TSTP Solution File: SWW470+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW470+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 01:17:05 EDT 2022
% Result : Timeout 300.07s 300.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW470+2 : TPTP v8.1.0. Released v5.3.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 5 12:43:14 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.46/1.77 ============================== Prover9 ===============================
% 1.46/1.77 Prover9 (32) version 2009-11A, November 2009.
% 1.46/1.77 Process 20470 was started by sandbox on n026.cluster.edu,
% 1.46/1.77 Sun Jun 5 12:43:16 2022
% 1.46/1.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20317_n026.cluster.edu".
% 1.46/1.77 ============================== end of head ===========================
% 1.46/1.77
% 1.46/1.77 ============================== INPUT =================================
% 1.46/1.77
% 1.46/1.77 % Reading from file /tmp/Prover9_20317_n026.cluster.edu
% 1.46/1.77
% 1.46/1.77 set(prolog_style_variables).
% 1.46/1.77 set(auto2).
% 1.46/1.77 % set(auto2) -> set(auto).
% 1.46/1.77 % set(auto) -> set(auto_inference).
% 1.46/1.77 % set(auto) -> set(auto_setup).
% 1.46/1.77 % set(auto_setup) -> set(predicate_elim).
% 1.46/1.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.46/1.77 % set(auto) -> set(auto_limits).
% 1.46/1.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.46/1.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.46/1.77 % set(auto) -> set(auto_denials).
% 1.46/1.77 % set(auto) -> set(auto_process).
% 1.46/1.77 % set(auto2) -> assign(new_constants, 1).
% 1.46/1.77 % set(auto2) -> assign(fold_denial_max, 3).
% 1.46/1.77 % set(auto2) -> assign(max_weight, "200.000").
% 1.46/1.77 % set(auto2) -> assign(max_hours, 1).
% 1.46/1.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.46/1.77 % set(auto2) -> assign(max_seconds, 0).
% 1.46/1.77 % set(auto2) -> assign(max_minutes, 5).
% 1.46/1.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.46/1.77 % set(auto2) -> set(sort_initial_sos).
% 1.46/1.77 % set(auto2) -> assign(sos_limit, -1).
% 1.46/1.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.46/1.77 % set(auto2) -> assign(max_megs, 400).
% 1.46/1.77 % set(auto2) -> assign(stats, some).
% 1.46/1.77 % set(auto2) -> clear(echo_input).
% 1.46/1.77 % set(auto2) -> set(quiet).
% 1.46/1.77 % set(auto2) -> clear(print_initial_clauses).
% 1.46/1.77 % set(auto2) -> clear(print_given).
% 1.46/1.77 assign(lrs_ticks,-1).
% 1.46/1.77 assign(sos_limit,10000).
% 1.46/1.77 assign(order,kbo).
% 1.46/1.77 set(lex_order_vars).
% 1.46/1.77 clear(print_given).
% 1.46/1.77
% 1.46/1.77 % formulas(sos). % not echoed (830 formulas)
% 1.46/1.77
% 1.46/1.77 ============================== end of input ==========================
% 1.46/1.77
% 1.46/1.77 % From the command line: assign(max_seconds, 300).
% 1.46/1.77
% 1.46/1.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.46/1.77
% 1.46/1.77 % Formulas that are not ordinary clauses:
% 1.46/1.77 1 (all B_1_1 all B_2_1 is_bool(big_se275732192ig_nat(B_1_1,B_2_1))) # label(gsy_c_Big__Operators_Osemilattice__big_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 2 (all B_1_1 (is_glb(B_1_1) -> is_vname(glb(B_1_1)))) # label(gsy_c_Com_Ovname_OGlb) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 3 (all B_1_1 (is_loc(B_1_1) -> is_vname(loc(B_1_1)))) # label(gsy_c_Com_Ovname_OLoc) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 4 (all B_1_1 is_bool(finite1200705745iple_a(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 5 (all B_1_1 is_bool(finite419198954a_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__Otri) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 6 (all B_1_1 is_bool(finite1317819144e_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__Otri_001) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 7 (all B_1_1 is_bool(finite1956789438t_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mt) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 8 (all B_1_1 all B_2_1 is_bool(finite1669978781iple_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 9 (all B_1_1 all B_2_1 is_bool(finite774711482_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_002) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 10 (all B_1_1 all B_2_1 is_bool(finite988810631ne_nat(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 11 (all B_1_1 all B_2_1 is_bool(finite950012314iple_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 12 (all B_1_1 all B_2_1 is_bool(finite506823037_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O_003) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 13 (all B_1_1 all B_2_1 is_bool(finite795500164em_nat(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 14 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 is_bool(evaln(B_1_1,B_2_1,B_3_1,B_4_1))) # label(gsy_c_Natural_Oevaln) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 15 (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].
