOOL(hAPP_f1378282496l_bool(P_1,A_4)) -> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),P_1)) = bot_bo942947096l_bool))) # label(fact_279_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 338 (all P_1 all A_4 ((hBOOL(hAPP_H242767318e_bool(P_1,A_4)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_4))),P_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)) & (-hBOOL(hAPP_H242767318e_bool(P_1,A_4)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_4))),P_1)) = bot_bo784226126e_bool))) # label(fact_280_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 339 (all P_1 all A_4 ((hBOOL(hAPP_pname_bool(P_1,A_4)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A_4))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(P_1,A_4)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A_4))),P_1)) = bot_bo844097828e_bool))) # label(fact_281_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 340 (all P_1 all A_4 ((hBOOL(hAPP_com_bool(P_1,A_4)) -> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(fequal_com,A_4))),P_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)) & (-hBOOL(hAPP_com_bool(P_1,A_4)) -> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(fequal_com,A_4))),P_1)) = bot_bot_fun_com_bool))) # label(fact_282_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 341 (all P_1 all A_4 ((hBOOL(hAPP_f1664156314l_bool(P_1,A_4)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A_4))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(P_1,A_4)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A_4))),P_1)) = bot_bo1649642514l_bool))) # label(fact_283_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 342 (all P_1 all A_4 ((hBOOL(hAPP_f1378282496l_bool(P_1,A_4)) -> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(fequal1475827639e_bool,A_4))),P_1)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool)) & (-hBOOL(hAPP_f1378282496l_bool(P_1,A_4)) -> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(fequal1475827639e_bool,A_4))),P_1)) = bot_bo942947096l_bool))) # label(fact_284_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 343 (all P_1 all A_4 ((hBOOL(hAPP_H242767318e_bool(P_1,A_4)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(fequal1440809015_state,A_4))),P_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)) & (-hBOOL(hAPP_H242767318e_bool(P_1,A_4)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(fequal1440809015_state,A_4))),P_1)) = bot_bo784226126e_bool))) # label(fact_285_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 344 (all A_4 hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)) # label(fact_286_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 345 (all A_4 hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)) # label(fact_287_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 346 (all A_4 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool)) # label(fact_288_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 347 (all A_4 hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool)) # label(fact_289_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 348 (all A_4 hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_4)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)) # label(fact_290_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 349 (all A_4 hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A_4)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)) # label(fact_291_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 350 (all A_4 hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(fequal_com,A_4)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)) # label(fact_292_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 351 (all A_4 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(fequal533582459e_bool,A_4)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool)) # label(fact_293_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 352 (all A_4 hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(fequal1475827639e_bool,A_4)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool)) # label(fact_294_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 353 (all A_4 hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(fequal1440809015_state,A_4)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)) # label(fact_295_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 354 (all C all G_2 (hBOOL(hoare_1795711768gleton) -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),dom_pname_com(body))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_2))),bot_bo784226126e_bool)))))) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))))))) # label(fact_296_MGF__lemma1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 355 (all Pn all B_4 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = hAPP_com_option_com(some_com,B_4) -> hBOOL(hAPP_com_bool(wt,B_4))))) # label(fact_297_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 356 (all B_1 all F all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f457085749e_bool(image_2605051_state(F),A))) -> -(all X_2 (B_1 = hAPP_c1455475371_state(F,X_2) -> -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)))))) # label(fact_298_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 357 (all B_1 all F all A (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A))) -> -(all X_2 (B_1 = hAPP_com_pname(F,X_2) -> -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))))))) # label(fact_299_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 358 (all B_1 all F all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1815646051m_bool(image_741143905te_com(F),A))) -> -(all X_2 (B_1 = hAPP_H46530577te_com(F,X_2) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)))))) # label(fact_300_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 359 (all B_1 all F all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A))) -> -(all X_2 (is_pname(X_2) -> (B_1 = hAPP_pname_com(F,X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))))))) # label(fact_301_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 360 (all B_1 all F all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A))) -> -(all X_2 (is_pname(X_2) -> (B_1 = hAPP_p1751618853_state(F,X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))))))) # label(fact_302_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 361 (all P_1 all A all Fa (hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,Fa),A)) -> (hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool)) -> ((all A_2 all F_2 (hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),A)) -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),F_2)) -> (hBOOL(hAPP_f990396704l_bool(P_1,F_2)) -> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),F_2)))))))) -> hBOOL(hAPP_f990396704l_bool(P_1,Fa))))))) # label(fact_303_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 362 (all P_1 all A all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) -> ((all A_2 all F_2 (is_fun_pname_bool(A_2) & is_fun1661590463l_bool(F_2) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),F_2)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_2)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),F_2))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa))))))) # label(fact_304_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 363 (all P_1 all A all Fa (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,Fa),A)) -> (hBOOL(hAPP_f1410040974l_bool(P_1,bot_bo942947096l_bool)) -> ((all A_2 all F_2 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,F_2)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_2),A)) -> (-hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_2),F_2)) -> (hBOOL(hAPP_f1410040974l_bool(P_1,F_2)) -> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_2),F_2)))))))) -> hBOOL(hAPP_f1410040974l_bool(P_1,Fa))))))) # label(fact_305_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 364 (all P_1 all A all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) -> ((all A_2 all F_2 (is_pname(A_2) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_2)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),F_2))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa))))))) # label(fact_306_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 365 (all P_1 all A all Fa (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Fa),A)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,bot_bo784226126e_bool)) -> ((all A_2 all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,F_2)) -> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),F_2)))))))) -> hBOOL(hAPP_f1378282496l_bool(P_1,Fa))))))) # label(fact_307_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 366 (all P (hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,P))) -> -(all Y_3 hAPP_p799580910on_com(body,P) != hAPP_com_option_com(some_com,Y_3)))) # label(fact_308_WTs__elim__cases_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 367 (all B all A ((all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),B)))) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)))) # label(fact_309_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 368 (all B all A ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)))) # label(fact_310_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 369 (all B all A ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_311_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 370 (all F all A all B (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f509793681e_bool(image_845802851_state(F),A))) -> (exists C_3 (is_fun1661590463l_bool(C_3) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3)) & B = hAPP_f509793681e_bool(image_845802851_state(F),C_3)))))) # label(fact_312_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 371 (all F all A all B (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f1216288071e_bool(image_1497401961_state(F),A))) -> (exists C_3 (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,C_3),A)) & hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,C_3)) & B = hAPP_f1216288071e_bool(image_1497401961_state(F),C_3)))))) # label(fact_313_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 372 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A))) -> (exists C_3 (is_fun1661590463l_bool(C_3) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3)) & B = hAPP_f674760225e_bool(image_1283814551_pname(F),C_3))))))) # label(fact_314_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 373 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f306376939e_bool(image_1863446033_pname(F),A))) -> (exists C_3 (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,C_3),A)) & hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,C_3)) & B = hAPP_f306376939e_bool(image_1863446033_pname(F),C_3))))))) # label(fact_315_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 374 (all F all A all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f1709493145l_bool(image_1403607267e_bool(F),A))) -> (exists C_3 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_3),A)) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,C_3)) & B = hAPP_f1709493145l_bool(image_1403607267e_bool(F),C_3))))))) # label(fact_316_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 375 (all F all A all B (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f849457489l_bool(image_995511119e_bool(F),A))) -> (exists C_3 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_3),A)) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,C_3)) & B = hAPP_f849457489l_bool(image_995511119e_bool(F),C_3)))))) # label(fact_317_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 376 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A))) -> (exists C_3 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_3),A)) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,C_3)) & B = hAPP_f1083669085e_bool(image_1774499931_pname(F),C_3))))))) # label(fact_318_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 377 (all F all A all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f434788991l_bool(image_47868345e_bool(F),C_3))))))) # label(fact_319_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 378 (all F all A all B (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f1492100075l_bool(image_234387449e_bool(F),A))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f1492100075l_bool(image_234387449e_bool(F),C_3)))))) # label(fact_320_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 379 (all F all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f759274231e_bool(image_pname_pname(F),C_3))))))) # label(fact_321_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 380 (all F all A all B (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f360545851e_bool(image_185131637_state(F),C_3)))))) # label(fact_322_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 381 (all P_1 all Fa (hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa)) -> (hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2)) -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),F_2)) -> (hBOOL(hAPP_f990396704l_bool(P_1,F_2)) -> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),F_2))))))) -> hBOOL(hAPP_f990396704l_bool(P_1,Fa)))))) # label(fact_324_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 382 (all P_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) -> ((all X_2 all F_2 (is_fun_pname_bool(X_2) & is_fun1661590463l_bool(F_2) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_2)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_2)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_2)))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)))))) # label(fact_325_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 383 (all P_1 all Fa (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(P_1,bot_bo942947096l_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,F_2)) -> (-hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),F_2)) -> (hBOOL(hAPP_f1410040974l_bool(P_1,F_2)) -> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),F_2))))))) -> hBOOL(hAPP_f1410040974l_bool(P_1,Fa)))))) # label(fact_326_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 384 (all P_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) -> ((all X_2 all F_2 (is_pname(X_2) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_2)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2)))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)))))) # label(fact_327_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 385 (all P_1 all Fa (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,bot_bo784226126e_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,F_2)) -> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2))))))) -> hBOOL(hAPP_f1378282496l_bool(P_1,Fa)))))) # label(fact_328_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 386 (all A_4 (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_4)) <-> A_4 = bot_bot_fun_com_bool | (exists A_7 exists A_2 (A_4 = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),A_7) & hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_7)))))) # label(fact_329_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 387 (all A_4 (is_fun1661590463l_bool(A_4) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_4)) <-> A_4 = bot_bo1649642514l_bool | (exists A_7 exists A_2 (is_fun1661590463l_bool(A_7) & is_fun_pname_bool(A_2) & A_4 = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A_7) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_7))))))) # label(fact_330_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 388 (all A_4 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_4)) <-> A_4 = bot_bo942947096l_bool | (exists A_7 exists A_2 (A_4 = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_2),A_7) & hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_7)))))) # label(fact_331_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 389 (all A_4 (is_fun_pname_bool(A_4) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_4)) <-> A_4 = bot_bo844097828e_bool | (exists A_7 exists A_2 (is_fun_pname_bool(A_7) & is_pname(A_2) & A_4 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_7) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_7))))))) # label(fact_332_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 390 (all A_4 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_4)) <-> A_4 = bot_bo784226126e_bool | (exists A_7 exists A_2 (A_4 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_7) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_7)))))) # label(fact_333_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 391 (all F all A (-hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f457085749e_bool(image_2605051_state(F),A))) -> (exists X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) & -hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_H313059897m_bool(hAPP_f235185669m_bool(cOMBC_114640782e_bool,hAPP_f475997903e_bool(cOMBB_1327031172ol_com(fequal1440809015_state),F)),hAPP_c1455475371_state(F,X_2))))))))))) # label(fact_334_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 392 (all F all A (-hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(image_661047967_state(F),A))) -> (exists X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) & -hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,hAPP_f596278895e_bool(cOMBB_1563888316_state(fequal1440809015_state),F)),hAPP_H574424047_state(F,X_2))))))))))) # label(fact_335_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 393 (all F all A (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f509793681e_bool(image_845802851_state(F),A))) -> (exists X_2 (is_fun_pname_bool(X_2) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) & -hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_H358531139l_bool(hAPP_f1186253673l_bool(cOMBC_1836455480e_bool,hAPP_f2113567599e_bool(cOMBB_1724041344e_bool(fequal1440809015_state),F)),hAPP_f1218207411_state(F,X_2))))))))))) # label(fact_336_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 394 (all F all A (-hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f1216288071e_bool(image_1497401961_state(F),A))) -> (exists X_2 (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A)) & -hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_H2039996199l_bool(hAPP_f1463049441l_bool(cOMBC_754402940e_bool,hAPP_f610934515e_bool(cOMBB_1840094962e_bool(fequal1440809015_state),F)),hAPP_f718417177_state(F,X_2))))))))))) # label(fact_337_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 395 (all F all A (-hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1438183293e_bool(image_com_pname(F),A))) -> (exists X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) & -hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_p1639923567m_bool(hAPP_f734198589m_bool(cOMBC_com_pname_bool,hAPP_f835719487e_bool(cOMBB_1083901850ol_com(fequal_pname),F)),hAPP_com_pname(F,X_2))))))))))) # label(fact_338_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 396 (all F all A (-hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1083669085e_bool(image_1774499931_pname(F),A))) -> (exists X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) & -hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_p606792009e_bool(hAPP_f1720171569e_bool(cOMBC_1952686190e_bool,hAPP_f777604691e_bool(cOMBB_1365368614_state(fequal_pname),F)),hAPP_H1193503499_pname(F,X_2))))))))))) # label(fact_339_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 397 (all F all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X_2))))))))))) # label(fact_340_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 398 (all F all A (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(F),A))) -> (exists X_2 (is_fun_pname_bool(X_2) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) & -hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,hAPP_f1385420507e_bool(cOMBB_598082538e_bool(fequal_pname),F)),hAPP_f1297739591_pname(F,X_2))))))))))) # label(fact_341_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 399 (all F all A (-hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f306376939e_bool(image_1863446033_pname(F),A))) -> (exists X_2 (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A)) & -hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_p1235466077l_bool(hAPP_f780571929l_bool(cOMBC_1558112230e_bool,hAPP_f700046015e_bool(cOMBB_1400714760e_bool(fequal_pname),F)),hAPP_f88366945_pname(F,X_2))))))))))) # label(fact_342_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 400 (all F all A (-hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f1709493145l_bool(image_1403607267e_bool(F),A))) -> (exists X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) & -hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f360545851e_bool(hAPP_f591683433e_bool(cOMBC_1984545208l_bool,hAPP_f381060343l_bool(cOMBB_1631414076_state(fequal533582459e_bool),F)),hAPP_H1776011827e_bool(F,X_2))))))))))) # label(fact_343_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 401 (all F all A (-hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f849457489l_bool(image_995511119e_bool(F),A))) -> (exists X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) & -hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,hAPP_f1191357267l_bool(cOMBB_639263758_state(fequal1475827639e_bool),F)),hAPP_H216526335e_bool(F,X_2))))))))))) # label(fact_344_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 402 (all F all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(F),A))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,hAPP_f567934427l_bool(cOMBB_408569982_pname(fequal533582459e_bool),F)),hAPP_p61793385e_bool(F,X_2))))))))))) # label(fact_345_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 403 (all F all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f1492100075l_bool(image_234387449e_bool(F),A))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f1083669085e_bool(hAPP_f568104217e_bool(cOMBC_1757633998l_bool,hAPP_f1143533991l_bool(cOMBB_949755692_pname(fequal1475827639e_bool),F)),hAPP_p606792009e_bool(F,X_2))))))))))) # label(fact_346_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 404 (all F all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(F),A))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_H1776011827e_bool(hAPP_f343137017e_bool(cOMBC_19854728e_bool,hAPP_f472107739e_bool(cOMBB_181781758_pname(fequal1440809015_state),F)),hAPP_p1751618853_state(F,X_2))))))))))) # label(fact_347_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 405 (all Pname_2 all Pname_1 (is_pname(Pname_2) & is_pname(Pname_1) -> (hAPP_pname_com(body_1,Pname_2) = hAPP_pname_com(body_1,Pname_1) <-> Pname_2 = Pname_1))) # label(fact_348_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 406 (all G_2 all Procs (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),Procs))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Procs))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Procs)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),Procs)))))) # label(fact_349_MGT__Body) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 407 (all A_4 all M (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),dom_com_com(M))) -> (exists B_3 hAPP_com_option_com(M,A_4) = hAPP_com_option_com(some_com,B_3)))) # label(fact_350_domD) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 408 (all A_4 all M (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho2070278094_pname(M))) -> (exists B_3 (is_pname(B_3) & hAPP_H1671063474_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_3))))) # label(fact_351_domD) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 409 (all A_4 all M (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho1607160812_state(M))) -> (exists B_3 hAPP_H1633077406_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_3)))) # label(fact_352_domD) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 410 (all A_4 all M (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_pname(M))) -> (exists B_3 (is_pname(B_3) & hAPP_p1252095976_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_3))))) # label(fact_353_domD) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 411 (all A_4 all M (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pn480909800_state(M))) -> (exists B_3 hAPP_p485182952_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_3)))) # label(fact_354_domD) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 412 (all A_4 all M (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M))) -> (exists B_3 hAPP_p799580910on_com(M,A_4) = hAPP_com_option_com(some_com,B_3)))) # label(fact_355_domD) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 413 (all X_1 (is_pname(X_1) -> hAPP_f1297739591_pname(the_elem_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1)) # label(fact_356_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 414 (all X_1 hAPP_f1276420679ol_com(the_elem_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = X_1) # label(fact_357_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 415 (all X_1 hAPP_f718417177_state(the_el2080696983_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1) # label(fact_358_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 416 (all F all B all A ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_H46530577te_com(F,X_2)),B)))) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1815646051m_bool(image_741143905te_com(F),A)),B)))) # label(fact_359_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 417 (all F all B all A ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1193503499_pname(F,X_2)),B)))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F),A)),B)))) # label(fact_360_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 418 (all F all B all A ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_pname_com(F,X_2)),B))))) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1206115581m_bool(image_pname_com(F),A)),B)))) # label(fact_361_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 419 (all F all B all A ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(F,X_2)),B))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(image_pname_pname(F),A)),B)))) # label(fact_362_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 420 (all F all B all A ((all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_c1455475371_state(F,X_2)),B)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f457085749e_bool(image_2605051_state(F),A)),B)))) # label(fact_363_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 421 (all F all B all A ((all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_com_pname(F,X_2)),B)))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1438183293e_bool(image_com_pname(F),A)),B)))) # label(fact_364_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 422 (all F all B all A ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_2)),B))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),B)))) # label(fact_365_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 423 (all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),X_1))) # label(fact_366_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 424 (all X_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),X_1))) # label(fact_367_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 425 (all X_1 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),X_1))) # label(fact_368_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 426 (all A (A != bot_bot_fun_com_bool <-> (exists X_2 exists B_2 (A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),B_2) & -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),B_2)))))) # label(fact_369_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 427 (all A (is_fun_pname_bool(A) -> (A != bot_bo844097828e_bool <-> (exists X_2 exists B_2 (is_pname(X_2) & is_fun_pname_bool(B_2) & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2))))))) # label(fact_370_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 428 (all A (A != bot_bo784226126e_bool <-> (exists X_2 exists B_2 (A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_2) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_2)))))) # label(fact_371_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 429 (all X_5 (is_pname(X_5) -> hAPP_o593586696_pname(the_pname_1,hAPP_p1252095976_pname(some_pname,X_5)) = X_5)) # label(fact_372_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 430 (all X_5 hAPP_o1912464824_state(the_Ho32424093_state,hAPP_H1633077406_state(some_H1043067815_state,X_5)) = X_5) # label(fact_373_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 431 (all X_5 hAPP_option_com_com(the_com,hAPP_com_option_com(some_com,X_5)) = X_5) # label(fact_374_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 432 (all G_2 all P_1 all Pn_1 all Q_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo784226126e_bool))))) # label(fact_375_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 433 (all P_1 all Pn_1 all Q_1 all G_2 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),G_2)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo784226126e_bool))))) # label(fact_376_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 434 hBOOL(hoare_1795711768gleton) <-> (exists S_1 exists T_2 S_1 != T_2) # label(fact_377_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 435 (all A all C all B ((-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))))) # label(fact_378_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 436 (all A all C all B ((-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))))) # label(fact_379_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 437 (all A all C all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))))) # label(fact_380_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 438 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))))) # label(fact_381_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 439 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))))) # label(fact_382_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 440 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_383_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 441 (all Fun1_2 all Com_1 all Fun2_2 all Fun1_1 all Com_2 all Fun2_1 (hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_2),Com_1),Fun2_2) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_1),Com_2),Fun2_1) <-> Fun1_2 = Fun1_1 & Com_1 = Com_2 & Fun2_2 = Fun2_1)) # label(fact_384_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 442 (all A all C all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))))) # label(fact_385_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 443 (all A all C all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))))) # label(fact_386_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 444 (all A all C all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))))) # label(fact_387_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 445 (all B all C all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))))) # label(fact_388_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 446 (all B all C all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))))) # label(fact_389_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 447 (all B all C all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))))) # label(fact_390_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 448 (all P_1 all A all B ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) -> hBOOL(hAPP_pname_bool(P_1,X_2))))) <-> (all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_pname_bool(P_1,X_2))))) & (all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) -> hBOOL(hAPP_pname_bool(P_1,X_2))))))) # label(fact_391_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 449 (all P_1 all A all B ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) -> hBOOL(hAPP_H242767318e_bool(P_1,X_2)))) <-> (all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) -> hBOOL(hAPP_H242767318e_bool(P_1,X_2)))) & (all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B)) -> hBOOL(hAPP_H242767318e_bool(P_1,X_2)))))) # label(fact_392_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 450 (all P_1 all A all B ((exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) & hBOOL(hAPP_pname_bool(P_1,X_2)))) <-> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & hBOOL(hAPP_pname_bool(P_1,X_2)))) | (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) & hBOOL(hAPP_pname_bool(P_1,X_2)))))) # label(fact_393_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 451 (all P_1 all A all B ((exists X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) & hBOOL(hAPP_H242767318e_bool(P_1,X_2)))) <-> (exists X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) & hBOOL(hAPP_H242767318e_bool(P_1,X_2)))) | (exists X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B)) & hBOOL(hAPP_H242767318e_bool(P_1,X_2)))))) # label(fact_394_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 452 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))) # label(fact_395_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 453 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1))) # label(fact_396_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 454 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) | hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)))) # label(fact_397_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.92/2.14 455 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) | hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)))) # label(fact_398_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 456 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_399_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 457 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1))) # label(fact_400_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 458 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),C_1))) # label(fact_401_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 459 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) # label(fact_402_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 460 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) # label(fact_403_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 461 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A)) # label(fact_404_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 462 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),A)) # label(fact_405_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 463 (all A all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B)))) # label(fact_406_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 464 (all A all B hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_407_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 465 (all A all B hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B)))) # label(fact_408_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 466 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B)))) # label(fact_409_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 467 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_410_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 468 (all A (is_fun_pname_bool(A) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),A) = A)) # label(fact_411_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 469 (all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),A) = A) # label(fact_412_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 470 (all P_1 all Q_1 hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))) # label(fact_413_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 471 (all P_1 all Q_1 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) # label(fact_414_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 472 (all P_1 all Q_1 hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),P_1)),Q_1)) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))) # label(fact_415_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 473 (all P_1 all Q_1 hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),P_1)),Q_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(collec637225377_state,P_1)),hAPP_f806699093e_bool(collec637225377_state,Q_1))) # label(fact_416_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 474 (all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = bot_bo844097828e_bool <-> A = bot_bo844097828e_bool & B = bot_bo844097828e_bool))) # label(fact_417_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 475 (all A all B (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = bot_bot_fun_com_bool <-> A = bot_bot_fun_com_bool & B = bot_bot_fun_com_bool)) # label(fact_418_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 476 (all A all B (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = bot_bo784226126e_bool <-> A = bot_bo784226126e_bool & B = bot_bo784226126e_bool)) # label(fact_419_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.14 477 (all A (is_fun_pname_bool(A) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),bot_bo844097828e_bool) = A)) # label(fact_420_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 478 (all A hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),bot_bot_fun_com_bool) = A) # label(fact_421_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 479 (all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),bot_bo784226126e_bool) = A) # label(fact_422_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 480 (all B (is_fun_pname_bool(B) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B) = B)) # label(fact_423_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 481 (all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,bot_bot_fun_com_bool),B) = B) # label(fact_424_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 482 (all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),B) = B) # label(fact_425_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 483 (all G_2 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_2)))))) # label(fact_426_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 484 (all G_2 all Fa (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,G_2)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,Fa),G_2)))))) # label(fact_427_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 485 (all G_2 all Fa (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,G_2)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Fa),G_2)))))) # label(fact_428_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 486 (all G_2 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_2)))))) # label(fact_429_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 487 (all Fa all G_2 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_2))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2)))) # label(fact_430_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 488 (all Fa all G_2 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,Fa),G_2))) <-> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) & hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,G_2)))) # label(fact_431_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 489 (all Fa all G_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Fa),G_2))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,G_2)))) # label(fact_432_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 490 (all Fa all G_2 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_2))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2)))) # label(fact_433_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 491 (all A_4 all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))) # label(fact_434_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 492 (all A_4 all B all C_1 hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,B),C_1))) # label(fact_435_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 493 (all A_4 all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1))) # label(fact_436_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 494 (all A all A_4 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) # label(fact_437_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 495 (all A all A_4 all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) # label(fact_438_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 496 (all A all A_4 all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) # label(fact_439_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 497 (all B all D all A all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),D)))))) # label(fact_440_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 498 (all B all D all A all C_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),D)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C_1),D)))))) # label(fact_441_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 499 (all B all A all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),C_1))))) # label(fact_442_Un__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 500 (all B all A all C_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),C_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),C_1))))) # label(fact_443_Un__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 501 (all B all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = A))) # label(fact_444_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 502 (all B all A (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = A)) # label(fact_445_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 503 (all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = B))) # label(fact_446_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 504 (all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = B)) # label(fact_447_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 505 (all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) <-> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = B))) # label(fact_448_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 506 (all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) <-> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = B)) # label(fact_449_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 507 (all B all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))) # label(fact_450_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 508 (all B all A hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)))) # label(fact_451_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 509 (all A all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))) # label(fact_452_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 510 (all A all B hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)))) # label(fact_453_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 511 (all F all A all B hAPP_f1083669085e_bool(image_1774499931_pname(F),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F),A)),hAPP_f1083669085e_bool(image_1774499931_pname(F),B))) # label(fact_454_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 512 (all F all A all B hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B))) # label(fact_455_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 513 (all A_4 all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4))),B)) # label(fact_456_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 514 (all A_4 all B hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),B)) # label(fact_457_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 515 (all A_4 all B hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),B)) # label(fact_458_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 516 (all A_4 all B hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),B) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),B)) # label(fact_459_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 517 (all A_4 all B hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_4))),B)) # label(fact_460_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 518 (all A_4 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)),A)) # label(fact_461_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 519 (all A_4 all A hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)),A)) # label(fact_462_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 520 (all A_4 all A hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)),A)) # label(fact_463_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 521 (all G_2 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),body_1)),Q_1)),Procs))))) # label(fact_464_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 522 (all Z all Y_2 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),Y_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1))))) # label(fact_465_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 523 (all Z all Y_2 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_1))))) # label(fact_466_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 524 (all Z all Y_2 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z),Y_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z),X_1))))) # label(fact_467_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 525 (all Y_2 all X_1 (is_fun_pname_bool(Y_2) & is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) -> X_1 = Y_2)))) # label(fact_468_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 526 (all Y_2 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) -> (hBOOL(X_1) <-> hBOOL(Y_2))))) # label(fact_469_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 527 (all Y_2 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) -> X_1 = Y_2))) # label(fact_470_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 528 (all Z all X_1 all Y_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z))))) # label(fact_471_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 529 (all Z all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z))))) # label(fact_472_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 530 (all Z all X_1 all Y_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),Z)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z))))) # label(fact_473_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 531 (all X_1 all Y_2 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) -> X_1 = Y_2)))) # label(fact_474_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 532 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) -> (hBOOL(X_1) <-> hBOOL(Y_2))))) # label(fact_475_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 533 (all X_1 all Y_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) -> X_1 = Y_2))) # label(fact_476_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 534 (all C all B_1 all A_4 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_4)) -> (B_1 = C -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A_4))))) # label(fact_477_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 535 (all C all B_1 all A_4 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_4)) -> ((hBOOL(B_1) <-> hBOOL(C)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),A_4))))) # label(fact_478_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 536 (all C all B_1 all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),A_4)) -> (B_1 = C -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),A_4))))) # label(fact_479_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 537 (all C all A_4 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),B_1)) -> (B_1 = C -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C))))) # label(fact_480_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 538 (all C all A_4 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),B_1)) -> ((hBOOL(B_1) <-> hBOOL(C)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C))))) # label(fact_481_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 539 (all C all A_4 all B_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),B_1)) -> (B_1 = C -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C))))) # label(fact_482_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 540 (all C all A_4 all B_1 (A_4 = B_1 -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A_4))))) # label(fact_483_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 541 (all C all B_1 all A_4 ((hBOOL(A_4) <-> hBOOL(B_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),B_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),A_4))))) # label(fact_484_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 542 (all C all A_4 all B_1 (A_4 = B_1 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),B_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),A_4))))) # label(fact_485_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 543 (all C all A_4 all B_1 (A_4 = B_1 -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C))))) # label(fact_486_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 544 (all C all B_1 all A_4 ((hBOOL(A_4) <-> hBOOL(B_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),C)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C))))) # label(fact_487_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 545 (all C all A_4 all B_1 (A_4 = B_1 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),C)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C))))) # label(fact_488_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 546 (all Y_2 all X_1 (is_fun_pname_bool(Y_2) & is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) <-> X_1 = Y_2)))) # label(fact_489_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 547 (all Y_2 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) <-> (hBOOL(X_1) <-> hBOOL(Y_2))))) # label(fact_490_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 548 (all Y_2 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_491_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 549 (all X_1 all Y_2 (X_1 = Y_2 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)))) # label(fact_492_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 550 (all Y_2 all X_1 ((hBOOL(X_1) <-> hBOOL(Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)))) # label(fact_493_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 551 (all X_1 all Y_2 (X_1 = Y_2 -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)))) # label(fact_494_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 552 (all X_1 all Y_2 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_2) -> (X_1 = Y_2 <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))))) # label(fact_495_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 553 (all Y_2 all X_1 ((hBOOL(X_1) <-> hBOOL(Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)))) # label(fact_496_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 554 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)))) # label(fact_497_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 555 (all A_4 all A_8 (is_pname(A_4) & is_pname(A_8) -> (hAPP_p1252095976_pname(some_pname,A_4) = hAPP_p1252095976_pname(some_pname,A_8) <-> A_4 = A_8))) # label(fact_498_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 556 (all A_4 all A_8 (hAPP_H1633077406_state(some_H1043067815_state,A_4) = hAPP_H1633077406_state(some_H1043067815_state,A_8) <-> A_4 = A_8)) # label(fact_499_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 557 (all A_4 all A_8 (hAPP_com_option_com(some_com,A_4) = hAPP_com_option_com(some_com,A_8) <-> A_4 = A_8)) # label(fact_500_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 558 (all G_2 all P_1 all C all Q_1 all C_1 ((hBOOL(C_1) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(cOMBB_1757942702_state(cOMBC_231445413l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),C_1)),C),Q_1)),bot_bo784226126e_bool))))) # label(fact_501_constant) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 559 (all Pn_1 all G_2 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procs)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(P_1,Pn_1)),hAPP_pname_com(body_1,Pn_1)),hAPP_p1637813682e_bool(Q_1,Pn_1))),bot_bo784226126e_bool)))))) # label(fact_502_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 560 (all A_4 (is_fun_pname_bool(A_4) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),bot_bo844097828e_bool)) -> A_4 = bot_bo844097828e_bool))) # label(fact_503_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 561 (all A_4 (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A_4),bot_bot_fun_com_bool)) -> A_4 = bot_bot_fun_com_bool)) # label(fact_504_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 562 (all A_4 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),bot_bot_bool)) -> (hBOOL(A_4) <-> hBOOL(bot_bot_bool)))) # label(fact_505_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 563 (all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),bot_bo784226126e_bool)) -> A_4 = bot_bo784226126e_bool)) # label(fact_506_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 564 (all A_4 (is_fun_pname_bool(A_4) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),bot_bo844097828e_bool)) <-> A_4 = bot_bo844097828e_bool))) # label(fact_507_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 565 (all A_4 (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A_4),bot_bot_fun_com_bool)) <-> A_4 = bot_bot_fun_com_bool)) # label(fact_508_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 566 (all A_4 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),bot_bot_bool)) <-> (hBOOL(A_4) <-> hBOOL(bot_bot_bool)))) # label(fact_509_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 567 (all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),bot_bo784226126e_bool)) <-> A_4 = bot_bo784226126e_bool)) # label(fact_510_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 568 (all A_4 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_4))) # label(fact_511_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 569 (all A_4 hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,bot_bot_fun_com_bool),A_4))) # label(fact_512_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 570 (all A_4 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_4))) # label(fact_513_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 571 (all A_4 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A_4))) # label(fact_514_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 572 (all X_1 all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))))) # label(fact_515_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 573 (all X_1 all F all G (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))))) # label(fact_516_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 574 (all X_1 all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))))) # label(fact_517_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 575 (all X_1 all F all G (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))))) # label(fact_518_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 576 (all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) <-> (all X_2 (is_pname(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))))) # label(fact_519_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 577 (all F all G (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2)))))) # label(fact_520_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 578 (all X_1 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_521_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 579 (all X_1 (hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_522_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 580 (all X_1 (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_523_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 581 (all X_2 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_524_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 582 (all X_2 (hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_525_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 583 (all X_2 (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_526_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 584 (all P_1 all Q_1 all G_2 all P_3 all C0_1 all Q_3 all U_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1)) -> ((all P_4 (is_fun_pname_bool(P_4) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f887530048e_bool(P_3,P_4)),hAPP_f792846925ol_com(C0_1,P_4)),hAPP_f887530048e_bool(Q_3,P_4))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f887530048e_bool(P_1,P_4)),hAPP_f792846925ol_com(C0_1,P_4)),hAPP_f887530048e_bool(Q_1,P_4))),bot_bo784226126e_bool)))))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f509793681e_bool(image_845802851_state(hAPP_f819036232_state(hAPP_f815143704_state(cOMBS_858986606_state,hAPP_f240260249_state(hAPP_f578932784_state(cOMBS_384351451_state,hAPP_f1633046421_state(cOMBB_1794358604e_bool(hoare_1191504582_state),P_3)),C0_1)),Q_3)),U_1))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f509793681e_bool(image_845802851_state(hAPP_f819036232_state(hAPP_f815143704_state(cOMBS_858986606_state,hAPP_f240260249_state(hAPP_f578932784_state(cOMBS_384351451_state,hAPP_f1633046421_state(cOMBB_1794358604e_bool(hoare_1191504582_state),P_1)),C0_1)),Q_1)),U_1))))))) # label(fact_527_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 585 (all P_1 all Q_1 all G_2 all P_3 all C0_1 all Q_3 all U_1 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,U_1)) -> ((all P_4 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1487042470e_bool(P_3,P_4)),hAPP_f1547517799ol_com(C0_1,P_4)),hAPP_f1487042470e_bool(Q_3,P_4))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1487042470e_bool(P_1,P_4)),hAPP_f1547517799ol_com(C0_1,P_4)),hAPP_f1487042470e_bool(Q_1,P_4))),bot_bo784226126e_bool))))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f1216288071e_bool(image_1497401961_state(hAPP_f578501918_state(hAPP_f886846002_state(cOMBS_57685138_state,hAPP_f824259881_state(hAPP_f37848848_state(cOMBS_1164062463_state,hAPP_f250550847_state(cOMBB_2049797414e_bool(hoare_1191504582_state),P_3)),C0_1)),Q_3)),U_1))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f1216288071e_bool(image_1497401961_state(hAPP_f578501918_state(hAPP_f886846002_state(cOMBS_57685138_state,hAPP_f824259881_state(hAPP_f37848848_state(cOMBS_1164062463_state,hAPP_f250550847_state(cOMBB_2049797414e_bool(hoare_1191504582_state),P_1)),C0_1)),Q_1)),U_1))))))) # label(fact_528_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 586 (all P_1 all Q_1 all G_2 all P_3 all C0_1 all Q_3 all U_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1)) -> ((all P_4 (is_pname(P_4) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(P_3,P_4)),hAPP_pname_com(C0_1,P_4)),hAPP_p1637813682e_bool(Q_3,P_4))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(P_1,P_4)),hAPP_pname_com(C0_1,P_4)),hAPP_p1637813682e_bool(Q_1,P_4))),bot_bo784226126e_bool)))))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_3)),C0_1)),Q_3)),U_1))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),C0_1)),Q_1)),U_1))))))) # label(fact_529_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 587 (all G_2 all C all Q_1 all P_1 ((all Z_2 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_1))),C),hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Q_1,Z_2)))),bot_bo784226126e_bool))))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))))) # label(fact_530_escape) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 588 (all G_2 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),body_1)),Q_1)),Procs))))) # label(fact_531_Body__sound__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 589 (all P_1 all G_2 all P_3 all C all Q_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_3),C),Q_1)),bot_bo784226126e_bool))) -> ((all Z_2 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_3,Z_2),S_1)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool)))))) # label(fact_532_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 590 (all Q_1 all G_2 all P_1 all C all Q_3 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_3)),bot_bo784226126e_bool))) -> ((all Z_2 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_2),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_1)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool)))))) # label(fact_533_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 591 (all P_1 all Q_1 all C (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool)))))) # label(fact_534_MGF__complete) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 592 (all A all B all X_1 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)) -> (-hBOOL(hAPP_pname_bool(A,X_1)) -> hBOOL(hAPP_pname_bool(B,X_1))))) # label(fact_535_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 593 (all A all B all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1)) -> (-hBOOL(hAPP_H242767318e_bool(A,X_1)) -> hBOOL(hAPP_H242767318e_bool(B,X_1))))) # label(fact_536_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 594 (all A all B all X_1 ((-hBOOL(hAPP_pname_bool(B,X_1)) -> hBOOL(hAPP_pname_bool(A,X_1))) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)))) # label(fact_537_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 595 (all A all B all X_1 ((-hBOOL(hAPP_H242767318e_bool(B,X_1)) -> hBOOL(hAPP_H242767318e_bool(A,X_1))) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1)))) # label(fact_538_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 596 (all Q_1 all P_1 all G_2 all P_3 all C all Q_3 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_3),C),Q_3)),bot_bo784226126e_bool))) -> ((all Z_2 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1)) -> (all S_2 ((all Z_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_3,Z_3),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_3),S_2)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_2)))))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool)))))) # label(fact_539_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 597 (all G_2 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) -> hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(G_2),Ts)))) # label(fact_540_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 598 (all X_2 (hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_2)) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),bot_bot_fun_com_bool)))) # label(fact_541_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 599 (all X_2 (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),bot_bo784226126e_bool)))) # label(fact_542_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 600 (all X_2 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),bot_bo844097828e_bool)))) # label(fact_543_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 601 (all Q_1 all P_1 all X_1 (hBOOL(hAPP_pname_bool(P_1,X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) -> hBOOL(hAPP_pname_bool(Q_1,X_1))))) # label(fact_544_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 602 (all Q_1 all P_1 all X_1 (hBOOL(hAPP_H242767318e_bool(P_1,X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,P_1),Q_1)) -> hBOOL(hAPP_H242767318e_bool(Q_1,X_1))))) # label(fact_545_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 603 (all X_1 all P_1 all Q_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) -> (hBOOL(hAPP_pname_bool(P_1,X_1)) -> hBOOL(hAPP_pname_bool(Q_1,X_1))))) # label(fact_546_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 604 (all X_1 all P_1 all Q_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,P_1),Q_1)) -> (hBOOL(hAPP_H242767318e_bool(P_1,X_1)) -> hBOOL(hAPP_H242767318e_bool(Q_1,X_1))))) # label(fact_547_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 605 (all A all B all X_1 (hBOOL(hAPP_pname_bool(B,X_1)) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)))) # label(fact_548_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 606 (all A all B all X_1 (hBOOL(hAPP_H242767318e_bool(B,X_1)) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1)))) # label(fact_549_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 607 (all B all A all X_1 (hBOOL(hAPP_pname_bool(A,X_1)) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)))) # label(fact_550_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 608 (all B all A all X_1 (hBOOL(hAPP_H242767318e_bool(A,X_1)) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1)))) # label(fact_551_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 609 (all R_1 all S (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S))) <-> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,R_1),S)))) # label(fact_552_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 610 (all R_1 all S (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),R_1)),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),S))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,R_1),S)))) # label(fact_553_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 611 (all R_1 all S (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,R_1),S)))) # label(fact_554_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 612 (all R_1 all S all X_2 (hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)),X_2)) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,R_1),S))))) # label(fact_555_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 613 (all R_1 all S all X_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),R_1)),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),S)),X_2)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,R_1),S))))) # label(fact_556_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 614 (all R_1 all S all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S))))) # label(fact_557_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 615 (all F all G ((all X_2 (is_pname(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)))) # label(fact_558_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 616 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)))) # label(fact_559_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 617 (all X_1 set_pname(hAPP_p1252095976_pname(some_pname,X_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) # label(fact_560_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 618 (all X_1 set_com(hAPP_com_option_com(some_com,X_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) # label(fact_561_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 619 (all X_1 set_Ho1741238126_state(hAPP_H1633077406_state(some_H1043067815_state,X_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) # label(fact_562_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 620 (all F all G all X_1 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))))) # label(fact_563_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 621 (all F all G all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F),G),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))))) # label(fact_564_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 622 (all F all G all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))) # label(fact_565_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 623 (all F all G all X_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2))))) # label(fact_566_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 624 hBOOL(hoare_1795711768gleton) -> (all T_2 -(all S_1 S_1 = T_2)) # label(fact_567_single__stateE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 625 (all X_1 all Y_2 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_2) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = bot_bo844097828e_bool <-> X_1 = bot_bo844097828e_bool & Y_2 = bot_bo844097828e_bool))) # label(fact_568_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 626 (all X_1 all Y_2 (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,X_1),Y_2) = bot_bot_fun_com_bool <-> X_1 = bot_bot_fun_com_bool & Y_2 = bot_bot_fun_com_bool)) # label(fact_569_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 627 (all X_1 all Y_2 ((hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) <-> hBOOL(bot_bot_bool)) <-> (hBOOL(X_1) <-> hBOOL(bot_bot_bool)) & (hBOOL(Y_2) <-> hBOOL(bot_bot_bool)))) # label(fact_570_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 628 (all X_1 all Y_2 (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = bot_bo784226126e_bool <-> X_1 = bot_bo784226126e_bool & Y_2 = bot_bo784226126e_bool)) # label(fact_571_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 629 (all X_1 all Xo (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),set_com(Xo))) <-> Xo = hAPP_com_option_com(some_com,X_1))) # label(fact_572_elem__set) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 630 (all X_1 all Xo (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),set_Ho1741238126_state(Xo))) <-> Xo = hAPP_H1633077406_state(some_H1043067815_state,X_1))) # label(fact_573_elem__set) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 631 (all X_1 all Xo (is_option_pname(Xo) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),set_pname(Xo))) <-> Xo = hAPP_p1252095976_pname(some_pname,X_1)))) # label(fact_574_elem__set) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 632 (all A_4 (is_fun_pname_bool(A_4) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),A_4) = A_4)) # label(fact_575_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 633 (all A_4 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),A_4)) <-> hBOOL(A_4))) # label(fact_576_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 634 (all A_4 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),A_4) = A_4) # label(fact_577_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 635 (all X_1 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),X_1) = X_1)) # label(fact_578_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 636 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),X_1)) <-> hBOOL(X_1))) # label(fact_579_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 637 (all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),X_1) = X_1) # label(fact_580_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 638 (all A_4 all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A_4)) # label(fact_581_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 639 (all A_4 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),A_4)))) # label(fact_582_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 640 (all A_4 all B_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),A_4)) # label(fact_583_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 641 (all X_1 all Y_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1)) # label(fact_584_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 642 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)))) # label(fact_585_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 643 (all X_1 all Y_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),X_1)) # label(fact_586_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 644 (all X_1 all Y_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1)) # label(fact_587_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 645 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)))) # label(fact_588_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 646 (all X_1 all Y_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),X_1)) # label(fact_589_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 647 (all A_4 all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)) # label(fact_590_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 648 (all A_4 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)))) # label(fact_591_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 649 (all A_4 all B_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)) # label(fact_592_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 650 (all X_1 all Y_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) # label(fact_593_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 651 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))) # label(fact_594_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 652 (all X_1 all Y_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) # label(fact_595_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 653 (all X_1 all Y_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) # label(fact_596_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 654 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))) # label(fact_597_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 655 (all X_1 all Y_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) # label(fact_598_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 656 (all B_1 all A_4 all C hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),C)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C))) # label(fact_599_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 657 (all B_1 all A_4 all C (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),C))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))))) # label(fact_600_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 658 (all B_1 all A_4 all C hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),C)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C))) # label(fact_601_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 659 (all X_1 all Y_2 all Z hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z))) # label(fact_602_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 660 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))))) # label(fact_603_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 661 (all X_1 all Y_2 all Z hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z))) # label(fact_604_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 662 (all X_1 all Y_2 all Z hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z))) # label(fact_605_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 663 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))))) # label(fact_606_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 664 (all X_1 all Y_2 all Z hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z))) # label(fact_607_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 665 (all A_4 all B_1 all C hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),C) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C))) # label(fact_608_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 666 (all A_4 all B_1 all C (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),C)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))))) # label(fact_609_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 667 (all A_4 all B_1 all C hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),C) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C))) # label(fact_610_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 668 (all X_1 all Y_2 all Z hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z))) # label(fact_611_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 669 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))))) # label(fact_612_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 670 (all X_1 all Y_2 all Z hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),Z) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z))) # label(fact_613_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 671 (all X_1 all Y_2 all Z hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z))) # label(fact_614_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 672 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))))) # label(fact_615_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 673 (all X_1 all Y_2 all Z hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),Z) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z))) # label(fact_616_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 674 (all X_1 all Y_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)))) # label(fact_617_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 675 (all X_1 all Y_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))) # label(fact_618_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 676 (all X_1 all Y_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)))) # label(fact_619_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 677 (all X_1 all Y_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)))) # label(fact_620_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 678 (all X_1 all Y_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))) # label(fact_621_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 679 (all X_1 all Y_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)))) # label(fact_622_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 680 (all Y_2 all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)))) # label(fact_623_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 681 (all Y_2 all X_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))) # label(fact_624_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 682 (all Y_2 all X_1 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)))) # label(fact_625_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 683 (all Y_2 all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)))) # label(fact_626_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 684 (all Y_2 all X_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))) # label(fact_627_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 685 (all Y_2 all X_1 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)))) # label(fact_628_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 686 (all X_1 all Y_2 (is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) <-> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = Y_2))) # label(fact_629_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 687 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) <-> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) <-> hBOOL(Y_2)))) # label(fact_630_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.15 688 (all X_1 all Y_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) <-> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = Y_2)) # label(fact_631_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 689 (all X_1 all Y_2 all Z (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z)))) # label(fact_632_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 690 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z)) & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z)))) # label(fact_633_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 691 (all X_1 all Y_2 all Z (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),Z)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),Z)))) # label(fact_634_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 692 (all B_1 all X_1 all A_4 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1))))) # label(fact_635_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 693 (all B_1 all X_1 all A_4 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))))) # label(fact_636_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 694 (all B_1 all X_1 all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),A_4)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1))))) # label(fact_637_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 695 (all A_4 all X_1 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1))))) # label(fact_638_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 696 (all A_4 all X_1 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))))) # label(fact_639_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 697 (all A_4 all X_1 all B_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),B_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1))))) # label(fact_640_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 698 (all X_1 all Y_2 (is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = Y_2))) # label(fact_641_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 699 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) <-> hBOOL(Y_2)))) # label(fact_642_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 700 (all X_1 all Y_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = Y_2)) # label(fact_643_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 701 (all Y_2 all X_1 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = X_1))) # label(fact_644_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 702 (all Y_2 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) <-> hBOOL(X_1)))) # label(fact_645_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 703 (all Y_2 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = X_1)) # label(fact_646_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 704 (all B_1 all A_4 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),X_1))))) # label(fact_647_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 705 (all B_1 all A_4 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),X_1))))) # label(fact_648_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 706 (all B_1 all A_4 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),X_1))))) # label(fact_649_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 707 (all Z all Y_2 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)),X_1))))) # label(fact_650_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 708 (all Z all Y_2 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)),X_1))))) # label(fact_651_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 709 (all Z all Y_2 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z),X_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)),X_1))))) # label(fact_652_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 710 (all B_1 all D_1 all A_4 all C (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C),D_1)))))) # label(fact_653_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 711 (all B_1 all D_1 all A_4 all C (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),D_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,C),D_1)))))) # label(fact_654_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 712 (all B_1 all D_1 all A_4 all C (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),D_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C),D_1)))))) # label(fact_655_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 713 (all A_4 all B_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),X_1)) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1))))) # label(fact_656_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 714 (all A_4 all B_1 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),X_1)) -> -(hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1)) -> -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1))))) # label(fact_657_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 715 (all A_4 all B_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),X_1)) -> -(hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),X_1)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_1))))) # label(fact_658_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 716 (all X_1 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),X_1) = X_1)) # label(fact_659_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 717 (all X_1 hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,bot_bot_fun_com_bool),X_1) = X_1) # label(fact_660_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 718 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,bot_bot_bool),X_1)) <-> hBOOL(X_1))) # label(fact_661_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 719 (all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),X_1) = X_1) # label(fact_662_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 720 (all X_1 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),bot_bo844097828e_bool) = X_1)) # label(fact_663_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 721 (all X_1 hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,X_1),bot_bot_fun_com_bool) = X_1) # label(fact_664_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 722 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),bot_bot_bool)) <-> hBOOL(X_1))) # label(fact_665_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 723 (all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),bot_bo784226126e_bool) = X_1) # label(fact_666_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 724 (all X_1 all P_1 all A ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),set_pname(A))) -> hBOOL(hAPP_pname_bool(P_1,X_2))))) -> (A = hAPP_p1252095976_pname(some_pname,X_1) -> hBOOL(hAPP_pname_bool(P_1,X_1))))) # label(fact_667_ospec) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 725 (all X_1 all P_1 all A ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),set_Ho1741238126_state(A))) -> hBOOL(hAPP_H242767318e_bool(P_1,X_2)))) -> (A = hAPP_H1633077406_state(some_H1043067815_state,X_1) -> hBOOL(hAPP_H242767318e_bool(P_1,X_1))))) # label(fact_668_ospec) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 726 (all X_1 all P_1 all A ((all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),set_com(A))) -> hBOOL(hAPP_com_bool(P_1,X_2)))) -> (A = hAPP_com_option_com(some_com,X_1) -> hBOOL(hAPP_com_bool(P_1,X_1))))) # label(fact_669_ospec) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 727 (all B all A all F all Fa (is_fun1661590463l_bool(B) & is_fun1661590463l_bool(A) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (B != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B))))))))) # label(fact_670_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 728 (all B all A all F all Fa (hBOOL(finite688249778e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (A != bot_bo942947096l_bool -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (B != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,A)),hAPP_f1216288071e_bool(Fa,B)))))))) # label(fact_671_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 729 (all B all A all F all Fa (hBOOL(finite666746948em_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (A != bot_bot_fun_com_bool -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,B)) -> (B != bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B)))))))) # label(fact_672_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 730 (all B all A all F all Fa (hBOOL(finite416071164_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (A != bot_bo784226126e_bool -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (B != bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,A)),hAPP_f718417177_state(Fa,B)))))))) # label(fact_673_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 731 (all B all A all F all Fa (is_fun_pname_bool(B) & is_fun_pname_bool(A) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (B != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B))))))))) # label(fact_674_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 732 (all B all A all F all Fa (is_fun1661590463l_bool(B) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (B != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,B)),hAPP_f674760225e_bool(Fa,A)) = hAPP_f674760225e_bool(Fa,A))))))) # label(fact_675_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 733 (all B all A all F all Fa (hBOOL(finite688249778e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (B != bot_bo942947096l_bool -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,B)),hAPP_f1216288071e_bool(Fa,A)) = hAPP_f1216288071e_bool(Fa,A)))))) # label(fact_676_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 734 (all B all A all F all Fa (hBOOL(finite666746948em_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (B != bot_bot_fun_com_bool -> (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,B),A)) -> hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,B)),hAPP_f1276420679ol_com(Fa,A)) = hAPP_f1276420679ol_com(Fa,A)))))) # label(fact_677_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 735 (all B all A all F all Fa (hBOOL(finite416071164_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (B != bot_bo784226126e_bool -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)) -> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,B)),hAPP_f718417177_state(Fa,A)) = hAPP_f718417177_state(Fa,A)))))) # label(fact_678_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 736 (all B all A all F all Fa (is_fun_pname_bool(B) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (B != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,B)),hAPP_f1297739591_pname(Fa,A)) = hAPP_f1297739591_pname(Fa,A))))))) # label(fact_679_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 737 (all G_2 all P_1 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),skip),P_1)),bot_bo784226126e_bool)))) # label(fact_680_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 738 (all X_1 all A all F all Fa (hBOOL(finite666746948em_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (A != bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)))))) # label(fact_681_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 739 (all X_1 all A all F all Fa (is_fun1661590463l_bool(A) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A))))))) # label(fact_682_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 740 (all X_1 all A all F all Fa (hBOOL(finite688249778e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (A != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,A)))))) # label(fact_683_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 741 (all X_1 all A all F all Fa (is_fun_pname_bool(A) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A))))))) # label(fact_684_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 742 (all X_1 all A all F all Fa (hBOOL(finite416071164_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (A != bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,A)))))) # label(fact_685_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 743 (all P_1 all Fa (hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa)) -> (Fa != bot_bot_fun_com_bool -> ((all X_2 hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),bot_bot_fun_com_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2)) -> (F_2 != bot_bot_fun_com_bool -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),F_2)) -> (hBOOL(hAPP_f990396704l_bool(P_1,F_2)) -> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),F_2)))))))) -> hBOOL(hAPP_f990396704l_bool(P_1,Fa))))))) # label(fact_686_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 744 (all P_1 all Fa (is_fun1661590463l_bool(Fa) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (Fa != bot_bo1649642514l_bool -> ((all X_2 (is_fun_pname_bool(X_2) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),bot_bo1649642514l_bool))))) -> ((all X_2 all F_2 (is_fun_pname_bool(X_2) & is_fun1661590463l_bool(F_2) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2)) -> (F_2 != bot_bo1649642514l_bool -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_2)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_2)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_2))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)))))))) # label(fact_687_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 745 (all P_1 all Fa (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) -> (Fa != bot_bo942947096l_bool -> ((all X_2 hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),bot_bo942947096l_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,F_2)) -> (F_2 != bot_bo942947096l_bool -> (-hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),F_2)) -> (hBOOL(hAPP_f1410040974l_bool(P_1,F_2)) -> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),F_2)))))))) -> hBOOL(hAPP_f1410040974l_bool(P_1,Fa))))))) # label(fact_688_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 746 (all P_1 all Fa (is_fun_pname_bool(Fa) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (Fa != bot_bo844097828e_bool -> ((all X_2 (is_pname(X_2) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool))))) -> ((all X_2 all F_2 (is_pname(X_2) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (F_2 != bot_bo844097828e_bool -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_2)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)))))))) # label(fact_689_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 747 (all P_1 all Fa (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) -> (Fa != bot_bo784226126e_bool -> ((all X_2 hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (F_2 != bot_bo784226126e_bool -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,F_2)) -> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2)))))))) -> hBOOL(hAPP_f1378282496l_bool(P_1,Fa))))))) # label(fact_690_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 748 (all G_2 all P_1 all B_1 all C hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B_1))),hAPP_com_com(while(B_1),C)),P_1)),bot_bo784226126e_bool)))) # label(fact_691_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 749 (all D_1 all R_1 all G_2 all P_1 all C all Q_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Q_1),D_1),R_1)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_com_com(hAPP_com_fun_com_com(semi,C),D_1)),R_1)),bot_bo784226126e_bool)))))) # label(fact_692_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 750 (all B_1 all C (hBOOL(hAPP_com_bool(wt,hAPP_com_com(while(B_1),C))) -> hBOOL(hAPP_com_bool(wt,C)))) # label(fact_693_WTs__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 751 (all C1 all C2 (hBOOL(hAPP_com_bool(wt,hAPP_com_com(hAPP_com_fun_com_com(semi,C1),C2))) -> -(hBOOL(hAPP_com_bool(wt,C1)) -> -hBOOL(hAPP_com_bool(wt,C2))))) # label(fact_694_WTs__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 752 (all X_1 all F all Fa (hBOOL(finite416071164_state(F,Fa)) -> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),X_1) = X_1)) # label(fact_695_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 753 (all X_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite89670078_pname(F,Fa)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),X_1) = X_1))) # label(fact_696_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 754 (all Com1_3 all Com2_3 skip != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_3),Com2_3)) # label(fact_697_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 755 (all Fun_1 all Com_2 skip != hAPP_com_com(while(Fun_1),Com_2)) # label(fact_698_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 756 (all Com1_3 all Com2_3 hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_3),Com2_3) != skip) # label(fact_699_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 757 (all Fun_1 all Com_2 hAPP_com_com(while(Fun_1),Com_2) != skip) # label(fact_700_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 758 (all Com1_2 all Com2_2 all Fun_1 all Com_2 hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) != hAPP_com_com(while(Fun_1),Com_2)) # label(fact_701_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 759 (all Fun_1 all Com_2 all Com1_2 all Com2_2 hAPP_com_com(while(Fun_1),Com_2) != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2)) # label(fact_702_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 760 (all Com1_2 all Com2_2 all Com1_1 all Com2_1 (hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) = hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_1),Com2_1) <-> Com1_2 = Com1_1 & Com2_2 = Com2_1)) # label(fact_703_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 761 (all Fun all Com_1 all Fun_1 all Com_2 (hAPP_com_com(while(Fun),Com_1) = hAPP_com_com(while(Fun_1),Com_2) <-> Fun = Fun_1 & Com_1 = Com_2)) # label(fact_704_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 762 (all Pname_1 all Fun all Com_1 hAPP_pname_com(body_1,Pname_1) != hAPP_com_com(while(Fun),Com_1)) # label(fact_705_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 763 (all Fun all Com_1 all Pname_1 hAPP_com_com(while(Fun),Com_1) != hAPP_pname_com(body_1,Pname_1)) # label(fact_706_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 764 (all B_1 all C (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_com_bool(wt,hAPP_com_com(while(B_1),C))))) # label(fact_707_While) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 765 (all Pname all Com1 all Com2 hAPP_pname_com(body_1,Pname) != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1),Com2)) # label(fact_708_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 766 (all Com1 all Com2 all Pname hAPP_com_com(hAPP_com_fun_com_com(semi,Com1),Com2) != hAPP_pname_com(body_1,Pname)) # label(fact_709_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 767 (all C1 all C0 (hBOOL(hAPP_com_bool(wt,C0)) -> (hBOOL(hAPP_com_bool(wt,C1)) -> hBOOL(hAPP_com_bool(wt,hAPP_com_com(hAPP_com_fun_com_com(semi,C0),C1)))))) # label(fact_710_WT_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 768 (all Pname skip != hAPP_pname_com(body_1,Pname)) # label(fact_711_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 769 (all Pname hAPP_pname_com(body_1,Pname) != skip) # label(fact_712_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 770 (all X_1 all A all F all Fa (hBOOL(finite666746948em_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)) = hAPP_f1276420679ol_com(Fa,A))))) # label(fact_714_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 771 (all X_1 all A all F all Fa (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)) = hAPP_f1297739591_pname(Fa,A))))) # label(fact_715_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 772 (all X_1 all A all F all Fa (hBOOL(finite416071164_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,A)) = hAPP_f718417177_state(Fa,A))))) # label(fact_716_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 773 (all X_1 all A all F all Fa (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)) = hAPP_f674760225e_bool(Fa,A))))) # label(fact_717_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 774 (all X_1 all A all F all Fa (hBOOL(finite688249778e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,A)) = hAPP_f1216288071e_bool(Fa,A))))) # label(fact_718_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 775 (all N all H_1 all F all Fa (is_fun1661590463l_bool(N) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> ((all X_2 all Y_3 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_3) -> hAPP_f759274231e_bool(H_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_3)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f759274231e_bool(H_1,X_2)),hAPP_f759274231e_bool(H_1,Y_3)))) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N)) -> (N != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(H_1,hAPP_f674760225e_bool(Fa,N)) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(image_2063528359e_bool(H_1),N)))))))) # label(fact_719_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 776 (all N all H_1 all F all Fa (hBOOL(finite688249778e_bool(F,Fa)) -> ((all X_2 all Y_3 hAPP_f806699093e_bool(H_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_2),Y_3)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f806699093e_bool(H_1,X_2)),hAPP_f806699093e_bool(H_1,Y_3))) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,N)) -> (N != bot_bo942947096l_bool -> hAPP_f806699093e_bool(H_1,hAPP_f1216288071e_bool(Fa,N)) = hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(image_390184709e_bool(H_1),N))))))) # label(fact_720_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 777 (all N all H_1 all F all Fa (is_fun_pname_bool(N) -> (hBOOL(finite89670078_pname(F,Fa)) -> ((all X_2 all Y_3 (is_pname(X_2) & is_pname(Y_3) -> hAPP_pname_pname(H_1,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_3)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H_1,X_2)),hAPP_pname_pname(H_1,Y_3)))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N)) -> (N != bot_bo844097828e_bool -> hAPP_pname_pname(H_1,hAPP_f1297739591_pname(Fa,N)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(image_pname_pname(H_1),N)))))))) # label(fact_721_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 778 (all N all H_1 all F all Fa (hBOOL(finite416071164_state(F,Fa)) -> ((all X_2 all Y_3 hAPP_H574424047_state(H_1,hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_3)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_H574424047_state(H_1,X_2)),hAPP_H574424047_state(H_1,Y_3))) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,N)) -> (N != bot_bo784226126e_bool -> hAPP_H574424047_state(H_1,hAPP_f718417177_state(Fa,N)) = hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(image_661047967_state(H_1),N))))))) # label(fact_722_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 779 (all N all H_1 all F all Fa (hBOOL(finite666746948em_com(F,Fa)) -> ((all X_2 all Y_3 hAPP_com_com(H_1,hAPP_com_com(hAPP_com_fun_com_com(F,X_2),Y_3)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_com_com(H_1,X_2)),hAPP_com_com(H_1,Y_3))) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,N)) -> (N != bot_bot_fun_com_bool -> hAPP_com_com(H_1,hAPP_f1276420679ol_com(Fa,N)) = hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(image_com_com(H_1),N))))))) # label(fact_723_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 780 (all X_4 hAPP_f1276420679ol_com(the_elem_com,X_4) = hAPP_f1276420679ol_com(the_com_1,hAPP_f1998868198m_bool(cOMBB_298914627ol_com(hAPP_f273696895l_bool(fequal_fun_com_bool,X_4)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool)))) # label(fact_724_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 781 (all X_4 hAPP_f1297739591_pname(the_elem_pname,X_4) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_4)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool)))) # label(fact_725_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 782 (all X_4 hAPP_f718417177_state(the_el2080696983_state,X_4) = hAPP_f718417177_state(the_Ho2067184133_state,hAPP_f1900156034e_bool(cOMBB_1282391997_state(hAPP_f849457489l_bool(fequal1475827639e_bool,X_4)),hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,insert1744391420_state),bot_bo784226126e_bool)))) # label(fact_726_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 783 (all X_1 all A all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> (A != bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A))))))) # label(fact_727_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 784 (all X_1 all A all F all Fa (is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (A != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)))))))) # label(fact_728_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 785 (all X_1 all A all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> (A != bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,A))))))) # label(fact_729_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 786 (all X_1 all A all F all Fa (is_fun1661590463l_bool(A) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) -> (A != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)))))))) # label(fact_730_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 787 (all X_1 all A all F all Fa (hBOOL(finite2009063477e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (-hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A)) -> (A != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,A))))))) # label(fact_731_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 788 (all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com),Fun2))) # label(fact_732_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 789 (all X_1 all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = X_1)) # label(fact_733_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 790 (all X_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1))) # label(fact_734_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 791 (all X_1 all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1)) # label(fact_735_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 792 (all A all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (A != bot_bot_fun_com_bool -> ((all X_2 all Y_3 hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_com_com(hAPP_com_fun_com_com(F,X_2),Y_3)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_3),bot_bot_fun_com_bool))))) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_f1276420679ol_com(Fa,A)),A))))))) # label(fact_736_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 793 (all A all F all Fa (is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> ((all X_2 all Y_3 (is_pname(X_2) & is_pname(Y_3) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_3),bot_bo844097828e_bool)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(Fa,A)),A)))))))) # label(fact_737_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 794 (all A all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (A != bot_bo784226126e_bool -> ((all X_2 all Y_3 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_3)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_3),bot_bo784226126e_bool))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_f718417177_state(Fa,A)),A))))))) # label(fact_738_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 795 (all A all F all Fa (is_fun1661590463l_bool(A) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> ((all X_2 all Y_3 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_3) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_3)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_3),bot_bo1649642514l_bool)))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f674760225e_bool(Fa,A)),A)))))))) # label(fact_739_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 796 (all A all F all Fa (hBOOL(finite2009063477e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (A != bot_bo942947096l_bool -> ((all X_2 all Y_3 hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_2),Y_3)),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,Y_3),bot_bo942947096l_bool))))) -> hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,hAPP_f1216288071e_bool(Fa,A)),A))))))) # label(fact_740_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 797 (all F all G all M_1 all N (M_1 = N -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),N)) -> hAPP_p1751618853_state(F,X_2) = hAPP_p1751618853_state(G,X_2)))) -> hAPP_f360545851e_bool(image_185131637_state(F),M_1) = hAPP_f360545851e_bool(image_185131637_state(G),N)))) # label(fact_741_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 798 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_H242767318e_bool(P_1,X_2)) -> hBOOL(hAPP_H242767318e_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(collec637225377_state,P_1)),hAPP_f806699093e_bool(collec637225377_state,Q_1))))) # label(fact_742_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 799 (all Q_1 all P_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))))) # label(fact_743_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 800 (all Q_1 all P_1 ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) -> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))) # label(fact_744_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 801 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_f1378282496l_bool(P_1,X_2)) -> hBOOL(hAPP_f1378282496l_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))))) # label(fact_745_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 802 (all Q_1 all P_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)))) # label(fact_746_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 803 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_H242767318e_bool(P_1,X_2)) -> hBOOL(hAPP_H242767318e_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,P_1),Q_1)))) # label(fact_747_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 804 (all A_4 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) -> (exists B_2 (A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B_2) & -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B_2)))))) # label(fact_748_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 805 (all A_4 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) -> (exists B_2 (is_fun_pname_bool(B_2) & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B_2))))))) # label(fact_749_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 806 (all A_4 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) -> (exists B_2 (A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B_2) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),B_2)))))) # label(fact_750_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 807 (all X_1 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> -(all B_2 (A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B_2) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B_2)))))) # label(fact_751_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 808 (all X_1 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> -(all B_2 (is_fun_pname_bool(B_2) -> (A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_2)))))))) # label(fact_752_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 809 (all X_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> -(all B_2 (A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_2) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_2)))))) # label(fact_753_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 810 (all A ((all Y_3 -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,Y_3),A))) -> A = bot_bot_fun_com_bool)) # label(fact_754_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 811 (all A (is_fun_pname_bool(A) -> ((all Y_3 (is_pname(Y_3) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_3),A)))) -> A = bot_bo844097828e_bool))) # label(fact_755_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 812 (all A ((all Y_3 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_3),A))) -> A = bot_bo784226126e_bool)) # label(fact_756_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 813 (all G_2 all C (hBOOL(hoare_1795711768gleton) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool)))))) # label(fact_757_MGT__alternD) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 814 (all C all F all B_1 all A_4 ((hBOOL(A_4) <-> hBOOL(hAPP_bool_bool(F,B_1))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),B_1)) -> ((all X_2 all Y_3 (is_bool(X_2) & is_bool(Y_3) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_3),X_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_3)),hAPP_bool_bool(F,X_2)))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,C)),A_4)))))) # label(fact_758_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 815 (all C all A_4 all F all B_1 (A_4 = hAPP_f759274231e_bool(F,B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1)) -> ((all X_2 all Y_3 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_3),X_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_3)),hAPP_f759274231e_bool(F,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,C)),A_4)))))) # label(fact_759_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 816 (all C all A_4 all F all B_1 (A_4 = hAPP_f806699093e_bool(F,B_1) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),B_1)) -> ((all X_2 all Y_3 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_3),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_3)),hAPP_f806699093e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,C)),A_4)))))) # label(fact_760_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 817 (all G_2 all C (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo784226126e_bool))))) # label(fact_761_MGT__alternI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 818 (all C hAPP_c1455475371_state(hoare_Mirabelle_MGT,C) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,fequal_state),C),evalc(C))) # label(fact_762_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 819 (all P all S_4 all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,P)),S_4),S1_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,P))),S_4),S1_2)))) # label(fact_763_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 820 (all Pn all S0_1 all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn))),S0_1),S1_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,Pn)),S0_1),S1_2)))) # label(fact_764_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 821 (all S_4 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_4),T_1)) -> T_1 = S_4)) # label(fact_765_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 822 (all S_4 hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_4),S_4))) # label(fact_766_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 823 (all C1 all S2_1 all C0 all S0_1 all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0_1),S1_2)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1_2),S2_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(hAPP_com_fun_com_com(semi,C0),C1)),S0_1),S2_1))))) # label(fact_767_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 824 (all S2 all C all S1_1 all B_1 all S0 (hBOOL(hAPP_state_bool(B_1,S0)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0),S1_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S1_1),S2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S0),S2)))))) # label(fact_768_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 825 (all C all B_1 all S_3 (-hBOOL(hAPP_state_bool(B_1,S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S_3),S_3)))) # label(fact_769_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 826 (all U all C_2 all S_4 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_4),T_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_4),U)) -> U = T_1))) # label(fact_770_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 827 (all C1 all C2 all S_4 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(hAPP_com_fun_com_com(semi,C1),C2)),S_4),T_1)) -> -(all S1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_4),S1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1),T_1)))))) # label(fact_771_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 828 (all B_1 all C all S_3 all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S_3),T)) -> ((T = S_3 -> hBOOL(hAPP_state_bool(B_1,S_3))) -> -(hBOOL(hAPP_state_bool(B_1,S_3)) -> (all S1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S_3),S1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S1),T)))))))) # label(fact_772_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 829 (all C all F all B_1 all A_4 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_4)) -> ((hBOOL(hAPP_bool_bool(F,B_1)) <-> hBOOL(C)) -> ((all X_2 all Y_3 (is_bool(X_2) & is_bool(Y_3) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_3),X_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_3)),hAPP_bool_bool(F,X_2)))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),hAPP_bool_bool(F,A_4))))))) # label(fact_773_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 830 (all F all C all B_1 all A_4 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_4)) -> (hAPP_f759274231e_bool(F,B_1) = C -> ((all X_2 all Y_3 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_3) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_3),X_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_3)),hAPP_f759274231e_bool(F,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),hAPP_f759274231e_bool(F,A_4))))))) # label(fact_774_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 831 (all F all C all B_1 all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),A_4)) -> (hAPP_f806699093e_bool(F,B_1) = C -> ((all X_2 all Y_3 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_3),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_3)),hAPP_f806699093e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),hAPP_f806699093e_bool(F,A_4))))))) # label(fact_775_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 832 (all B all A all F all Fa (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B))),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B))))))) # label(fact_776_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 833 (all B all A all F all Fa (hBOOL(finite2009063477e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) != bot_bo942947096l_bool -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B))),hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B))) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,A)),hAPP_f1216288071e_bool(Fa,B))))))) # label(fact_777_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 834 (all B all A all F all Fa (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) != bot_bo844097828e_bool -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B))))))) # label(fact_778_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 835 (all B all A all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) != bot_bo784226126e_bool -> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))),hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,A)),hAPP_f718417177_state(Fa,B))))))) # label(fact_779_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 836 (all B all A all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,B)) -> (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) != bot_bot_fun_com_bool -> hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B))))))) # label(fact_780_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 837 (all B all A all F all Fa (is_fun1661590463l_bool(B) & is_fun1661590463l_bool(A) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (B != bot_bo1649642514l_bool -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B)))))))))) # label(fact_781_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 838 (all B all A all F all Fa (hBOOL(finite2009063477e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (A != bot_bo942947096l_bool -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (B != bot_bo942947096l_bool -> (hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) = bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,A)),hAPP_f1216288071e_bool(Fa,B))))))))) # label(fact_782_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 839 (all B all A all F all Fa (is_fun_pname_bool(B) & is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (B != bot_bo844097828e_bool -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B)))))))))) # label(fact_783_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 840 (all B all A all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (A != bot_bo784226126e_bool -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (B != bot_bo784226126e_bool -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,A)),hAPP_f718417177_state(Fa,B))))))))) # label(fact_784_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 841 (all B all A all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (A != bot_bot_fun_com_bool -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,B)) -> (B != bot_bot_fun_com_bool -> (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B))))))))) # label(fact_785_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.16 842 (all X_1 all A all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = X_1) & (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) != bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)))))))) # label(fact_786_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 843 (all X_1 all A all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = X_1) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))))))) # label(fact_787_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 844 (all X_1 all A all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = X_1) & (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))))))) # label(fact_788_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 845 (all X_1 all A all F all Fa (is_fun_pname_bool(X_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = X_1) & (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool))))))))) # label(fact_789_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 846 (all X_1 all A all F all Fa (hBOOL(finite2009063477e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) = bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = X_1) & (hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)))))))) # label(fact_790_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 847 (all X_1 all A all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,A) = X_1) & (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) != bot_bot_fun_com_bool -> hAPP_f1276420679ol_com(Fa,A) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))))))))) # label(fact_791_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 848 (all X_1 all A all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,A) = X_1) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,A) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))))))))) # label(fact_792_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 849 (all X_1 all A all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,A) = X_1) & (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool -> hAPP_f718417177_state(Fa,A) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))))))))) # label(fact_793_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 850 (all X_1 all A all F all Fa (is_fun_pname_bool(X_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,A) = X_1) & (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))))))))) # label(fact_794_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 851 (all X_1 all A all F all Fa (hBOOL(finite2009063477e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A)) -> (hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) = bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,A) = X_1) & (hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(Fa,A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool))))))))) # label(fact_795_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 852 (all X_3 -hBOOL(is_none_pname(hAPP_p1252095976_pname(some_pname,X_3)))) # label(fact_796_is__none__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 