% 1.46/1.77 16 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 17 (all B_1_1 all B_2_1 is_bool(hAPP_H1421470952a_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__HOL__) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 18 (all B_1_1 all B_2_1 is_bool(hAPP_H513860823e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 19 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 20 (all B_1_1 all B_2_1 is_bool(hAPP_f540970102l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_Mtc) # label(hypothesis) # label(non_clause). [assumption].
% 1.46/1.77 21 (all B_1_1 all B_2_1 is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 22 (all B_1_1 all B_2_1 is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 23 (all B_1_1 all B_2_1 is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 24 (all Ga hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),bot_bo1181479936a_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 25 (all Ga hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),bot_bo1055319631e_bool))) # label(fact_1_empty) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 26 (all Fun1_2 all Com_1 all Fun2_2 all Fun1_1 all Com all Fun2_1 (hoare_1575745797_state(Fun1_2,Com_1,Fun2_2) = hoare_1575745797_state(Fun1_1,Com,Fun2_1) <-> Fun1_2 = Fun1_1 & Com_1 = Com & Fun2_2 = Fun2_1)) # label(fact_2_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 27 (all Fun1_2 all Com_1 all Fun2_2 all Fun1_1 all Com all Fun2_1 (hoare_1760757500iple_a(Fun1_2,Com_1,Fun2_2) = hoare_1760757500iple_a(Fun1_1,Com,Fun2_1) <-> Fun1_2 = Fun1_1 & Com_1 = Com & Fun2_2 = Fun2_1)) # label(fact_3_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 28 (all Ga all G_1 all Ts (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(G_1),Ts)) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),G_1)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 29 (all Ga all G_1 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts))))) # label(fact_5_cut) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 30 (all Ts all Ga all T_1 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T_1),bot_bo1181479936a_bool))) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T_1),Ts)))))) # label(fact_6_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 31 (all Ts all Ga all T_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T_1),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T_1),Ts)))))) # label(fact_7_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 32 (all Ga all Pa all Ca all Q_1 all C ((hBOOL(C) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_1)),bot_bo1181479936a_bool)))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),Pa))),C),Ca,Q_1)),bot_bo1181479936a_bool))))) # label(fact_8_constant) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 33 (all Ga all Pa all Ca all Q_1 all C ((hBOOL(C) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_1)),bot_bo1055319631e_bool)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(hAPP_f1398071125e_bool(cOMBB_1757942702_state,cOMBC_231445413l_bool),hAPP_f1283379615l_bool(hAPP_f1345202233l_bool(cOMBB_1759179140_state,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),Pa))),C),Ca,Q_1)),bot_bo1055319631e_bool))))) # label(fact_9_constant) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 34 (all Ga all Ca all Q_1 all Pa ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_7),S_2)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_2)),Ca,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(Q_1,Z_7)))),bot_bo1181479936a_bool))))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_1)),bot_bo1181479936a_bool))))) # label(fact_10_escape) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 35 (all Ga all Ca all Q_1 all Pa ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_7),S_2)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_2)),Ca,hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Q_1,Z_7)))),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_1)),bot_bo1055319631e_bool))))) # label(fact_11_escape) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 36 (all Q_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_3)),bot_bo1181479936a_bool))) -> ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_7),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_7),S_2)))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_1)),bot_bo1181479936a_bool)))))) # label(fact_12_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 37 (all Q_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_3)),bot_bo1055319631e_bool))) -> ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_7),S_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_7),S_2)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_1)),bot_bo1055319631e_bool)))))) # label(fact_13_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 38 (all Pa all Ga all P_2 all Ca all Q_1 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(P_2,Ca,Q_1)),bot_bo1181479936a_bool))) -> ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_7),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_7),S_2)))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_1)),bot_bo1181479936a_bool)))))) # label(fact_14_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 39 (all Pa all Ga all P_2 all Ca all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_2,Ca,Q_1)),bot_bo1055319631e_bool))) -> ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_7),S_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_7),S_2)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_1)),bot_bo1055319631e_bool)))))) # label(fact_15_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 40 (all Q_1 all Pa all Ga all P_2 all Ca all Q_3 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(P_2,Ca,Q_3)),bot_bo1181479936a_bool))) -> ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_7),S_2)) -> (all S_3 ((all Z_8 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_8),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_8),S_3)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_7),S_3)))))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_1)),bot_bo1181479936a_bool)))))) # label(fact_16_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 41 (all Q_1 all Pa all Ga all P_2 all Ca all Q_3 