853 (all X_3 -hBOOL(is_non1379144176_state(hAPP_H1633077406_state(some_H1043067815_state,X_3)))) # label(fact_797_is__none__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 854 (all X_3 -hBOOL(is_none_com(hAPP_com_option_com(some_com,X_3)))) # label(fact_798_is__none__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 855 (all Q_1 all G_2 all C all P_1 ((all Z_2 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1)) -> (exists P_2 exists Q_2 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_2),C),Q_2)),bot_bo784226126e_bool))) & (all S_2 ((all Z_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_3),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_3),S_2)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_2)))))))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))))) # label(fact_799_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 856 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) -> -(hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) -> -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))))) # label(fact_800_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 857 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_801_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 858 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) -> -(hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))))) # label(fact_802_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 859 (all B all C all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))))) # label(fact_803_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 860 (all B all C all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))))) # label(fact_804_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 861 (all B all C all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))))) # label(fact_805_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 862 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) -> -(hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))))) # label(fact_806_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 863 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_807_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 864 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) -> -(hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))))) # label(fact_808_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 865 (all B all C all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))))) # label(fact_809_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 866 (all B all C all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))))) # label(fact_810_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 867 (all B all C all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)))))) # label(fact_811_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 868 (all G_2 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,Fa),G_2))))) # label(fact_812_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 869 (all G_2 all Fa (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa)) | hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,G_2)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,Fa),G_2))))) # label(fact_813_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 870 (all G_2 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Fa),G_2))))) # label(fact_814_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 871 (all G_2 all Fa (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa)) | hBOOL(hAPP_f1378282496l_bool(finite694102371_state,G_2)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Fa),G_2))))) # label(fact_815_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 872 (all B all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B))))) # label(fact_816_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 873 (all B all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B))))) # label(fact_817_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 874 (all B all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_818_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 875 (all B all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))))) # label(fact_819_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 876 (all R_1 all S all X_2 (hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)),X_2)) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,R_1),S))))) # label(fact_820_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 877 (all R_1 all S all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,R_1),S))))) # label(fact_821_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 878 (all R_1 all S all X_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),R_1)),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),S)),X_2)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,R_1),S))))) # label(fact_822_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 879 (all A all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,B),A)) = bot_bot_fun_com_bool) # label(fact_823_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 880 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = bot_bo844097828e_bool) # label(fact_824_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 881 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)) = bot_bo784226126e_bool) # label(fact_825_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 882 (all A all B (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) = A)) # label(fact_826_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 883 (all A all B (is_fun_pname_bool(A) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = A))) # label(fact_827_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 884 (all A all B (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = bot_bo784226126e_bool -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B) = A)) # label(fact_828_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 885 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) -> -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)))) # label(fact_829_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 886 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_830_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 887 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)))) # label(fact_831_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 888 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)))) # label(fact_832_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 889 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_833_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 890 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)))) # label(fact_834_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 891 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)))) # label(fact_835_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 892 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)))) # label(fact_836_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 893 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)))) # label(fact_837_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 894 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) -> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)))) # label(fact_838_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 895 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)))) # label(fact_839_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 896 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)))) # label(fact_840_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 897 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) & hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)))) # label(fact_841_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 898 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_842_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 899 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) & hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)))) # label(fact_843_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 900 (all C all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) & -hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)))) # label(fact_844_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 901 (all C all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_845_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 902 (all C all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)))) # label(fact_846_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 903 (all A all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B)))) # label(fact_847_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 904 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_848_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 905 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B)))) # label(fact_849_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 906 (all A all B hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_850_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 907 (all A all B hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B)))) # label(fact_851_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 908 (all A all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(cOMBB_bool_bool_com(fNot),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B))))) # label(fact_852_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 909 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))))) # label(fact_853_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 910 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B))))) # label(fact_854_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 911 (all A all B hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))))) # label(fact_855_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 912 (all A all B hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_f734420447l_bool(cOMBB_1686148692e_bool(fNot),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B))))) # label(fact_856_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 913 (all X_1 all A all P_1 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(collect_com,P_1)))) <-> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) & hBOOL(hAPP_com_bool(P_1,X_1)))) # label(fact_857_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 914 (all X_1 all A all P_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(collect_pname,P_1)))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) & hBOOL(hAPP_pname_bool(P_1,X_1)))) # label(fact_858_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 915 (all X_1 all A all P_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(collec637225377_state,P_1)))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) & hBOOL(hAPP_H242767318e_bool(P_1,X_1)))) # label(fact_859_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 916 (all X_1 all A all P_1 (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)))) <-> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) & hBOOL(hAPP_f1664156314l_bool(P_1,X_1)))) # label(fact_860_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 917 (all X_1 all A all P_1 (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),hAPP_f734420447l_bool(collec1987918285e_bool,P_1)))) <-> hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A)) & hBOOL(hAPP_f1378282496l_bool(P_1,X_1)))) # label(fact_861_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 918 (all P_1 all Q_1 hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),P_1)),Q_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(collec637225377_state,P_1)),hAPP_f806699093e_bool(collec637225377_state,Q_1))) # label(fact_862_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 919 (all P_1 all Q_1 hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))) # label(fact_863_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 920 (all P_1 all Q_1 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) # label(fact_864_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 921 (all P_1 all Q_1 hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),P_1)),Q_1)) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))) # label(fact_865_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 922 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1))) # label(fact_866_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 923 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),C_1))) # label(fact_867_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 924 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1))) # label(fact_868_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 925 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),C_1))) # label(fact_869_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 926 (all A all B (is_fun_pname_bool(A) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) = A)) # label(fact_870_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 927 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)) = A) # label(fact_871_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 928 (all X_1 all Y_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),X_1))) # label(fact_872_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 929 (all X_1 all Y_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),X_1))) # label(fact_873_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 930 (all X_1 all Y_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),X_1))) # label(fact_874_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 931 (all X_1 all Y_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),X_1))) # label(fact_875_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 932 (all X_1 all Y_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),X_1))) # label(fact_876_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 933 (all X_1 all Y_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),X_1))) # label(fact_877_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 934 (all X_1 all Y_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),Y_2))) # label(fact_878_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 935 (all X_1 all Y_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),Y_2))) # label(fact_879_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 936 (all X_1 all Y_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),Y_2))) # label(fact_880_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 937 (all X_1 all Y_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),Y_2))) # label(fact_881_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 938 (all X_1 all Y_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),Y_2))) # label(fact_882_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 939 (all X_1 all Y_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),Y_2))) # label(fact_883_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 940 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) <-> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)) <-> hBOOL(X_1)))) # label(fact_884_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 941 (all X_1 all Y_2 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) <-> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = X_1))) # label(fact_885_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 942 (all X_1 all Y_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) <-> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2) = X_1)) # label(fact_886_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 943 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z)))) # label(fact_887_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 944 (all X_1 all Y_2 all Z (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)))) # label(fact_888_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 945 (all X_1 all Y_2 all Z (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z)))) # label(fact_889_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 946 (all B_1 all A_4 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),X_1)))) # label(fact_890_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 947 (all B_1 all A_4 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),X_1)))) # label(fact_891_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 948 (all B_1 all A_4 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),X_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)),X_1)))) # label(fact_892_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 949 (all A_4 all B_1 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),X_1)))) # label(fact_893_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 950 (all A_4 all B_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),X_1)))) # label(fact_894_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 951 (all A_4 all B_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)),X_1)))) # label(fact_895_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 952 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)) <-> hBOOL(X_1)))) # label(fact_896_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 953 (all X_1 all Y_2 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = X_1))) # label(fact_897_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 954 (all X_1 all Y_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2) = X_1)) # label(fact_898_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 955 (all Y_2 all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)) <-> hBOOL(Y_2)))) # label(fact_899_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 956 (all Y_2 all X_1 (is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = Y_2))) # label(fact_900_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 957 (all Y_2 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2) = Y_2)) # label(fact_901_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 958 (all B_1 all X_1 all A_4 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)))))) # label(fact_902_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 959 (all B_1 all X_1 all A_4 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)))))) # label(fact_903_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 960 (all B_1 all X_1 all A_4 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),A_4)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),B_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)))))) # label(fact_904_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 961 (all Z all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)))))) # label(fact_905_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 962 (all Z all X_1 all Y_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)))))) # label(fact_906_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 963 (all Z all X_1 all Y_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)))))) # label(fact_907_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 964 (all B_1 all D_1 all A_4 all C (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),D_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,C),D_1)))))) # label(fact_908_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 965 (all B_1 all D_1 all A_4 all C (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C),D_1)))))) # label(fact_909_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 966 (all B_1 all D_1 all A_4 all C (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),D_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C),D_1)))))) # label(fact_910_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 967 (all X_1 all A_4 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1))) -> -(hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4)) -> -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1))))) # label(fact_911_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 968 (all X_1 all A_4 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1))))) # label(fact_912_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 969 (all X_1 all A_4 all B_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1))) -> -(hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),A_4)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),B_1))))) # label(fact_913_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 970 (all X_1 hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,X_1),bot_bot_fun_com_bool) = bot_bot_fun_com_bool) # label(fact_914_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 971 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),bot_bot_bool)) <-> hBOOL(bot_bot_bool))) # label(fact_915_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 972 (all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),bot_bo844097828e_bool) = bot_bo844097828e_bool) # label(fact_916_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 973 (all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),bot_bo784226126e_bool) = bot_bo784226126e_bool) # label(fact_917_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 974 (all X_1 hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,bot_bot_fun_com_bool),X_1) = bot_bot_fun_com_bool) # label(fact_918_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 975 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,bot_bot_bool),X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_919_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 976 (all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),X_1) = bot_bo844097828e_bool) # label(fact_920_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 977 (all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,bot_bo784226126e_bool),X_1) = bot_bo784226126e_bool) # label(fact_921_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 978 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) <-> hBOOL(X_1))) # label(fact_922_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 979 (all X_1 all Y_2 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = X_1)) # label(fact_923_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 980 (all X_1 all Y_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) = X_1) # label(fact_924_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 981 (all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2))) <-> hBOOL(X_1))) # label(fact_925_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 982 (all X_1 all Y_2 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)) = X_1)) # label(fact_926_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 983 (all X_1 all Y_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)) = X_1) # label(fact_927_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 984 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))))) # label(fact_928_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 985 (all X_1 all Y_2 all Z hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z))) # label(fact_929_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 986 (all X_1 all Y_2 all Z hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Z))) # label(fact_930_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 987 (all X_1 all Y_2 all Z (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))))) # label(fact_931_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 988 (all X_1 all Y_2 all Z hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z))) # label(fact_932_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 989 (all X_1 all Y_2 all Z hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z))) # label(fact_933_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 990 (all Y_2 all Z all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),X_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Z),X_1))))) # label(fact_934_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 991 (all Y_2 all Z all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)),X_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),X_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Z),X_1))) # label(fact_935_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 992 (all Y_2 all Z all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)),X_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),X_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Z),X_1))) # label(fact_936_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 993 (all Y_2 all Z all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Z),X_1))))) # label(fact_937_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 994 (all Y_2 all Z all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)),X_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Z),X_1))) # label(fact_938_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 995 (all Y_2 all Z all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)),X_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),X_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Z),X_1))) # label(fact_939_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 996 (all A hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),A) = bot_bot_fun_com_bool) # label(fact_940_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 997 (all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),A) = bot_bo844097828e_bool) # label(fact_941_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 998 (all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),A) = bot_bo784226126e_bool) # label(fact_942_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 999 (all A hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),bot_bot_fun_com_bool) = A) # label(fact_943_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1000 (all A (is_fun_pname_bool(A) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),bot_bo844097828e_bool) = A)) # label(fact_944_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1001 (all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),bot_bo784226126e_bool) = A) # label(fact_945_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1002 (all A hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,bot_bot_fun_com_bool),A) = bot_bot_fun_com_bool) # label(fact_946_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1003 (all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,bot_bo844097828e_bool),A) = bot_bo844097828e_bool) # label(fact_947_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1004 (all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,bot_bo784226126e_bool),A) = bot_bo784226126e_bool) # label(fact_948_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1005 (all A all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))))) # label(fact_949_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1006 (all A all B (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B))) <-> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))))) # label(fact_950_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1007 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_951_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1008 (all A all B (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))))) # label(fact_952_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1009 (all A all X_1 all B (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) # label(fact_953_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1010 (all A all X_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) # label(fact_954_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1011 (all A all X_1 all B (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) # label(fact_955_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1012 (all A all X_1 all B ((hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)) & (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))))) # label(fact_956_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1013 (all A all X_1 all B ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_957_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1014 (all A all X_1 all B ((hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))))) # label(fact_958_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1015 (all A all B (hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool <-> (all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) -> (all Xa (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,Xa),B)) -> X_2 != Xa)))))) # label(fact_959_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1016 (all A all B (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool <-> (all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (all Xa (is_pname(Xa) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B)) -> X_2 != Xa)))))))) # label(fact_960_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1017 (all A all B (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = bot_bo784226126e_bool <-> (all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) -> (all Xa (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Xa),B)) -> X_2 != Xa)))))) # label(fact_961_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1018 (all A hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),bot_bot_fun_com_bool) = bot_bot_fun_com_bool) # label(fact_962_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1019 (all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),bot_bo844097828e_bool) = bot_bo844097828e_bool) # label(fact_963_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1020 (all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),bot_bo784226126e_bool) = bot_bo784226126e_bool) # label(fact_964_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1021 (all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,bot_bot_fun_com_bool),B) = bot_bot_fun_com_bool) # label(fact_965_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1022 (all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),B) = bot_bo844097828e_bool) # label(fact_966_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1023 (all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,bot_bo784226126e_bool),B) = bot_bo784226126e_bool) # label(fact_967_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1024 (all C_1 all A all B (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,C_1),A)) = A)))) # label(fact_968_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1025 (all C_1 all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),C_1)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_1),A)) = A))) # label(fact_969_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1026 (all D all B all A all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,D),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,C_1),D)))))) # label(fact_970_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1027 (all D all B all A all C_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,D),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_1),D)))))) # label(fact_971_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1028 (all A all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),A))) # label(fact_972_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1029 (all A all B hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),A))) # label(fact_973_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1030 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),C_1))) # label(fact_974_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1031 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),C_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),C_1))) # label(fact_975_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1032 (all B all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A)) # label(fact_976_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1033 (all B all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),A)) # label(fact_977_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1034 (all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) # label(fact_978_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1035 (all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) # label(fact_979_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1036 (all B all A_4 all C_1 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1)))) # label(fact_980_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1037 (all B all A_4 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)))) # label(fact_981_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1038 (all B all A_4 all C_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)))) # label(fact_982_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1039 (all B all A_4 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))) # label(fact_983_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1040 (all B all A_4 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))) # label(fact_984_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1041 (all B all A_4 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))) # label(fact_985_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1042 (all B all A_4 all C_1 (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1))) # label(fact_986_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1043 (all B all A_4 all C_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))) # label(fact_987_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1044 (all B all A_4 all C_1 (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1))) # label(fact_988_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1045 (all B all A_4 all A (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) # label(fact_989_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1046 (all B all A_4 all A (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) # label(fact_990_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1047 (all B all A_4 all A (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) # label(fact_991_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1048 (all A_4 all A all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) # label(fact_992_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1049 (all A_4 all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) # label(fact_993_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1050 (all A_4 all A all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) # label(fact_994_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.17 1051 (all B all A_4 all C_1 ((hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1))) & (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1)))) # label(fact_995_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1052 (all B all A_4 all C_1 ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)))) # label(fact_996_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1053 (all B all A_4 all C_1 ((hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1))) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)))) # label(fact_997_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1054 (all B all A_4 all A ((hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) & (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))) # label(fact_998_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1055 (all B all A_4 all A ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))) # label(fact_999_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1056 (all B all A_4 all A ((hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))) # label(fact_1000_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1057 (all B all D all A all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),D)))))) # label(fact_1001_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1058 (all B all D all A all C_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),D)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C_1),D)))))) # label(fact_1002_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1059 (all B all C_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))))) # label(fact_1003_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1060 (all B all C_1 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),B)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))))) # label(fact_1004_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1061 (all B all A (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = B))) # label(fact_1005_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1062 (all B all A (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = B)) # label(fact_1006_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1063 (all A all B (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = A))) # label(fact_1007_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1064 (all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = A)) # label(fact_1008_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1065 (all A all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),B))) # label(fact_1009_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1066 (all A all B hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),B))) # label(fact_1010_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1067 (all A all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),A))) # label(fact_1011_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1068 (all A all B hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),A))) # label(fact_1012_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1069 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A))) # label(fact_1013_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1070 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C_1),A))) # label(fact_1014_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1071 (all B all C_1 all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A))) # label(fact_1015_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1072 (all B all C_1 all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C_1),A))) # label(fact_1016_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1073 (all B all C_1 all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A))) # label(fact_1017_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1074 (all B all C_1 all A hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C_1),A))) # label(fact_1018_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1075 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1))) # label(fact_1019_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1076 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),C_1))) # label(fact_1020_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1077 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),C_1))) # label(fact_1021_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1078 (all A all B all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),C_1))) # label(fact_1022_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1079 (all X_1 all Y_2 all Z hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))))) # label(fact_1023_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1080 (all X_1 all Y_2 all Z hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z))))) # label(fact_1024_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1081 (all X_1 all Y_2 all Z hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Z))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z))))) # label(fact_1025_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1082 (all X_1 all Y_2 all Z hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))))) # label(fact_1026_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1083 (all X_1 all Y_2 all Z hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z))))) # label(fact_1027_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1084 (all X_1 all Y_2 all Z hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z))))) # label(fact_1028_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1085 (all A_4 all A (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) -> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) = A)) # label(fact_1029_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1086 (all A_4 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) = A))) # label(fact_1030_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1087 (all A_4 all A (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))) = A)) # label(fact_1031_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1088 (all X_1 all A (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = A)) # label(fact_1032_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1089 (all X_1 all A (is_fun_pname_bool(A) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A))) # label(fact_1033_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1090 (all X_1 all A (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = A)) # label(fact_1034_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1091 (all A_4 all A hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)) # label(fact_1035_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1092 (all A_4 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)) # label(fact_1036_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1093 (all A_4 all A hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A)) # label(fact_1037_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1094 (all A all A_4 all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))),B)) # label(fact_1038_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1095 (all A all A_4 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))),B)) # label(fact_1039_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1096 (all A all A_4 all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))),B)) # label(fact_1040_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1097 (all A all A_4 all B hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) # label(fact_1041_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1098 (all A all A_4 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) # label(fact_1042_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1099 (all A all A_4 all B hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))) # label(fact_1043_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1100 (all A all A_4 all B (hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)))) <-> hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))))) # label(fact_1044_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1101 (all A all A_4 all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_1045_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1102 (all A all A_4 all B (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))))) # label(fact_1046_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1103 (all A all A_4 all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),B)))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B))))) # label(fact_1047_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1104 (all A all A_4 all B (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),B)))) <-> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B))))) # label(fact_1048_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1105 (all F all A all B hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B))),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))) # label(fact_1049_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1106 (all A all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = B))) # label(fact_1050_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1107 (all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)) = B)) # label(fact_1051_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1108 (all A all B all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),C_1)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))))) # label(fact_1052_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1109 (all A all B all C_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),C_1)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1))))) # label(fact_1053_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1110 (all F all A all B hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B))))) # label(fact_1054_image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1111 (all A all B all C_1 (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A)))) # label(fact_1055_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1112 (all A all B all C_1 (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),A)))) # label(fact_1056_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1113 (all P_1 all F all G all S hAPP_f360545851e_bool(image_185131637_state(hAPP_f1343550633_state(hAPP_f799842582_state(cOMBS_853737105_state,hAPP_f1655792756_state(hAPP_f2119427284_state(cOMBS_140201078_state,hAPP_f1836930278_state(cOMBB_143651633_pname(if_Hoa443228806_state),P_1)),F)),G)),S) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,P_1)))),hAPP_f360545851e_bool(image_185131637_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1)))))) # label(fact_1057_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1114 (all P_1 all F all G dom_pname_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,hAPP_f755519727on_com(cOMBB_1394247784_pname(if_option_com),P_1)),F)),G)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(G)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1))))) # label(fact_1058_dom__if) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1115 (all A all X_1 all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))),B)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B)))))) # label(fact_1059_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1116 (all A all X_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))))) # label(fact_1060_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1117 (all A all X_1 all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B)))))) # label(fact_1061_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1118 (all A all X_1 all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B))) <-> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))),B))) & (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))))) # label(fact_1062_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1119 (all A all X_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) <-> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))))) # label(fact_1063_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1120 (all A all X_1 all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B))) <-> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B))) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))))) # label(fact_1064_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1121 (all P_1 all A (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (hBOOL(hAPP_f990396704l_bool(P_1,A)) -> ((all A_2 all A_7 (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_7)) -> (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),A_7)) -> (hBOOL(hAPP_f990396704l_bool(P_1,A_7)) -> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A_7),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),bot_bot_fun_com_bool)))))))) -> hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool)))))) # label(fact_1065_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1122 (all P_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> ((all A_2 all A_7 (is_pname(A_2) & is_fun_pname_bool(A_7) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_7)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_7)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,A_7)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_7),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)))))) # label(fact_1066_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1123 (all P_1 all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,A)) -> ((all A_2 all A_7 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_7)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_7)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,A_7)) -> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_7),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)))))))) -> hBOOL(hAPP_f1378282496l_bool(P_1,bot_bo784226126e_bool)))))) # label(fact_1067_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1124 (all P_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,A)) -> ((all A_2 all A_7 (is_fun_pname_bool(A_2) & is_fun1661590463l_bool(A_7) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_7)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_7)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,A_7)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_7),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),bot_bo1649642514l_bool))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)))))) # label(fact_1068_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1125 (all P_1 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(P_1,A)) -> ((all A_2 all A_7 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_7)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_2),A_7)) -> (hBOOL(hAPP_f1410040974l_bool(P_1,A_7)) -> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A_7),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_2),bot_bo942947096l_bool)))))))) -> hBOOL(hAPP_f1410040974l_bool(P_1,bot_bo942947096l_bool)))))) # label(fact_1069_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1126 (all F all G all A dom_pname_com(overri1496249029on_com(F,G,A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),dom_pname_com(G)))))),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),dom_pname_com(G)))))) # label(fact_1070_dom__override__on) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1127 (all Q_1 all P_1 all A all B (hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) -> ((all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) -> (hBOOL(hAPP_com_bool(P_1,X_2)) -> hBOOL(hAPP_com_bool(Q_1,X_2))))) -> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(collect_com,P_1))),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),hAPP_f1682609283m_bool(collect_com,Q_1))))))) # label(fact_1071_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1128 (all Q_1 all P_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),hAPP_f759274231e_bool(collect_pname,Q_1))))))) # label(fact_1072_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1129 (all Q_1 all P_1 all A all B (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) -> ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) -> (hBOOL(hAPP_H242767318e_bool(P_1,X_2)) -> hBOOL(hAPP_H242767318e_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(collec637225377_state,P_1))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),hAPP_f806699093e_bool(collec637225377_state,Q_1))))))) # label(fact_1073_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1130 (all Q_1 all P_1 all A all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) -> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2)))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,B),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))))) # label(fact_1074_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1131 (all Q_1 all P_1 all A all B (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),B)) -> ((all X_2 (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A)) -> (hBOOL(hAPP_f1378282496l_bool(P_1,X_2)) -> hBOOL(hAPP_f1378282496l_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),hAPP_f734420447l_bool(collec1987918285e_bool,P_1))),hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,B),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))))))) # label(fact_1075_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1132 (all X_1 all Y_2 all Z ((all X_2 all Y_3 all Z_1 (is_bool(X_2) & is_bool(Y_3) & is_bool(Z_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_3),Z_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_3)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1)))))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z)))))) # label(fact_1076_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1133 (all X_1 all Y_2 all Z ((all X_2 all Y_3 all Z_1 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_3) & is_fun_pname_bool(Z_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_3),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1)))) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z)))) # label(fact_1077_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1134 (all X_1 all Y_2 all Z ((all X_2 all Y_3 all Z_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_3),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_3)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Z_1))) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Z)))) # label(fact_1078_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1135 (all X_1 all Y_2 all Z ((all X_2 all Y_3 all Z_1 (is_bool(X_2) & is_bool(Y_3) & is_bool(Z_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_3),Z_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),Y_3)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),Z_1)))))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z)))))) # label(fact_1079_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1136 (all X_1 all Y_2 all Z ((all X_2 all Y_3 all Z_1 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_3) & is_fun_pname_bool(Z_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_3),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Z_1)))) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)))) # label(fact_1080_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1137 (all X_1 all Y_2 all Z ((all X_2 all Y_3 all Z_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_3),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_2),Y_3)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_2),Z_1))) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z)))) # label(fact_1081_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1138 (all A all B_1 ((hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool))) -> hAPP_f1276420679ol_com(partial_flat_lub_com(B_1),A) = B_1) & (-hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool))) -> hAPP_f1276420679ol_com(partial_flat_lub_com(B_1),A) = hAPP_f1276420679ol_com(the_com_1,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool))))))) # label(fact_1082_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1139 (all A all B_1 (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool))) -> hAPP_f1297739591_pname(partia752020666_pname(B_1),A) = B_1) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool))) -> hAPP_f1297739591_pname(partia752020666_pname(B_1),A) = hAPP_f1297739591_pname(the_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool))))))) # label(fact_1083_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1140 (all A all B_1 ((hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool))) -> hAPP_f718417177_state(partia325231104_state(B_1),A) = B_1) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool))) -> hAPP_f718417177_state(partia325231104_state(B_1),A) = hAPP_f718417177_state(the_Ho2067184133_state,hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool))))))) # label(fact_1084_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1141 (all F all Y_2 all X_1 all A ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f360545851e_bool(image_185131637_state(fun_up1055265789_state(F,X_1,Y_2)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f360545851e_bool(image_185131637_state(fun_up1055265789_state(F,X_1,Y_2)),A) = hAPP_f360545851e_bool(image_185131637_state(F),A)))) # label(fact_1088_fun__upd__image) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1142 (all F all A all B (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) <-> hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A)) & hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),B)) & hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A))) = bot_bo784226126e_bool)) # label(fact_1095_inj__on__Un) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1143 (all F all X_1 (dom_pname_com(F) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) <-> (exists V F = fun_up879233478on_com(hAPP_o129566686on_com(cOMBK_413306633_pname,none_com),X_1,hAPP_com_option_com(some_com,V))))) # label(fact_1096_dom__eq__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1144 (all B all A (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,B),A) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(finite1275301314m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,minus_59609839m_bool)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool))),B),A))) # label(fact_1097_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1145 (all B all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(finite315386934e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,minus_1015773161e_bool)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))),B),A))) # label(fact_1098_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1146 (all B all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(finite1230907212e_bool(hAPP_f241329646e_bool(cOMBB_604855927_state(hAPP_f2061951445e_bool(cOMBC_528733435e_bool,minus_1805465033e_bool)),hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,insert1744391420_state),bot_bo784226126e_bool))),B),A))) # label(fact_1099_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1147 (all B all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,B),A) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(finite1627341516l_bool(hAPP_f1149191722l_bool(cOMBB_631815671e_bool(hAPP_f1477350485l_bool(cOMBC_694979519l_bool,minus_1290075917l_bool)),hAPP_f417341722l_bool(hAPP_f836143551l_bool(cOMBC_772615479l_bool,insert1325755072e_bool),bot_bo1649642514l_bool))),B),A))) # label(fact_1100_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1148 (all B all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,B),A) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(finite1943735070l_bool(hAPP_f1316144452l_bool(cOMBB_494346593e_bool(hAPP_f1573805579l_bool(cOMBC_1377256501l_bool,minus_1929235165l_bool)),hAPP_f2059879088l_bool(hAPP_f476955937l_bool(cOMBC_1639502213l_bool,insert1720618162e_bool),bot_bo942947096l_bool))),B),A))) # label(fact_1101_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1149 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f360545851e_bool(image_185131637_state(F),A) = finite1443934175_pname(semila176469292e_bool,hAPP_f103229774e_bool(hAPP_f376349141e_bool(cOMBC_59067399e_bool,hAPP_f2028971360e_bool(cOMBB_667059641_pname(insert1744391420_state),F)),bot_bo784226126e_bool),bot_bo784226126e_bool,A))) # label(fact_1102_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1150 (all A hBOOL(hAPP_f1664156314l_bool(inj_on737724108_pname(some_pname),A))) # label(fact_1103_inj__Some) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1151 (all A hBOOL(hAPP_f1378282496l_bool(inj_on264996226_state(some_H1043067815_state),A))) # label(fact_1104_inj__Some) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1152 (all A hBOOL(hAPP_f990396704l_bool(inj_on11367768on_com(some_com),A))) # label(fact_1105_inj__Some) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1153 (all A_6 none_com != hAPP_com_option_com(some_com,A_6)) # label(fact_1106_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1154 (all A_6 none_pname != hAPP_p1252095976_pname(some_pname,A_6)) # label(fact_1107_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1155 (all A_6 none_H175086635_state != hAPP_H1633077406_state(some_H1043067815_state,A_6)) # label(fact_1108_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1156 (all A_5 hAPP_com_option_com(some_com,A_5) != none_com) # label(fact_1109_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1157 (all A_5 hAPP_p1252095976_pname(some_pname,A_5) != none_pname) # label(fact_1110_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1158 (all A_5 hAPP_H1633077406_state(some_H1043067815_state,A_5) != none_H175086635_state) # label(fact_1111_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1159 (all X_1 ((all Y_3 X_1 != hAPP_com_option_com(some_com,Y_3)) <-> X_1 = none_com)) # label(fact_1112_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1160 (all X_1 (is_option_pname(X_1) -> ((all Y_3 (is_pname(Y_3) -> X_1 != hAPP_p1252095976_pname(some_pname,Y_3))) <-> X_1 = none_pname))) # label(fact_1113_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1161 (all X_1 ((all Y_3 X_1 != hAPP_H1633077406_state(some_H1043067815_state,Y_3)) <-> X_1 = none_H175086635_state)) # label(fact_1114_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1162 (all X_1 (X_1 != none_com <-> (exists Y_3 X_1 = hAPP_com_option_com(some_com,Y_3)))) # label(fact_1115_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1163 (all X_1 (is_option_pname(X_1) -> (X_1 != none_pname <-> (exists Y_3 (is_pname(Y_3) & X_1 = hAPP_p1252095976_pname(some_pname,Y_3)))))) # label(fact_1116_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1164 (all X_1 (X_1 != none_H175086635_state <-> (exists Y_3 X_1 = hAPP_H1633077406_state(some_H1043067815_state,Y_3)))) # label(fact_1117_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1165 (all M dom_pname_com(M) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,hAPP_f919496731m_bool(cOMBB_418828222_pname(fequal_option_com),M)),none_com)))) # label(fact_1118_dom__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1166 (all A_4 all M (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M))) <-> hAPP_p799580910on_com(M,A_4) != none_com)) # label(fact_1119_domIff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1167 (all F all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(F),A))) -> (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_1120_finite__imageD) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1168 (all F all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) -> (hAPP_f360545851e_bool(image_185131637_state(F),A) = hAPP_f360545851e_bool(image_185131637_state(F),B) <-> A = B)))) # label(fact_1121_inj__on__Un__image__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1169 (all X_1 (hBOOL(is_none_com(X_1)) <-> X_1 = none_com)) # label(fact_1122_is__none__def) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1170 (all X_1 all Y_2 all F all A (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_2),hAPP_f360545851e_bool(image_185131637_state(F),A))) -> hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(fun_up1055265789_state(F,X_1,Y_2)),A))))) # label(fact_1124_inj__on__fun__updI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1171 (all B_1 all A_4 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_4),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),A)))))) # label(fact_1125_sup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1172 (all B_1 all A_4 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_4),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),B_1),A)))))) # label(fact_1126_sup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1173 (all B_1 all A_4 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_4),A)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),A)))))) # label(fact_1127_sup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1174 (all B_1 all A_4 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_4),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)))))) # label(fact_1128_fold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1175 (all B_1 all A_4 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_4),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),B_1),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)))))) # label(fact_1129_fold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1176 (all B_1 all A_4 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_4),A)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila310582991f_bool),B_1),A)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)))))) # label(fact_1130_fold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1177 (all B_1 all A_4 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),A)))) # label(fact_1131_fold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1178 (all B_1 all A_4 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),B_1),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),B_1),A)))) # label(fact_1132_fold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1179 (all B_1 all A_4 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,A_4),A))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),A)))))) # label(fact_1133_fold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1180 (all B_1 all A_4 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),A)))) # label(fact_1134_fold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1181 (all B_1 all A_4 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),B_1),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),B_1),A)))) # label(fact_1135_fold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1182 (all F (dom_pname_com(F) = bot_bo844097828e_bool <-> (all X_2 (is_pname(X_2) -> hAPP_p799580910on_com(F,X_2) = none_com)))) # label(fact_1136_dom__eq__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1183 (all Xo (set_com(Xo) = bot_bot_fun_com_bool <-> Xo = none_com)) # label(fact_1141_set__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1184 (all Xo (is_option_pname(Xo) -> (set_pname(Xo) = bot_bo844097828e_bool <-> Xo = none_pname))) # label(fact_1142_set__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1185 (all Xo (set_Ho1741238126_state(Xo) = bot_bo784226126e_bool <-> Xo = none_H175086635_state)) # label(fact_1143_set__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1186 (all F all A (is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(image_2063528359e_bool(F),A)),A)) -> (hBOOL(hAPP_f1935102916l_bool(inj_on1490514707e_bool(F),A)) -> hAPP_f559147733l_bool(image_2063528359e_bool(F),A) = A))))) # label(fact_1144_endo__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1187 (all F all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,hAPP_f734420447l_bool(image_390184709e_bool(F),A)),A)) -> (hBOOL(hAPP_f1410040974l_bool(inj_on2143431281e_bool(F),A)) -> hAPP_f734420447l_bool(image_390184709e_bool(F),A) = A)))) # label(fact_1145_endo__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1188 (all F all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(image_pname_pname(F),A)),A)) -> (hBOOL(hAPP_f1664156314l_bool(inj_on_pname_pname(F),A)) -> hAPP_f759274231e_bool(image_pname_pname(F),A) = A))))) # label(fact_1146_endo__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1189 (all F all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(image_661047967_state(F),A)),A)) -> (hBOOL(hAPP_f1378282496l_bool(inj_on535898123_state(F),A)) -> hAPP_f806699093e_bool(image_661047967_state(F),A) = A)))) # label(fact_1147_endo__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1190 (all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),hAPP_f559147733l_bool(image_2063528359e_bool(F),A))) -> hBOOL(hAPP_f1935102916l_bool(inj_on1490514707e_bool(F),A))))) # label(fact_1148_finite__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1191 (all F all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),hAPP_f734420447l_bool(image_390184709e_bool(F),A))) -> hBOOL(hAPP_f1410040974l_bool(inj_on2143431281e_bool(F),A))))) # label(fact_1149_finite__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1192 (all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(image_pname_pname(F),A))) -> hBOOL(hAPP_f1664156314l_bool(inj_on_pname_pname(F),A))))) # label(fact_1150_finite__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1193 (all F all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(image_661047967_state(F),A))) -> hBOOL(hAPP_f1378282496l_bool(inj_on535898123_state(F),A))))) # label(fact_1151_finite__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1194 (all B all A all F all C_1 (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B)))))) # label(fact_1152_inj__on__image__Int) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1195 (all B all A all F all C_1 (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B)))))) # label(fact_1153_inj__on__image__set__diff) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1196 (all B all A (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(finite1275301314m_bool(insert_com),B),A))) # label(fact_1154_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1197 (all B all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(finite315386934e_bool(insert_pname),B),A))) # label(fact_1155_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1198 (all B all A (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(finite1230907212e_bool(insert1744391420_state),B),A))) # label(fact_1156_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1199 (all B all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(finite1627341516l_bool(insert1325755072e_bool),B),A))) # label(fact_1157_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1200 (all B all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(finite1943735070l_bool(insert1720618162e_bool),B),A))) # label(fact_1158_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1201 (all A all F all X_1 (hAPP_p799580910on_com(F,X_1) = none_com -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),A))) # label(fact_1159_dom__minus) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1202 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),X_1)) <-> hBOOL(X_1))) # label(fact_1160_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1203 (all X_1 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),X_1) = X_1)) # label(fact_1161_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1204 (all X_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),X_1) = X_1) # label(fact_1162_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1205 (all X_1 all A all F all Fa (hBOOL(finite860057415ne_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> (-hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A)) -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_f1276420679ol_com(hAPP_c1546426672ol_com(finite_fold_com_com(F),X_1),A))))) # label(fact_1163_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1206 (all X_1 all A all F all Fa (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f1297739591_pname(hAPP_p1630511146_pname(finite1657623752_pname(F),X_1),A))))) # label(fact_1164_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1207 (all X_1 all A all F all Fa (hBOOL(finite683959609_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A)) -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_f718417177_state(hAPP_H1440241088_state(finite212984546_state(F),X_1),A))))) # label(fact_1165_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1208 (all X_1 all A all F all Fa (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(F),X_1),A))))) # label(fact_1166_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1209 (all X_1 all A all F all Fa (hBOOL(finite2009063477e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (-hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A)) -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(F),X_1),A))))) # label(fact_1167_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1210 (all A_4 all A all F all Fa (hBOOL(finite666746948em_com(F,Fa)) -> (hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) -> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)) = hAPP_f1276420679ol_com(hAPP_c1546426672ol_com(finite_fold_com_com(F),A_4),A)))) # label(fact_1168_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1211 (all A_4 all A all F all Fa (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)) = hAPP_f1297739591_pname(hAPP_p1630511146_pname(finite1657623752_pname(F),A_4),A)))) # label(fact_1169_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1212 (all A_4 all A all F all Fa (hBOOL(finite416071164_state(F,Fa)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) -> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A)) = hAPP_f718417177_state(hAPP_H1440241088_state(finite212984546_state(F),A_4),A)))) # label(fact_1170_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1213 (all A_4 all A all F all Fa (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(F),A_4),A)))) # label(fact_1171_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1214 (all A_4 all A all F all Fa (hBOOL(finite688249778e_bool(F,Fa)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A)) = hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(F),A_4),A)))) # label(fact_1172_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1215 (all Pn (hAPP_p799580910on_com(body,Pn) != none_com -> hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,Pn))))) # label(fact_1173_WT_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1216 (all F all A_4 all A (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A))) <-> hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A)) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,A_4)),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))))))) # label(fact_1174_inj__on__insert) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1217 (all F all X_1 all Y_2 ((Y_2 = none_com -> dom_pname_com(fun_up879233478on_com(F,X_1,Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) & (Y_2 != none_com -> dom_pname_com(fun_up879233478on_com(F,X_1,Y_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F))))) # label(fact_1175_dom__fun__upd) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1218 (all C all B_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),C)),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),C),A)))))) # label(fact_1176_inf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1219 (all C all B_1 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> ((all X_2 (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_2)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B_1),C)),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),C),A)))))) # label(fact_1177_inf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1220 (all C all B_1 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_2))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,B_1),C)),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila310582991f_bool),C),A)))))) # label(fact_1178_inf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.18 1221 (all C all B_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_2),B_1))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),C),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C)))))) # label(fact_1179_fold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1222 (all C all B_1 all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> ((all X_2 (hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),B_1)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),C),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C)))))) # label(fact_1180_fold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1223 (all C all B_1 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> ((all X_2 (is_bool(X_2) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),B_1))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),C),A)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C)))))) # label(fact_1181_fold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1224 (all A_3 all A (A != bot_bo784226126e_bool -> ((exists F_1 (hBOOL(hAPP_f1378282496l_bool(inj_on63516655_pname(F_1),A)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F_1),A)),A_3)))) <-> (exists G_1 hAPP_f360545851e_bool(image_185131637_state(G_1),A_3) = A)))) # label(fact_1182_inj__on__iff__surj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1225 (all A_3 all A (is_fun_pname_bool(A) -> (A != bot_bo844097828e_bool -> ((exists F_1 (hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F_1),A)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F_1),A)),A_3)))) <-> (exists G_1 hAPP_f1083669085e_bool(image_1774499931_pname(G_1),A_3) = A))))) # label(fact_1183_inj__on__iff__surj) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1226 (all Y_1 (Y_1 != none_com -> -(all A_2 Y_1 != hAPP_com_option_com(some_com,A_2)))) # label(fact_1184_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1227 (all Y_1 (is_option_pname(Y_1) -> (Y_1 != none_pname -> -(all A_2 (is_pname(A_2) -> Y_1 != hAPP_p1252095976_pname(some_pname,A_2)))))) # label(fact_1185_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1228 (all Y_1 (Y_1 != none_H175086635_state -> -(all A_2 Y_1 != hAPP_H1633077406_state(some_H1043067815_state,A_2)))) # label(fact_1186_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1229 (all G all B all F all A exists A_1 (is_fun_pname_bool(A_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A)) & (all X_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f1083669085e_bool(image_1774499931_pname(G),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A_1))))))) & (exists H ((all X_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_p1751618853_state(H,X_2) = hAPP_p1751618853_state(F,X_2))) & (all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),A_1))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(H,X_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A_1)))) & X_2 = hAPP_H1193503499_pname(G,hAPP_p1751618853_state(H,X_2))))))))) # label(fact_1187_Cantor__Bernstein__aux) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1230 (all G all B all F all A exists A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),A)) & (all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f360545851e_bool(image_185131637_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A_1))))))) & (exists H ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1)) -> hAPP_H1193503499_pname(H,X_2) = hAPP_H1193503499_pname(F,X_2))) & (all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),A_1))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1193503499_pname(H,X_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A_1)))) & X_2 = hAPP_p1751618853_state(G,hAPP_H1193503499_pname(H,X_2)))))))) # label(fact_1188_Cantor__Bernstein__aux) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1231 (all F all A hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),vimage1011814463_state(F,A))),A))) # label(fact_1189_image__vimage__subset) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1232 (all M all A dom_pname_com(restri1382200118me_com(M,A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(M)),A)) # label(fact_1190_dom__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1233 (all B all A (is_fun1661590463l_bool(B) & is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (B != bot_bo1649642514l_bool -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,A)),hAPP_f674760225e_bool(big_la28065288e_bool,B))))))))) # label(fact_1191_Inf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1234 (all B all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (A != bot_bo942947096l_bool -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (B != bot_bo942947096l_bool -> (hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) = bot_bo942947096l_bool -> hAPP_f1216288071e_bool(big_la236972906e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f1216288071e_bool(big_la236972906e_bool,A)),hAPP_f1216288071e_bool(big_la236972906e_bool,B)))))))) # label(fact_1192_Inf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1235 (all B all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B))),hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,A)),hAPP_f674760225e_bool(big_la28065288e_bool,B)))))) # label(fact_1193_Inf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1236 (all B all A (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) -> (hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) != bot_bo942947096l_bool -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f1216288071e_bool(big_la236972906e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B))),hAPP_f1216288071e_bool(big_la236972906e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B))) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f1216288071e_bool(big_la236972906e_bool,A)),hAPP_f1216288071e_bool(big_la236972906e_bool,B)))))) # label(fact_1194_Inf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1237 (all X_1 hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),top_top_fun_com_bool))) # label(fact_1195_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1238 (all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),top_to2127735616e_bool))) # label(fact_1196_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1239 (all X_1 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),top_to215444530e_bool))) # label(fact_1197_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1240 (all F all X_1 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_1)),hAPP_f360545851e_bool(image_185131637_state(F),top_to2127735616e_bool)))) # label(fact_1198_rangeI) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1241 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1242 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1243 (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].
% 1.94/2.19 1244 (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].
% 1.94/2.19 1245 (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].
% 1.94/2.19 1246 (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].
% 1.94/2.19 1247 (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].
% 1.94/2.19 1248 (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].
% 1.94/2.19 1249 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1250 (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].
% 1.94/2.19 1251 (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].
% 1.94/2.19 1252 (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].
% 1.94/2.19 1253 (all X all P (-hBOOL(hAPP_f327114704l_bool(fAll_state,P)) | hBOOL(hAPP_state_bool(P,X)))) # label(help_fAll_1_1_fAll_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1254 (all X all Y (-hBOOL(hAPP_com_bool(hAPP_c1396316405m_bool(fequal_com,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Ocom_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1255 (all X all Y (X != Y | hBOOL(hAPP_com_bool(hAPP_c1396316405m_bool(fequal_com,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Ocom_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1256 (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].
% 1.94/2.19 1257 (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].
% 1.94/2.19 1258 (all X all Y (-hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1259 (all X all Y (X != Y | hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1260 (all P all Q (is_bool(P) -> hAPP_com_bool(hAPP_b1153789088m_bool(cOMBK_bool_com,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ocom_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1261 (all P all Q hAPP_pname_com(hAPP_c1494068046me_com(cOMBK_com_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Com__Ocom_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1262 (all P all Q (is_bool(P) -> hAPP_pname_bool(hAPP_b76515610e_bool(cOMBK_bool_pname,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1263 (all X all Y hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1264 (all X all Y hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1265 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1266 (all P all Q (is_pname(P) -> hAPP_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1267 (all X all Y (-hBOOL(hAPP_option_com_bool(hAPP_o1684370239m_bool(fequal_option_com,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1268 (all X all Y (X != Y | hBOOL(hAPP_option_com_bool(hAPP_o1684370239m_bool(fequal_option_com,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1269 (all X all Y (-hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(fequal_fun_com_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1270 (all X all Y (X != Y | hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(fequal_fun_com_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1271 (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].
% 1.94/2.19 1272 (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].
% 1.94/2.19 1273 (all P all Q all R hAPP_com_bool(hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,P),Q),R) = hAPP_com_bool(hAPP_c1396316405m_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Com__Ocom_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1274 (all P all Q all R hAPP_com_bool(hAPP_f1682609283m_bool(cOMBB_bool_bool_com(P),Q),R) = hAPP_bool_bool(P,hAPP_com_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ocom_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1275 (all P all Q all R hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_c1580157610l_bool(P,R),hAPP_com_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ocom_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1276 (all P all Q all R hAPP_com_bool(hAPP_p1639923567m_bool(hAPP_f734198589m_bool(cOMBC_com_pname_bool,P),Q),R) = hAPP_pname_bool(hAPP_c1967741679e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1277 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_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].
% 1.94/2.19 1278 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1279 (all P all Q all R hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1280 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f649174806e_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].
% 1.94/2.19 1281 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1282 (all P all Q all R hAPP_pname_bool(hAPP_p61793385e_bool(hAPP_f22061361e_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].
% 1.94/2.19 1283 (all P all Q all R hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1284 (all P all Q hAPP_p799580910on_com(hAPP_o129566686on_com(cOMBK_413306633_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Opname_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1285 (all P all Q (is_bool(P) -> hAPP_f1664156314l_bool(hAPP_b357632156l_bool(cOMBK_1857069011e_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1286 (all P all Q hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(cOMBK_631994958_state,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1287 (all X all Y hAPP_H574424047_state(hAPP_H280516760_state(hAPP_b993469484_state(if_Hoa443228806_state,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1288 (all X all Y hAPP_H574424047_state(hAPP_H280516760_state(hAPP_b993469484_state(if_Hoa443228806_state,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1289 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1290 (all X all Y (-hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1291 (all X all Y (X != Y | hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1292 (all P all Q all R hAPP_pname_com(hAPP_f96342628me_com(cOMBB_923936821_pname(P),Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1293 (all P all Q all R hAPP_pname_bool(hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,P),Q),R) = hAPP_option_com_bool(hAPP_p558118546m_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1294 (all P all Q all R hAPP_com_bool(hAPP_f1998868198m_bool(cOMBB_298914627ol_com(P),Q),R) = hAPP_f990396704l_bool(P,hAPP_c1396316405m_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1295 (all P all Q all R hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,P),Q),R) = hAPP_f990396704l_bool(hAPP_c667411853l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1296 (all P all Q all R hAPP_c1580157610l_bool(hAPP_f954469007l_bool(cOMBB_886968260ol_com(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_com_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].
% 1.94/2.19 1297 (all P all Q all R hAPP_c1967741679e_bool(hAPP_f835719487e_bool(cOMBB_1083901850ol_com(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_com_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1298 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_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].
% 1.94/2.19 1299 (all P all Q all R hAPP_p393069232l_bool(hAPP_f1402196763l_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_011) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1300 (all P all Q all R hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_012) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1301 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f624840228l_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].
% 1.94/2.19 1302 (all P all Q all R hAPP_pname_bool(hAPP_f42430548e_bool(cOMBB_530759491_pname(P),Q),R) = hAPP_f1664156314l_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1303 (all P all Q all R hAPP_state_bool(hAPP_f1012183542e_bool(cOMBB_1911358915_state(P),Q),R) = hAPP_f327114704l_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1304 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f661147897e_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].
% 1.94/2.19 1305 (all P all Q all R hAPP_s1806633685e_bool(hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_s1874344717e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__fun_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1306 (all P all Q all R hAPP_f1664156314l_bool(hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1307 (all P all Q all R hAPP_p61793385e_bool(hAPP_f1336811455e_bool(cOMBB_542850580_pname(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_013) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1308 (all P all Q hAPP_H46530577te_com(hAPP_c57939194te_com(cOMBK_131063602_state,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Com__Ocom_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1309 (all P all Q hAPP_c1455475371_state(hAPP_H275587026_state(cOMBK_869602456te_com,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1310 (all P all Q (is_bool(P) -> hAPP_H242767318e_bool(hAPP_b974863576e_bool(cOMBK_988866959_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1311 (all P all Q (is_pname(P) -> hAPP_H1193503499_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1312 (all P all Q hAPP_p1751618853_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___014) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1313 (all X all Y (-hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1314 (all X all Y (X != Y | hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1315 (all P all Q all R hAPP_p799580910on_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,P),Q),R) = hAPP_o356497025on_com(hAPP_p1086945780on_com(P,R),hAPP_p799580910on_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1316 (all P all Q all R hAPP_com_bool(hAPP_H313059897m_bool(hAPP_f235185669m_bool(cOMBC_114640782e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_c1311333443e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1317 (all P all Q all R hAPP_p1751618853_state(hAPP_f1377420673_state(cOMBB_271860050_pname(P),Q),R) = hAPP_c1455475371_state(P,hAPP_pname_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1318 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBB_325909978_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H242767318e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1319 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1270401638l_bool(P,R),hAPP_H242767318e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1320 (all P all Q all R hAPP_c1396316405m_bool(hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,P),Q),R) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool__015) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1321 (all P all Q all R hAPP_pname_bool(hAPP_H1776011827e_bool(hAPP_f343137017e_bool(cOMBC_19854728e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_p606792009e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1322 (all P all Q all R hAPP_H242767318e_bool(hAPP_p606792009e_bool(hAPP_f1720171569e_bool(cOMBC_1952686190e_bool,P),Q),R) = hAPP_pname_bool(hAPP_H1776011827e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1323 (all P all Q all R hAPP_f1476298914l_bool(hAPP_f143162813l_bool(cOMBB_2095475776e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1324 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f434788991l_bool(hAPP_f1297925993l_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].
% 1.94/2.19 1325 (all P all Q all R hAPP_f759274231e_bool(hAPP_f1385420507e_bool(cOMBB_598082538e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1326 (all P all Q all R hAPP_p61793385e_bool(hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_018) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1327 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_s1226857760e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1328 (all P all Q (is_bool(P) -> hAPP_f1378282496l_bool(hAPP_b167205134l_bool(cOMBK_293339231e_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____uwg) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1329 (all P all Q all R hAPP_p558118546m_bool(hAPP_f919496731m_bool(cOMBB_418828222_pname(P),Q),R) = hAPP_o1684370239m_bool(P,hAPP_p799580910on_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__fun_Itc__Opt) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1330 (all P all Q all R hAPP_f1378282496l_bool(hAPP_f734420447l_bool(cOMBB_1686148692e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1378282496l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1331 (all P all Q all R hAPP_H1270401638l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H242767318e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_019) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1332 (all P all Q all R hAPP_f1378282496l_bool(hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f2067558332l_bool(P,R),hAPP_f1378282496l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1333 (all P all Q all R hAPP_pname_bool(hAPP_f1083669085e_bool(hAPP_f568104217e_bool(cOMBC_1757633998l_bool,P),Q),R) = hAPP_f1378282496l_bool(hAPP_p1235466077l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1334 (all P all Q all R hAPP_H242767318e_bool(hAPP_f360545851e_bool(hAPP_f591683433e_bool(cOMBC_1984545208l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_H358531139l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___020) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1335 (all P all Q all R hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,P),Q),R) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1336 (all P all Q all R hAPP_f1664156314l_bool(hAPP_H358531139l_bool(hAPP_f1186253673l_bool(cOMBC_1836455480e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_f360545851e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1337 (all P all Q all R hAPP_f1378282496l_bool(hAPP_p1235466077l_bool(hAPP_f780571929l_bool(cOMBC_1558112230e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f1083669085e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1338 (all P all Q all R hAPP_H1776011827e_bool(hAPP_f777604691e_bool(cOMBB_1365368614_state(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_H1193503499_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_021) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1339 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f1145991873l_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_022) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1340 (all P all Q all R hAPP_p338031245l_bool(hAPP_f567934427l_bool(cOMBB_408569982_pname(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1341 (all P all Q all R hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(cOMBB_1759179140_state(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1342 (all P all Q all R hAPP_f759274231e_bool(hAPP_f1388330588e_bool(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1343 (all P all Q all R hAPP_s336103912e_bool(hAPP_f249262236e_bool(cOMBB_1476898461_state(P),Q),R) = hAPP_f1863945078e_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_024) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1344 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f1935169308e_bool(cOMBB_1036740637_state(P),Q),R) = hAPP_f1012183542e_bool(P,hAPP_s336103912e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1345 (all P all Q all R hAPP_p1086945780on_com(hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,P),Q),R) = hAPP_o334540577on_com(hAPP_p1164893188on_com(P,R),hAPP_p799580910on_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J__025) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1346 (all P all Q all R hAPP_H242767318e_bool(hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_H216526335e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___026) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1347 (all P all Q all R hAPP_p1751618853_state(hAPP_f1343550633_state(hAPP_f799842582_state(cOMBS_853737105_state,P),Q),R) = hAPP_H574424047_state(hAPP_p1947457250_state(P,R),hAPP_p1751618853_state(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1348 (all P all Q all R hAPP_f2067558332l_bool(hAPP_f118042163l_bool(cOMBB_1749019442e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1378282496l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_027) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1349 (all P all Q all R hAPP_c566651504m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(P),Q),R) = hAPP_f1120618594m_bool(P,hAPP_c1396316405m_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1350 (all P all Q all R hAPP_f1083669085e_bool(hAPP_f700046015e_bool(cOMBB_1400714760e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f88366945_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_028) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1351 (all P all Q all R hAPP_p1751618853_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,P),Q),R) = hAPP_f497755132_state(hAPP_p1331349103_state(P,R),hAPP_p1637813682e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1352 (all P all Q all R hAPP_f1935102916l_bool(hAPP_f510955609l_bool(hAPP_f1879335953l_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].
% 1.94/2.19 1353 (all P all Q all R hAPP_s1874344717e_bool(hAPP_f873506917e_bool(cOMBB_1757942702_state(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_s2001034685l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1354 (all P all Q all R hAPP_p905327722e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(P),Q),R) = hAPP_f1388330588e_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_029) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1355 (all P all Q all R hAPP_p1164893188on_com(hAPP_f755519727on_com(cOMBB_1394247784_pname(P),Q),R) = hAPP_b1679505845on_com(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Option__Ooption_Itc__Com_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1356 (all P all Q all R hAPP_c1311333443e_bool(hAPP_f475997903e_bool(cOMBB_1327031172ol_com(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_c1455475371_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1357 (all P all Q all R hAPP_H242767318e_bool(hAPP_f1900156034e_bool(cOMBB_1282391997_state(P),Q),R) = hAPP_f1378282496l_bool(P,hAPP_H216526335e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1358 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,P),Q),R) = hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___030) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1359 (all P all Q all R hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(hAPP_f1463049441l_bool(cOMBC_754402940e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_f806699093e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_031) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1360 (all P all Q all R hAPP_p606792009e_bool(hAPP_f472107739e_bool(cOMBB_181781758_pname(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_p1751618853_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___032) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1361 (all P all Q all R hAPP_H358531139l_bool(hAPP_f381060343l_bool(cOMBB_1631414076_state(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_H1776011827e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_033) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1362 (all P all Q all R hAPP_p1331349103_state(hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,P),Q),R) = hAPP_c27135337_state(hAPP_p357103842_state(P,R),hAPP_pname_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1363 (all P all Q all R hAPP_f1218207411_state(hAPP_f819036232_state(hAPP_f815143704_state(cOMBS_858986606_state,P),Q),R) = hAPP_f497755132_state(hAPP_f1867816801_state(P,R),hAPP_f887530048e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1364 (all P all Q all R hAPP_f434788991l_bool(hAPP_f417341722l_bool(hAPP_f836143551l_bool(cOMBC_772615479l_bool,P),Q),R) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_034) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1365 (all P all Q all R hAPP_s1226857760e_bool(hAPP_f1138284024e_bool(cOMBB_20296667_state(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_s2001034685l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_035) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1366 (all P all Q all R hAPP_f1378282496l_bool(hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,P),Q),R) = hAPP_f1378282496l_bool(hAPP_f849457489l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_036) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1367 (all P all Q all R hAPP_f360545851e_bool(hAPP_f2113567599e_bool(cOMBB_1724041344e_bool(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_f1218207411_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___037) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1368 (all P all Q all R hAPP_p606792009e_bool(hAPP_f103229774e_bool(hAPP_f376349141e_bool(cOMBC_59067399e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_p105983054e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw_038) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1369 (all P all Q all R hAPP_f1867816801_state(hAPP_f240260249_state(hAPP_f578932784_state(cOMBS_384351451_state,P),Q),R) = hAPP_c27135337_state(hAPP_f2099268820_state(P,R),hAPP_f792846925ol_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1370 (all P all Q all R hAPP_f559147733l_bool(hAPP_f230953622l_bool(hAPP_f1477350485l_bool(cOMBC_694979519l_bool,P),Q),R) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__039) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1371 (all P all Q all R hAPP_H216526335e_bool(hAPP_f596278895e_bool(cOMBB_1563888316_state(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_H574424047_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___040) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1372 (all P all Q all R hAPP_p1947457250_state(hAPP_f1655792756_state(hAPP_f2119427284_state(cOMBS_140201078_state,P),Q),R) = hAPP_H280516760_state(hAPP_p1159359355_state(P,R),hAPP_p1751618853_state(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__041) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1373 (all P all Q all R hAPP_f1378282496l_bool(hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,P),Q),R) = hAPP_f1410040974l_bool(hAPP_f631019661l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_042) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1374 (all P all Q all R hAPP_p1235466077l_bool(hAPP_f1143533991l_bool(cOMBB_949755692_pname(P),Q),R) = hAPP_f849457489l_bool(P,hAPP_p606792009e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_043) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1375 (all P all Q all R hAPP_f718417177_state(hAPP_f578501918_state(hAPP_f886846002_state(cOMBS_57685138_state,P),Q),R) = hAPP_f497755132_state(hAPP_f1554347387_state(P,R),hAPP_f1487042470e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_044) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1376 (all P all Q all R hAPP_f806699093e_bool(hAPP_f610934515e_bool(cOMBB_1840094962e_bool(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_f718417177_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___045) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1377 (all P all Q all R hAPP_H216526335e_bool(hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___046) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1378 (all P all Q all R hAPP_p1159359355_state(hAPP_f1836930278_state(cOMBB_143651633_pname(P),Q),R) = hAPP_b993469484_state(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____uwg) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1379 (all P all Q all R hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(hAPP_f1901243753l_bool(cOMBC_991209188l_bool,P),Q),R) = hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1380 (all P all Q all R hAPP_f1554347387_state(hAPP_f824259881_state(hAPP_f37848848_state(cOMBS_1164062463_state,P),Q),R) = hAPP_c27135337_state(hAPP_f403544558_state(P,R),hAPP_f1547517799ol_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_047) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1381 (all P all Q all R hAPP_p357103842_state(hAPP_f804744487_state(cOMBB_2084106034_pname(P),Q),R) = hAPP_f274181323_state(P,hAPP_p1637813682e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___048) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1382 (all P all Q all R hAPP_f1320879424l_bool(hAPP_f1149191722l_bool(cOMBB_631815671e_bool(P),Q),R) = hAPP_f230953622l_bool(P,hAPP_f434788991l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.94/2.19 1383 (all P all Q all R hAPP_H2039996199l_bool(hAPP_f1191357267l_bool(cOMBB_639263758_state(P),Q),R) = hAPP_f849457489l_bool(P,hAPP_H216526335e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_049) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1384 (all P all Q all R hAPP_f806699093e_bool(hAPP_f1794460506e_bool(hAPP_f2061951445e_bool(cOMBC_528733435e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_050) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1385 (all P all Q all R hAPP_p105983054e_bool(hAPP_f2028971360e_bool(cOMBB_667059641_pname(P),Q),R) = hAPP_H1902130436e_bool(P,hAPP_p1751618853_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___051) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1386 (all P all Q all R hAPP_f2099268820_state(hAPP_f1633046421_state(cOMBB_1794358604e_bool(P),Q),R) = hAPP_f274181323_state(P,hAPP_f887530048e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___052) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1387 (all P all Q all R hAPP_f849457489l_bool(hAPP_f2059879088l_bool(hAPP_f476955937l_bool(cOMBC_1639502213l_bool,P),Q),R) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_053) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1388 (all P all Q all R hAPP_f403544558_state(hAPP_f250550847_state(cOMBB_2049797414e_bool(P),Q),R) = hAPP_f274181323_state(P,hAPP_f1487042470e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___054) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1389 (all P all Q all R hAPP_H1902130436e_bool(hAPP_f241329646e_bool(cOMBB_604855927_state(P),Q),R) = hAPP_f1794460506e_bool(P,hAPP_H216526335e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_055) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1390 (all P all Q all R hAPP_f734420447l_bool(hAPP_f1847120l_bool(hAPP_f1573805579l_bool(cOMBC_1377256501l_bool,P),Q),R) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg___056) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23 1391 (all P all Q all R hAPP_f1472090462l_bool(hAPP_f1316144452l_bool(cOMBB_494346593e_bool(P),Q),R) = hAPP_f1847120l_bool(P,hAPP_f849457489l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 2.01/2.23
% 2.01/2.23 ============================== end of process non-clausal formulas ===
% 2.01/2.23
% 2.01/2.23 ============================== PROCESS INITIAL CLAUSES ===============
% 2.01/2.23
% 2.01/2.23 ============================== PREDICATE ELIMINATION =================
% 2.01/2.23 1392 is_option_pname(none_pname) # label(gsy_c_Option_Ooption_ONone_000tc__Com__Opname) # label(axiom). [assumption].
% 2.01/2.23 1393 -is_option_pname(A) | is_bool(is_none_pname(A)) # label(gsy_c_Option_Ois__none_000tc__Com__Opname) # label(axiom). [clausify(24)].
% 2.01/2.23 Derived: is_bool(is_none_pname(none_pname)). [resolve(1392,a,1393,a)].
% 2.01/2.23 1394 -is_option_pname(A) | is_fun_pname_bool(set_pname(A)) # label(gsy_c_Option_Oset_000tc__Com__Opname) # label(axiom). [clausify(26)].
% 2.01/2.23 Derived: is_fun_pname_bool(set_pname(none_pname)). [resolve(1394,a,1392,a)].
% 2.01/2.23 1395 -is_pname(A) | is_option_pname(hAPP_p1252095976_pname(B,A)) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J) # label(axiom). [clausify(33)].
% 2.01/2.23 Derived: -is_pname(A) | is_bool(is_none_pname(hAPP_p1252095976_pname(B,A))). [resolve(1395,b,1393,a)].
% 2.01/2.23 Derived: -is_pname(A) | is_fun_pname_bool(set_pname(hAPP_p1252095976_pname(B,A))). [resolve(1395,b,1394,a)].
% 2.01/2.23 1396 is_option_pname(hAPP_H1671063474_pname(A,B)) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_002) # label(axiom). [clausify(42)].
% 2.01/2.23 Derived: is_bool(is_none_pname(hAPP_H1671063474_pname(A,B))). [resolve(1396,a,1393,a)].
% 2.01/2.23 Derived: is_fun_pname_bool(set_pname(hAPP_H1671063474_pname(A,B))). [resolve(1396,a,1394,a)].
% 2.15/2.35 1397 -is_option_pname(A) | is_pname(hAPP_o593586696_pname(B,A)) # label(gsy_c_hAPP_000tc__Option__Ooption_Itc__Com__Opname_J_000tc__Com__Opname) # label(axiom). [clausify(47)].
% 2.15/2.35 Derived: is_pname(hAPP_o593586696_pname(A,none_pname)). [resolve(1397,a,1392,a)].
% 2.15/2.35 Derived: is_pname(hAPP_o593586696_pname(A,hAPP_p1252095976_pname(B,C))) | -is_pname(C). [resolve(1397,a,1395,b)].
% 2.15/2.35 Derived: is_pname(hAPP_o593586696_pname(A,hAPP_H1671063474_pname(B,C))). [resolve(1397,a,1396,a)].
% 2.15/2.35 1398 -is_option_pname(A) | -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(A))) | hAPP_p1252095976_pname(some_pname,B) = A # label(fact_574_elem__set) # label(axiom). [clausify(631)].
% 2.15/2.35 Derived: -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),set_pname(none_pname))) | hAPP_p1252095976_pname(some_pname,A) = none_pname. [resolve(1398,a,1392,a)].
% 2.15/2.35 Derived: -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),set_pname(hAPP_p1252095976_pname(B,C)))) | hAPP_p1252095976_pname(some_pname,A) = hAPP_p1252095976_pname(B,C) | -is_pname(C). [resolve(1398,a,1395,b)].
% 2.15/2.35 Derived: -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),set_pname(hAPP_H1671063474_pname(B,C)))) | hAPP_p1252095976_pname(some_pname,A) = hAPP_H1671063474_pname(B,C). [resolve(1398,a,1396,a)].
% 2.15/2.35 1399 -is_option_pname(A) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(A))) | hAPP_p1252095976_pname(some_pname,B) != A # label(fact_574_elem__set) # label(axiom). [clausify(631)].
% 2.15/2.35 Derived: hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),set_pname(hAPP_p1252095976_pname(B,C)))) | hAPP_p1252095976_pname(some_pname,A) != hAPP_p1252095976_pname(B,C) | -is_pname(C). [resolve(1399,a,1395,b)].
% 2.15/2.35 Derived: hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),set_pname(hAPP_H1671063474_pname(B,C)))) | hAPP_p1252095976_pname(some_pname,A) != hAPP_H1671063474_pname(B,C). [resolve(1399,a,1396,a)].
% 2.15/2.35 1400 -is_option_pname(A) | is_pname(f248(A)) | A = none_pname # label(fact_1113_not__Some__eq) # label(axiom). [clausify(1160)].
% 2.15/2.35 Derived: is_pname(f248(none_pname)) | none_pname = none_pname. [resolve(1400,a,1392,a)].
% 2.15/2.35 Derived: is_pname(f248(hAPP_p1252095976_pname(A,B))) | hAPP_p1252095976_pname(A,B) = none_pname | -is_pname(B). [resolve(1400,a,1395,b)].
% 2.15/2.35 Derived: is_pname(f248(hAPP_H1671063474_pname(A,B))) | hAPP_H1671063474_pname(A,B) = none_pname. [resolve(1400,a,1396,a)].
% 2.15/2.35 1401 -is_option_pname(A) | hAPP_p1252095976_pname(some_pname,f248(A)) = A | A = none_pname # label(fact_1113_not__Some__eq) # label(axiom). [clausify(1160)].
% 2.15/2.35 Derived: hAPP_p1252095976_pname(some_pname,f248(none_pname)) = none_pname | none_pname = none_pname. [resolve(1401,a,1392,a)].
% 2.15/2.35 Derived: hAPP_p1252095976_pname(some_pname,f248(hAPP_p1252095976_pname(A,B))) = hAPP_p1252095976_pname(A,B) | hAPP_p1252095976_pname(A,B) = none_pname | -is_pname(B). [resolve(1401,a,1395,b)].
% 2.15/2.35 Derived: hAPP_p1252095976_pname(some_pname,f248(hAPP_H1671063474_pname(A,B))) = hAPP_H1671063474_pname(A,B) | hAPP_H1671063474_pname(A,B) = none_pname. [resolve(1401,a,1396,a)].
% 2.15/2.35 1402 -is_option_pname(A) | -is_pname(B) | hAPP_p1252095976_pname(some_pname,B) != A | A != none_pname # label(fact_1113_not__Some__eq) # label(axiom). [clausify(1160)].
% 2.15/2.35 Derived: -is_pname(A) | hAPP_p1252095976_pname(some_pname,A) != none_pname | none_pname != none_pname. [resolve(1402,a,1392,a)].
% 2.15/2.35 Derived: -is_pname(A) | hAPP_p1252095976_pname(some_pname,A) != hAPP_p1252095976_pname(B,C) | hAPP_p1252095976_pname(B,C) != none_pname | -is_pname(C). [resolve(1402,a,1395,b)].
% 2.15/2.35 Derived: -is_pname(A) | hAPP_p1252095976_pname(some_pname,A) != hAPP_H1671063474_pname(B,C) | hAPP_H1671063474_pname(B,C) != none_pname. [resolve(1402,a,1396,a)].
% 2.15/2.35 1403 -is_option_pname(A) | A = none_pname | is_pname(f251(A)) # label(fact_1116_not__None__eq) # label(axiom). [clausify(1163)].
% 2.15/2.35 Derived: none_pname = none_pname | is_pname(f251(none_pname)). [resolve(1403,a,1392,a)].
% 2.15/2.35 Derived: hAPP_p1252095976_pname(A,B) = none_pname | is_pname(f251(hAPP_p1252095976_pname(A,B))) | -is_pname(B). [resolve(1403,a,1395,b)].
% 3.68/3.96 Derived: hAPP_H1671063474_pname(A,B) = none_pname | is_pname(f251(hAPP_H1671063474_pname(A,B))). [resolve(1403,a,1396,a)].
% 3.68/3.96 1404 -is_option_pname(A) | A = none_pname | hAPP_p1252095976_pname(some_pname,f251(A)) = A # label(fact_1116_not__None__eq) # label(axiom). [clausify(1163)].
% 3.68/3.96 Derived: none_pname = none_pname | hAPP_p1252095976_pname(some_pname,f251(none_pname)) = none_pname. [resolve(1404,a,1392,a)].
% 3.68/3.96 Derived: hAPP_p1252095976_pname(A,B) = none_pname | hAPP_p1252095976_pname(some_pname,f251(hAPP_p1252095976_pname(A,B))) = hAPP_p1252095976_pname(A,B) | -is_pname(B). [resolve(1404,a,1395,b)].
% 3.68/3.96 Derived: hAPP_H1671063474_pname(A,B) = none_pname | hAPP_p1252095976_pname(some_pname,f251(hAPP_H1671063474_pname(A,B))) = hAPP_H1671063474_pname(A,B). [resolve(1404,a,1396,a)].
% 3.68/3.96 1405 -is_option_pname(A) | A != none_pname | -is_pname(B) | hAPP_p1252095976_pname(some_pname,B) != A # label(fact_1116_not__None__eq) # label(axiom). [clausify(1163)].
% 3.68/3.96 1406 -is_option_pname(A) | set_pname(A) != bot_bo844097828e_bool | A = none_pname # label(fact_1142_set__empty__eq) # label(axiom). [clausify(1184)].
% 3.68/3.96 Derived: set_pname(none_pname) != bot_bo844097828e_bool | none_pname = none_pname. [resolve(1406,a,1392,a)].
% 3.68/3.96 Derived: set_pname(hAPP_p1252095976_pname(A,B)) != bot_bo844097828e_bool | hAPP_p1252095976_pname(A,B) = none_pname | -is_pname(B). [resolve(1406,a,1395,b)].
% 3.68/3.96 Derived: set_pname(hAPP_H1671063474_pname(A,B)) != bot_bo844097828e_bool | hAPP_H1671063474_pname(A,B) = none_pname. [resolve(1406,a,1396,a)].
% 3.68/3.96 1407 -is_option_pname(A) | set_pname(A) = bot_bo844097828e_bool | A != none_pname # label(fact_1142_set__empty__eq) # label(axiom). [clausify(1184)].
% 3.68/3.96 Derived: set_pname(none_pname) = bot_bo844097828e_bool | none_pname != none_pname. [resolve(1407,a,1392,a)].
% 3.68/3.96 Derived: set_pname(hAPP_p1252095976_pname(A,B)) = bot_bo844097828e_bool | hAPP_p1252095976_pname(A,B) != none_pname | -is_pname(B). [resolve(1407,a,1395,b)].
% 3.68/3.96 Derived: set_pname(hAPP_H1671063474_pname(A,B)) = bot_bo844097828e_bool | hAPP_H1671063474_pname(A,B) != none_pname. [resolve(1407,a,1396,a)].
% 3.68/3.96 1408 -is_option_pname(A) | A = none_pname | is_pname(f265(A)) # label(fact_1185_option_Oexhaust) # label(axiom). [clausify(1227)].
% 3.68/3.96 Derived: none_pname = none_pname | is_pname(f265(none_pname)). [resolve(1408,a,1392,a)].
% 3.68/3.96 Derived: hAPP_p1252095976_pname(A,B) = none_pname | is_pname(f265(hAPP_p1252095976_pname(A,B))) | -is_pname(B). [resolve(1408,a,1395,b)].
% 3.68/3.96 Derived: hAPP_H1671063474_pname(A,B) = none_pname | is_pname(f265(hAPP_H1671063474_pname(A,B))). [resolve(1408,a,1396,a)].
% 3.68/3.96 1409 -is_option_pname(A) | A = none_pname | hAPP_p1252095976_pname(some_pname,f265(A)) = A # label(fact_1185_option_Oexhaust) # label(axiom). [clausify(1227)].
% 3.68/3.96 Derived: none_pname = none_pname | hAPP_p1252095976_pname(some_pname,f265(none_pname)) = none_pname. [resolve(1409,a,1392,a)].
% 3.68/3.96 Derived: hAPP_p1252095976_pname(A,B) = none_pname | hAPP_p1252095976_pname(some_pname,f265(hAPP_p1252095976_pname(A,B))) = hAPP_p1252095976_pname(A,B) | -is_pname(B). [resolve(1409,a,1395,b)].
% 3.68/3.96 Derived: hAPP_H1671063474_pname(A,B) = none_pname | hAPP_p1252095976_pname(some_pname,f265(hAPP_H1671063474_pname(A,B))) = hAPP_H1671063474_pname(A,B). [resolve(1409,a,1396,a)].
% 3.68/3.96
% 3.68/3.96 ============================== end predicate elimination =============
% 3.68/3.96
% 3.68/3.96 Auto_denials: (non-Horn, no changes).
% 3.68/3.96
% 3.68/3.96 Term ordering decisions:
% 3.68/3.96 Function symbol KB weights: ord_le313189616e_bool=1. ord_le1449778818e_bool=1. member_pname=1. bot_bo784226126e_bool=1. semila278973382e_bool=1. semila1168014441p_bool=1. insert1744391420_state=1. member1667945571_state=1. bot_bo844097828e_bool=1. semila176469292e_bool=1. member_com=1. ord_less_eq_bool=1. finite_finite_pname=1. insert_pname=1. bot_bot_fun_com_bool=1. semila1635148844e_bool=1. insert_com=1. finite595471783e_bool=1. finite694102371_state=1. semila1874263622e_bool=1. finite627955595e_bool=1. semila310582991f_bool=1. bot_bo1649642514l_bool=1. minus_1015773161e_bool=1. hoare_1191504582_state=1. minus_1805465033e_bool=1. bot_bo942947096l_bool=1. collect_pname=1. finite_finite_com=1. ord_le1708315510m_bool=1. fconj=1. collec1974731493e_bool=1. collec637225377_state=1. semila980496562m_bool=1. collec1987918285e_bool=1. none_pname=1. insert1325755072e_bool=1. minus_59609839m_bool=1. bot_bot_bool=1. insert1720618162e_bool=1. member799430823e_bool=1. ord_le675606854l_bool=1. fdisj=1. member131361931e_bool=1. semila605046092m_bool=1. ord_le694194916l_bool=1. cOMBC_1058051404l_bool=1. some_pname=1. collect_com=1. cOMBC_538205282l_bool=1. some_com=1. cOMBC_1904837336l_bool=1. body_1=1. cOMBS_568398431l_bool=1. cOMBS_865875691l_bool=1. semila1130628874l_bool=1. cOMBS_1162100051l_bool=1. cOMBS_350070575l_bool=1. none_com=1. semila1028267552l_bool=1. some_H1043067815_state=1. wt=1. body=1. fequal1440809015_state=1. fequal_pname=1. hoare_Mirabelle_MGT=1. minus_1290075917l_bool=1. minus_1929235165l_bool=1. cOMBS_1020065803_state=1. cOMBS_1524960158_state=1. fNot=1. fequal1475827639e_bool=1. fequal533582459e_bool=1. cOMBS_com_bool_bool=1. semi=1. semila1672697786l_bool=1. semila1782091504l_bool=1. fequal_com=1. cOMBC_1484018740l_bool=1. cOMBC_1988546018l_bool=1. fFalse=1. the_com=1. fimplies=1. finite_finite_bool=1. cOMBC_1149511130e_bool=1. cOMBC_1284144636l_bool=1. cOMBC_1350613978l_bool=1. cOMBC_1967329268e_bool=1. cOMBC_com_com_bool=1. fequal_state=1. hoare_1795711768gleton=1. big_la236972906e_bool=1. big_la28065288e_bool=1. cOMBS_384351451_state=1. cOMBS_858986606_state=1. fTrue=1. none_H175086635_state=1. cOMBS_1164062463_state=1. cOMBS_57685138_state=1. bool=1. cOMBC_1123258281e_bool=1. cOMBC_1229155955e_bool=1. cOMBC_1977231931m_bool=1. cOMBC_952831051e_bool=1. cOMBK_131063602_state=1. cOMBK_2086841362_pname=1. cOMBK_413306633_pname=1. cOMBK_497473068_state=1. cOMBK_869602456te_com=1. cOMBS_1378840469l_bool=1. member_bool=1. skip=1. wT_bodies=1. cOMBC_1880008793e_bool=1. cOMBC_231445413l_bool=1. cOMBC_471052088e_bool=1. cOMBC_528733435e_bool=1. cOMBC_788185579m_bool=1. cOMBK_631994958_state=1. fAll_state=1. fa=1. fequal_fun_com_bool=1. fequal_option_com=1. if_Hoa443228806_state=1. if_option_com=1. pname=1. top_to2127735616e_bool=1. cOMBC_1004116266e_bool=1. cOMBC_114640782e_bool=1. cOMBC_1377256501l_bool=1. cOMBC_1381995473m_bool=1. cOMBC_1558112230e_bool=1. cOMBC_1639502213l_bool=1. cOMBC_1757633998l_bool=1. cOMBC_1836455480e_bool=1. cOMBC_1952686190e_bool=1. cOMBC_1984545208l_bool=1. cOMBC_19854728e_bool=1. cOMBC_2027030106e_bool=1. cOMBC_59067399e_bool=1. cOMBC_694979519l_bool=1. cOMBC_754402940e_bool=1. cOMBC_772615479l_bool=1. cOMBC_7971162l_bool=1. cOMBC_991209188l_bool=1. cOMBC_com_pname_bool=1. cOMBK_1857069011e_bool=1. cOMBK_293339231e_bool=1. cOMBK_988866959_state=1. cOMBK_bool_com=1. cOMBK_bool_pname=1. cOMBK_com_pname=1. cOMBK_pname_pname=1. cOMBS_140201078_state=1. cOMBS_1529518335on_com=1. cOMBS_853737105_state=1. cOMBS_904531235on_com=1. insert_bool=1. pn=1. the_Ho2067184133_state=1. the_com_1=1. the_el2080696983_state=1. the_elem_com=1. the_elem_pname=1. the_pname=1. collec1613912337l_bool=1. collec895295961l_bool=1. finite1203709595l_bool=1. finite786885583l_bool=1. the_Ho32424093_state=1. the_pname_1=1. top_to215444530e_bool=1. top_top_fun_com_bool=1. y=1. c1=1. c2=1. hAPP_f759274231e_bool=1. hAPP_f1664156314l_bool=1. hAPP_f1378282496l_bool=1. hAPP_f806699093e_bool=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. hAPP_f1388330588e_bool=1. hAPP_f1794460506e_bool=1. hAPP_f1682609283m_bool=1. hAPP_f990396704l_bool=1. hAPP_f434788991l_bool=1. hAPP_f1935102916l_bool=1. hAPP_f849457489l_bool=1. hAPP_p338031245l_bool=1. hAPP_f1410040974l_bool=1. hAPP_H1902130436e_bool=1. hAPP_H2039996199l_bool=1. hAPP_f559147733l_bool=1. hAPP_f734420447l_bool=1. hAPP_p905327722e_bool=1. hAPP_c667411853l_bool=1. hAPP_c566651504m_bool=1. hAPP_pname_bool=1. hAPP_f1120618594m_bool=1. hAPP_H242767318e_bool=1. hAPP_f360545851e_bool=1. hAPP_f674760225e_bool=1. hAPP_f273696895l_bool=1. hAPP_com_bool=1. hAPP_f1216288071e_bool=1. hAPP_c27135337_state=1. hAPP_f274181323_state=1. hAPP_f497755132_state=1. hAPP_state_bool=1. hAPP_p1252095976_pname=1. hAPP_f230953622l_bool=1. hAPP_s1806633685e_bool=1. hAPP_f1847120l_bool=1. hAPP_com_com=1. hAPP_f1297739591_pname=1. hAPP_f1320879424l_bool=1. hAPP_f1083669085e_bool=1. hAPP_f1472090462l_bool=1. hAPP_f718417177_state=1. hAPP_f1276420679ol_com=1. hAPP_f510955609l_bool=1. hAPP_f1516997247l_bool=1. hAPP_H1671063474_pname=1. hAPP_f661147897e_bool=1. hAPP_f556039215l_bool=1. hAPP_com_option_com=1. hAPP_f1184122441e_bool=1. hAPP_f387058535l_bool=1. hAPP_p1751618853_state=1. hAPP_p61793385e_bool=1. hAPP_pname_com=1. hAPP_H216526335e_bool=1. hAPP_com_fun_com_com=1. hAPP_pname_pname=1. hAPP_f631019661l_bool=1. hAPP_f578650245m_bool=1. hAPP_H574424047_state=1. hAPP_c1455475371_state=1. hAPP_f1402196763l_bool=1. hAPP_f1702629984e_bool=1. hAPP_f649174806e_bool=1. hAPP_f832587837l_bool=1. hAPP_p799580910on_com=1. hAPP_H1633077406_state=1. hAPP_f457085749e_bool=1. hAPP_f118042163l_bool=1. hAPP_f143162813l_bool=1. hAPP_f524831474l_bool=1. hAPP_f624840228l_bool=1. hAPP_f1815646051m_bool=1. hAPP_H280516760_state=1. hAPP_c1396316405m_bool=1. hAPP_b1787118453l_bool=1. hAPP_f509793681e_bool=1. hAPP_p1170154830_pname=1. hAPP_f1811131990_state=1. hAPP_f1922754332_state=1. hAPP_f460309545_state=1. hAPP_f804744487_state=1. hAPP_f914896950_state=1. hAPP_f246190092e_bool=1. finite1282449217_pname=1. hAPP_f328772264m_bool=1. hAPP_f954469007l_bool=1. finite1626890877e_bool=1. hAPP_H1193503499_pname=1. hAPP_f1206115581m_bool=1. hAPP_f1712138014e_bool=1. finite683959609_state=1. finite860057415ne_com=1. hAPP_f1145991873l_bool=1. hAPP_f1236719585l_bool=1. finite2009063477e_bool=1. finite89670078_pname=1. hAPP_f1438183293e_bool=1. hAPP_f1492100075l_bool=1. finite1268145088e_bool=1. hAPP_f1297925993l_bool=1. hAPP_f1348212993l_bool=1. hAPP_f1709493145l_bool=1. hAPP_f1902016361e_bool=1. hAPP_f22061361e_bool=1. hAPP_f306376939e_bool=1. finite416071164_state=1. hAPP_H46530577te_com=1. hAPP_com_pname=1. hAPP_f908845385m_bool=1. hAPP_p1637813682e_bool=1. finite666746948em_com=1. finite688249778e_bool=1. hAPP_H1776011827e_bool=1. hAPP_f1633046421_state=1. hAPP_f240260249_state=1. hAPP_f578932784_state=1. hAPP_f815143704_state=1. hAPP_f819036232_state=1. hAPP_option_com_com=1. hAPP_p606792009e_bool=1. hAPP_f1283379615l_bool=1. hAPP_f1377420673_state=1. hAPP_f1487042470e_bool=1. hAPP_f1863945078e_bool=1. hAPP_f887530048e_bool=1. hAPP_f96342628me_com=1. hAPP_H358531139l_bool=1. hAPP_f250550847_state=1. hAPP_f37848848_state=1. hAPP_f578501918_state=1. hAPP_f824259881_state=1. hAPP_f886846002_state=1. hAPP_H1938877132_state=1. hAPP_H275587026_state=1. hAPP_c57939194te_com=1. hAPP_f1138284024e_bool=1. hAPP_f1759915619e_bool=1. hAPP_f1802364479e_bool=1. hAPP_f180827860e_bool=1. hAPP_f698292281e_bool=1. hAPP_f721468006m_bool=1. hAPP_f874203478e_bool=1. hAPP_f915354021e_bool=1. hAPP_f947797701m_bool=1. hAPP_o129566686on_com=1. hAPP_o593586696_pname=1. hAPP_option_com_bool=1. hAPP_p1227118702_pname=1. hAPP_p1235466077l_bool=1. fun=1. hAPP_b1095269219e_bool=1. hAPP_b1679505845on_com=1. hAPP_b357632156l_bool=1. hAPP_b76515610e_bool=1. hAPP_b993469484_state=1. hAPP_c1967741679e_bool=1. hAPP_f1218207411_state=1. hAPP_f1547517799ol_com=1. hAPP_f182188835e_bool=1. hAPP_f1898485935m_bool=1. hAPP_f1935169308e_bool=1. hAPP_f2061951445e_bool=1. hAPP_f241329646e_bool=1. hAPP_f249262236e_bool=1. hAPP_f327114704l_bool=1. hAPP_f42430548e_bool=1. hAPP_f57617970m_bool=1. hAPP_f647826488e_bool=1. hAPP_f701449317e_bool=1. hAPP_f792846925ol_com=1. hAPP_f873506917e_bool=1. hAPP_f88366945_pname=1. hAPP_o1092643708e_bool=1. hAPP_o1684370239m_bool=1. hAPP_o334540577on_com=1. hAPP_o356497025on_com=1. hAPP_s2001034685l_bool=1. hAPP_s58564346l_bool=1. hAPP_H1270401638l_bool=1. hAPP_H1440241088_state=1. hAPP_H313059897m_bool=1. hAPP_b1153789088m_bool=1. hAPP_b167205134l_bool=1. hAPP_b2019457360e_bool=1. hAPP_b496459037l_bool=1. hAPP_b974863576e_bool=1. hAPP_c1311333443e_bool=1. hAPP_c1494068046me_com=1. hAPP_c1546426672ol_com=1. hAPP_c1580157610l_bool=1. hAPP_f1012183542e_bool=1. hAPP_f103229774e_bool=1. hAPP_f1143533991l_bool=1. hAPP_f1149191722l_bool=1. hAPP_f1178960312l_bool=1. hAPP_f1186253673l_bool=1. hAPP_f1191357267l_bool=1. hAPP_f1259673775l_bool=1. hAPP_f1316144452l_bool=1. hAPP_f1336811455e_bool=1. hAPP_f1343550633_state=1. hAPP_f1385420507e_bool=1. hAPP_f1463049441l_bool=1. hAPP_f1476298914l_bool=1. hAPP_f1477350485l_bool=1. hAPP_f1554347387_state=1. hAPP_f1573805579l_bool=1. hAPP_f1655792756_state=1. hAPP_f167292325e_bool=1. hAPP_f1673966486on_com=1. hAPP_f1720171569e_bool=1. hAPP_f1836930278_state=1. hAPP_f1867816801_state=1. hAPP_f1879335953l_bool=1. hAPP_f1900156034e_bool=1. hAPP_f1901243753l_bool=1. hAPP_f1998868198m_bool=1. hAPP_f2028971360e_bool=1. hAPP_f2059879088l_bool=1. hAPP_f2067558332l_bool=1. hAPP_f2082757169l_bool=1. hAPP_f2093196134on_com=1. hAPP_f2099268820_state=1. hAPP_f2113567599e_bool=1. hAPP_f2119427284_state=1. hAPP_f2123220539on_com=1. hAPP_f235185669m_bool=1. hAPP_f343137017e_bool=1. hAPP_f376349141e_bool=1. hAPP_f381060343l_bool=1. hAPP_f389811538l_bool=1. hAPP_f403544558_state=1. hAPP_f417341722l_bool=1. hAPP_f472107739e_bool=1. hAPP_f475997903e_bool=1. hAPP_f476955937l_bool=1. hAPP_f567934427l_bool=1. hAPP_f568104217e_bool=1. hAPP_f591683433e_bool=1. hAPP_f596278895e_bool=1. hAPP_f610934515e_bool=1. hAPP_f644196280e_bool=1. hAPP_f648377725on_com=1. hAPP_f700046015e_bool=1. hAPP_f734198589m_bool=1. hAPP_f755519727on_com=1. hAPP_f777604691e_bool=1. hAPP_f780571929l_bool=1. hAPP_f799842582_state=1. hAPP_f817621513e_bool=1. hAPP_f835719487e_bool=1. hAPP_f836143551l_bool=1. hAPP_f837293113e_bool=1. hAPP_f919496731m_bool=1. hAPP_f961197973l_bool=1. hAPP_p105983054e_bool=1. hAPP_p1086945780on_com=1. hAPP_p1159359355_state=1. hAPP_p1164893188on_com=1. hAPP_p1331349103_state=1. hAPP_p1630511146_pname=1. hAPP_p1639923567m_bool=1. hAPP_p1947457250_state=1. hAPP_p357103842_state=1. hAPP_p393069232l_bool=1. hAPP_p485182952_state=1. hAPP_p558118546m_bool=1. hAPP_s1226857760e_bool=1. hAPP_s1874344717e_bool=1. hAPP_s336103912e_bool=1. vimage1011814463_state=1. hAPP_f347786453l_bool=1. hAPP_f783502055l_bool=1. hAPP_o1912464824_state=1. restri1382200118me_com=1. f20=1. f37=1. f38=1. f39=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f116=1. f117=1. f130=1. f131=1. f136=1. f137=1. f138=1. f139=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f148=1. f149=1. f150=1. f175=1. f176=1. f177=1. f178=1. f179=1. f180=1. f181=1. f182=1. f183=1. f184=1. f185=1. f186=1. f207=1. f208=1. f209=1. f210=1. f211=1. f212=1. f213=1. f214=1. f215=1. f216=1. f217=1. f218=1. f219=1. f220=1. f221=1. f222=1. f246=1. f260=1. f261=1. f262=1. f263=1. image_185131637_state=1. hoare_512830354_state=1. image_1774499931_pname=1. dom_pname_com=1. evalc=1. cOMBB_1291456124_state=1. cOMBB_675860798_pname=1. inj_on621632009_state=1. image_2605051_state=1. image_pname_pname=1. cOMBB_1749019442e_bool=1. cOMBB_2095475776e_bool=1. image_741143905te_com=1. while=1. set_pname=1. image_845802851_state=1. cOMBB_2084106034_pname=1. finite446335722e_bool=1. cOMBB_886968260ol_com=1. finite1909292976l_bool=1. finite391880392e_bool=1. image_1497401961_state=1. image_pname_com=1. image_1283814551_pname=1. image_234387449e_bool=1. image_47868345e_bool=1. image_com_pname=1. image_1403607267e_bool=1. image_1863446033_pname=1. image_995511119e_bool=1. cOMBB_1794358604e_bool=1. set_Ho1741238126_state=1. set_com=1. cOMBB_1759179140_state=1. cOMBB_188601460_state=1. cOMBB_271860050_pname=1. cOMBB_647938656_pname=1. cOMBB_923936821_pname=1. image_2063528359e_bool=1. image_661047967_state=1. cOMBB_2049797414e_bool=1. dom_Ho2070278094_pname=1. cOMBB_20296667_state=1. dom_Ho1607160812_state=1. dom_com_com=1. dom_pname_pname=1. hoare_919241616_state=1. image_390184709e_bool=1. is_none_com=1. cOMBB_1036740637_state=1. cOMBB_1476898461_state=1. cOMBB_1686148692e_bool=1. cOMBB_1757942702_state=1. cOMBB_1911358915_state=1. cOMBB_1919352417_pname=1. cOMBB_2112550369ol_com=1. cOMBB_307249310e_bool=1. cOMBB_325909978_state=1. cOMBB_604855927_state=1. cOMBB_bool_bool_com=1. dom_pn480909800_state=1. finite1653727294m_bool=1. finite2017903282e_bool=1. finite2036162504e_bool=1. inj_on_pname_pname=1. is_none_pname=1. cOMBB_1083901850ol_com=1. cOMBB_1282391997_state=1. cOMBB_1327031172ol_com=1. cOMBB_1365368614_state=1. cOMBB_1394247784_pname=1. cOMBB_1400714760e_bool=1. cOMBB_143651633_pname=1. cOMBB_1563888316_state=1. cOMBB_160679318_state=1. cOMBB_1631414076_state=1. cOMBB_1724041344e_bool=1. cOMBB_181781758_pname=1. cOMBB_1840094962e_bool=1. cOMBB_298914627ol_com=1. cOMBB_408569982_pname=1. cOMBB_418828222_pname=1. cOMBB_494346593e_bool=1. cOMBB_530759491_pname=1. cOMBB_542850580_pname=1. cOMBB_598082538e_bool=1. cOMBB_631815671e_bool=1. cOMBB_639263758_state=1. cOMBB_667059641_pname=1. cOMBB_949755692_pname=1. finite1230907212e_bool=1. finite1275301314m_bool=1. finite1627341516l_bool=1. finite1657623752_pname=1. finite1765632844e_bool=1. finite1943735070l_bool=1. finite212984546_state=1. finite315386934e_bool=1. finite318301748l_bool=1. finite367769966e_bool=1. finite_fold_com_com=1. inj_on1490514707e_bool=1. inj_on2143431281e_bool=1. inj_on535898123_state=1. inj_on63516655_pname=1. inj_on737724108_pname=1. partia325231104_state=1. partia752020666_pname=1. partial_flat_lub_com=1. image_com_com=1. inj_on11367768on_com=1. inj_on264996226_state=1. is_non1379144176_state=1. undefi17486888e_bool=1. undefi64961550l_bool=1. undefined_bool=1. undefined_pname=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f36=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f98=1. f99=1. f100=1. f101=1. f102=1. f103=1. f132=1. f161=1. f162=1. f163=1. f187=1. f188=1. f189=1. f247=1. f248=1. f249=1. f250=1. f251=1. f252=1. f253=1. f264=1. f265=1. f266=1. fun_up879233478on_com=1. fun_up1055265789_state=1. overri1496249029on_com=1. f17=1. f18=1. f19=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f97=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f110=1. f111=1. f112=1. f113=1. f114=1. f115=1. f133=1. f134=1. f135=1. f164=1. f165=1. f166=1. f167=1. f168=1. f169=1. f170=1. f171=1. f172=1. f173=1. f228=1. f229=1. f230=1. f231=1. f232=1. f233=1. f234=1. f235=1. f236=1. f237=1. f238=1. f239=1. f240=1. f241=1. f242=1. f243=1. f244=1. f245=1. f254=1. f255=1. f256=1. f257=1. f258=1. f259=1. finite1443934175_pname=1. f121=1. f122=1. f151=1. f152=1. f153=1. f154=1. f155=1. f156=1. f157=1. f158=1. f159=1. f160=1. f174=1. f190=1. f191=1. f192=1. f193=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f200=1. f201=1. f202=1. f203=1. f204=1. f205=1. f223=1. f224=1. f225=1. f226=1. f227=1. f267=1. f268=1. f269=1. f270=1. f123=1. f124=1. f125=1. f126=1. f127=1. f128=1. f129=1. f206=1. f118=1. f119=1. f120=1.
% 7.30/7.56
% 7.30/7.56 ============================== end of process initial clauses ========
% 7.30/7.56
% 7.30/7.56 ============================== CLAUSES FOR SEARCH ====================
% 7.30/7.56
% 7.30/7.56 ============================== end of clauses for search =============
% 7.30/7.56
% 7.30/7.56 ============================== SEARCH ================================
% 7.30/7.56
% 7.30/7.56 % Starting search at 2.05 seconds.
% 7.30/7.56
% 7.30/7.56 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 64 (0.00 of 3.05 sec).
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=39.000, iters=3645
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=34.000, iters=3497
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=33.000, iters=3445
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=30.000, iters=3348
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=29.000, iters=3342
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=28.000, iters=3355
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=27.000, iters=3335
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=26.000, iters=3434
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=25.000, iters=3477
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=24.000, iters=3371
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=23.000, iters=3345
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=22.000, iters=3387
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=21.000, iters=3380
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=20.000, iters=3339
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=19.000, iters=3345
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=18.000, iters=3476
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=17.000, iters=3408
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=16.000, iters=3394
% 7.30/7.56
% 7.30/7.56 Low Water (keep): wt=15.000, iters=3350
% 24.86/25.08
% 24.86/25.08 Low Water (keep): wt=14.000, iters=3362
% 24.86/25.08
% 24.86/25.08 Low Water (keep): wt=13.000, iters=3351
% 24.86/25.08
% 24.86/25.08 Low Water (keep): wt=12.000, iters=3413
% 24.86/25.08
% 24.86/25.08 Low Water (keep): wt=11.000, iters=3397
% 24.86/25.08
% 24.86/25.08 Low Water (displace): id=5601, wt=57.000
% 24.86/25.08
% 24.86/25.08 Low Water (displace): id=14840, wt=8.000
% 24.86/25.08
% 24.86/25.08 Low Water (keep): wt=10.000, iters=3335
% 24.86/25.08
% 24.86/25.08 Low Water (keep): wt=9.000, iters=3335
% 24.86/25.08
% 24.86/25.08 ============================== PROOF =================================
% 24.86/25.08 % SZS status Theorem
% 24.86/25.08 % SZS output start Refutation
% 24.86/25.08
% 24.86/25.08 % Proof 1 at 22.83 (+ 0.35) seconds.
% 24.86/25.08 % Length of proof is 28.
% 24.86/25.08 % Level of proof is 6.
% 24.86/25.08 % Maximum clause weight is 27.000.
% 24.86/25.08 % Given clauses 9379.
% 24.86/25.08
% 24.86/25.08 68 (all G_2 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),bot_bo784226126e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 24.86/25.08 72 (all G_2 all G_3 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_3),Ts)) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),G_3)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 24.86/25.08 129 (all C (hBOOL(hoare_1795711768gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))))))) # label(fact_66_MGF) # label(axiom) # label(non_clause). [assumption].
% 24.86/25.08 298 (all P_1 hAPP_f806699093e_bool(collec637225377_state,P_1) = P_1) # label(fact_240_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 24.86/25.08 353 (all A_4 hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(fequal1440809015_state,A_4)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)) # label(fact_295_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 24.86/25.08 355 (all Pn all B_4 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = hAPP_com_option_com(some_com,B_4) -> hBOOL(hAPP_com_bool(wt,B_4))))) # label(fact_297_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 24.86/25.08 1165 (all M dom_pname_com(M) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,hAPP_f919496731m_bool(cOMBB_418828222_pname(fequal_option_com),M)),none_com)))) # label(fact_1118_dom__def) # label(axiom) # label(non_clause). [assumption].
% 24.86/25.08 1486 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(A),bot_bo784226126e_bool)) # label(fact_0_empty) # label(axiom). [clausify(68)].
% 24.86/25.08 1490 -hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(A),B)) | -hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(C),A)) | hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(C),B)) # label(fact_4_cut) # label(axiom). [clausify(72)].
% 24.86/25.08 1572 -hBOOL(hoare_1795711768gleton) | -hBOOL(wT_bodies) | -hBOOL(hAPP_com_bool(wt,A)) | hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,A)),bot_bo784226126e_bool))) # label(fact_66_MGF) # label(axiom). [clausify(129)].
% 24.86/25.08 1807 hAPP_f806699093e_bool(collec637225377_state,A) = A # label(fact_240_Collect__def) # label(axiom). [clausify(298)].
% 24.86/25.08 1916 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A),bot_bo784226126e_bool) = hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(fequal1440809015_state,A)) # label(fact_295_singleton__conv2) # label(axiom). [clausify(353)].
% 24.86/25.08 1917 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A),bot_bo784226126e_bool) = hAPP_H216526335e_bool(fequal1440809015_state,A). [copy(1916),rewrite([1807(8)])].
% 24.86/25.08 1924 -hBOOL(wT_bodies) | hAPP_com_option_com(some_com,A) != hAPP_p799580910on_com(body,B) | hBOOL(hAPP_com_bool(wt,A)) # label(fact_297_WT__bodiesD) # label(axiom). [clausify(355)].
% 24.86/25.08 3364 hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,hAPP_f919496731m_bool(cOMBB_418828222_pname(fequal_option_com),A)),none_com))) = dom_pname_com(A) # label(fact_1118_dom__def) # label(axiom). [clausify(1165)].
% 24.88/25.08 3365 dom_pname_com(A) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,hAPP_f919496731m_bool(cOMBB_418828222_pname(fequal_option_com),A)),none_com))). [copy(3364),flip(a)].
% 24.88/25.08 3689 hBOOL(hoare_1795711768gleton) # label(conj_0) # label(hypothesis). [assumption].
% 24.88/25.08 3690 hBOOL(wT_bodies) # label(conj_1) # label(hypothesis). [assumption].
% 24.88/25.08 3695 hAPP_p799580910on_com(body,pn) = hAPP_com_option_com(some_com,y) # label(conj_5) # label(hypothesis). [assumption].
% 24.88/25.08 3698 -hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,y)),bot_bo784226126e_bool))) # label(conj_7) # label(negated_conjecture). [assumption].
% 24.88/25.08 3699 -hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,hAPP_f919496731m_bool(cOMBB_418828222_pname(fequal_option_com),body)),none_com))))),hAPP_H216526335e_bool(fequal1440809015_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,y)))). [copy(3698),rewrite([3365(7),1917(27)])].
% 24.88/25.08 3837 -hBOOL(hAPP_com_bool(wt,A)) | hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_H216526335e_bool(fequal1440809015_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,A)))). [back_rewrite(1572),rewrite([1917(15)]),unit_del(a,3689),unit_del(b,3690)].
% 24.88/25.08 4011 hAPP_com_option_com(some_com,A) != hAPP_p799580910on_com(body,B) | hBOOL(hAPP_com_bool(wt,A)). [back_unit_del(1924),unit_del(a,3690)].
% 24.88/25.08 4233 -hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),A)) | hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(B),A)). [resolve(1490,b,1486,a)].
% 24.88/25.08 10665 hBOOL(hAPP_com_bool(wt,y)). [resolve(4011,a,3695,a(flip))].
% 24.88/25.08 11778 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_H216526335e_bool(fequal1440809015_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,y)))). [resolve(10665,a,3837,a)].
% 24.88/25.08 35037 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(A),hAPP_H216526335e_bool(fequal1440809015_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,y)))). [resolve(11778,a,4233,a)].
% 24.88/25.08 35038 $F. [resolve(35037,a,3699,a)].
% 24.88/25.08
% 24.88/25.08 % SZS output end Refutation
% 24.88/25.08 ============================== end of proof ==========================
% 24.88/25.08
% 24.88/25.08 ============================== STATISTICS ============================
% 24.88/25.08
% 24.88/25.08 Given=9379. Generated=444467. Kept=33079. proofs=1.
% 24.88/25.08 Usable=9113. Sos=9922. Demods=1094. Limbo=0, Disabled=16306. Hints=0.
% 24.88/25.08 Megabytes=282.77.
% 24.88/25.08 User_CPU=22.83, System_CPU=0.35, Wall_clock=23.
% 24.88/25.08
% 24.88/25.08 ============================== end of statistics =====================
% 24.88/25.08
% 24.88/25.08 ============================== end of search =========================
% 24.88/25.08
% 24.88/25.08 THEOREM PROVED
% 24.88/25.08 % SZS status Theorem
% 24.88/25.08
% 24.88/25.08 Exiting with 1 proof.
% 24.88/25.08
% 24.88/25.08 Process 25792 exit (max_proofs) Sat Jun 4 14:11:56 2022
% 24.88/25.08 Prover9 interrupted
%------------------------------------------------------------------------------