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_2,Ca,Q_3)),bot_bo1055319631e_bool))) -> ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_7),S_2)) -> (all S_3 ((all Z_8 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_8),S_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_8),S_3)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_7),S_3)))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_1)),bot_bo1055319631e_bool)))))) # label(fact_17_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 42 (all A_1 all Ba all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),A))) -> (A_1 != Ba -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))))) # label(fact_18_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 43 (all A_1 all Ba all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),A))) -> (A_1 != Ba -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))))) # label(fact_19_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 44 (all A_1 all Ba all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),A))) -> (A_1 != Ba -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))))) # label(fact_20_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 45 (all Ba all A_1 all B ((-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B)) -> A_1 = Ba) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),B))))) # label(fact_21_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 46 (all Ba all A_1 all B ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B)) -> A_1 = Ba) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),B))))) # label(fact_22_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 47 (all Ba all A_1 all B ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B)) -> A_1 = Ba) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),B))))) # label(fact_23_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 48 (all A_1 -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),bot_bo1181479936a_bool))) # label(fact_24_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 49 (all A_1 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),bot_bo1055319631e_bool))) # label(fact_25_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 50 (all A_1 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),bot_bot_fun_nat_bool))) # label(fact_26_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 51 (all A_1 collec268032053iple_a(hAPP_H1190454433a_bool(fequal879838495iple_a,A_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) # label(fact_27_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 52 (all A_1 collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) # label(fact_28_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 53 (all A_1 collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,A_1)) = hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_1),bot_bo1701429464l_bool)) # label(fact_29_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 54 (all A_1 collec727977250_state(hAPP_H1645666623e_bool(fequal1531560888_state,A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) # label(fact_30_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 55 (all A_1 collec268032053iple_a(hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) # label(fact_31_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 56 (all A_1 collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) # label(fact_32_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 57 (all A_1 collect_fun_nat_bool(hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,fequal_fun_nat_bool),A_1)) = hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_1),bot_bo1701429464l_bool)) # label(fact_33_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 58 (all A_1 collec727977250_state(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) # label(fact_34_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 59 (all Pa all A_1 ((hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_H1190454433a_bool(fequal879838495iple_a,A_1))),Pa)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) & (-hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_H1190454433a_bool(fequal879838495iple_a,A_1))),Pa)) = bot_bo1181479936a_bool))) # label(fact_35_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 60 (all Pa all A_1 ((hBOOL(hAPP_nat_bool(Pa,A_1)) -> collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(fequal_nat,A_1))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_1)) -> collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(fequal_nat,A_1))),Pa)) = bot_bot_fun_nat_bool))) # label(fact_36_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 61 (all Pa all A_1 ((hBOOL(hAPP_f54304608l_bool(Pa,A_1)) -> collect_fun_nat_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,fconj),hAPP_f103356543l_bool(fequal_fun_nat_bool,A_1))),Pa)) = hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_1),bot_bo1701429464l_bool)) & (-hBOOL(hAPP_f54304608l_bool(Pa,A_1)) -> collect_fun_nat_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,fconj),hAPP_f103356543l_bool(fequal_fun_nat_bool,A_1))),Pa)) = bot_bo1701429464l_bool))) # label(fact_37_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 62 (all Pa all A_1 ((hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> collec727977250_state(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A_1))),Pa)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) & (-hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> collec727977250_state(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A_1))),Pa)) = bot_bo1055319631e_bool))) # label(fact_38_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 63 (all Pa all A_1 ((hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),Pa)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) & (-hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),Pa)) = bot_bo1181479936a_bool))) # label(fact_39_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 64 (all Pa all A_1 ((hBOOL(hAPP_nat_bool(Pa,A_1)) -> collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_1))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_1)) -> collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_1))),Pa)) = bot_bot_fun_nat_bool))) # label(fact_40_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 65 (all Pa all A_1 ((hBOOL(hAPP_f54304608l_bool(Pa,A_1)) -> collect_fun_nat_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,fconj),hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,fequal_fun_nat_bool),A_1))),Pa)) = hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_1),bot_bo1701429464l_bool)) & (-hBOOL(hAPP_f54304608l_bool(Pa,A_1)) -> collect_fun_nat_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,fconj),hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,fequal_fun_nat_bool),A_1))),Pa)) = bot_bo1701429464l_bool))) # label(fact_41_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 66 (all Pa all A_1 ((hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> collec727977250_state(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),Pa)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) & (-hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> collec727977250_state(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),Pa)) = bot_bo1055319631e_bool))) # label(fact_42_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 67 (all A_1 all A (A = bot_bo1181479936a_bool -> -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)))) # label(fact_43_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 68 (all A_1 all A (A = bot_bo1055319631e_bool -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)))) # label(fact_44_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 69 (all A_1 all A (A = bot_bot_fun_nat_bool -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)))) # label(fact_45_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 70 (all Pa (collect_nat(Pa) = bot_bot_fun_nat_bool <-> (all X_2 -hBOOL(hAPP_nat_bool(Pa,X_2))))) # label(fact_46_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 71 (all Pa (collec268032053iple_a(Pa) = bot_bo1181479936a_bool <-> (all X_2 -hBOOL(hAPP_H1421470952a_bool(Pa,X_2))))) # label(fact_47_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 72 (all Pa (collect_fun_nat_bool(Pa) = bot_bo1701429464l_bool <-> (all X_2 -hBOOL(hAPP_f54304608l_bool(Pa,X_2))))) # label(fact_48_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 73 (all Pa (collec727977250_state(Pa) = bot_bo1055319631e_bool <-> (all X_2 -hBOOL(hAPP_H513860823e_bool(Pa,X_2))))) # label(fact_49_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 74 (all Ca -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),bot_bo1181479936a_bool))) # label(fact_50_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 75 (all Ca -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),bot_bo1055319631e_bool))) # label(fact_51_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 76 (all Ca -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_52_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 77 (all Pa (bot_bot_fun_nat_bool = collect_nat(Pa) <-> (all X_2 -hBOOL(hAPP_nat_bool(Pa,X_2))))) # label(fact_53_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 78 (all Pa (bot_bo1181479936a_bool = collec268032053iple_a(Pa) <-> (all X_2 -hBOOL(hAPP_H1421470952a_bool(Pa,X_2))))) # label(fact_54_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 79 (all Pa (bot_bo1701429464l_bool = collect_fun_nat_bool(Pa) <-> (all X_2 -hBOOL(hAPP_f54304608l_bool(Pa,X_2))))) # label(fact_55_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 80 (all Pa (bot_bo1055319631e_bool = collec727977250_state(Pa) <-> (all X_2 -hBOOL(hAPP_H513860823e_bool(Pa,X_2))))) # label(fact_56_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 81 (all A ((exists X_2 hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))) <-> A != bot_bo1181479936a_bool)) # label(fact_57_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 82 (all A ((exists X_2 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A))) <-> A != bot_bo1055319631e_bool)) # label(fact_58_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 83 (all A ((exists X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))) <-> A != bot_bot_fun_nat_bool)) # label(fact_59_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 84 (all A ((all X_2 -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))) <-> A = bot_bo1181479936a_bool)) # label(fact_60_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 85 (all A ((all X_2 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A))) <-> A = bot_bo1055319631e_bool)) # label(fact_61_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 86 (all A ((all X_2 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))) <-> A = bot_bot_fun_nat_bool)) # label(fact_62_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 87 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) = A)) # label(fact_67_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 88 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A) = A)) # label(fact_68_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 89 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) = A)) # label(fact_69_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 90 (all Ba all A_1 all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),B))))) # label(fact_70_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 91 (all Ba all A_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),B))))) # label(fact_71_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 92 (all Ba all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),B))))) # label(fact_72_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 93 (all B all X_1 all A (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B)) -> (hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),B) <-> A = B)))) # label(fact_73_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 94 (all B all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B) <-> A = B)))) # label(fact_74_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 95 (all B all X_1 all A (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) -> (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B) <-> A = B)))) # label(fact_75_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 96 (all Y_7 all A all X_1 (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_7),A),X_1)) <-> Y_7 = X_1 | hBOOL(hAPP_H1421470952a_bool(A,X_1)))) # label(fact_76_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 97 (all Y_7 all A all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_7),A),X_1)) <-> Y_7 = X_1 | hBOOL(hAPP_nat_bool(A,X_1)))) # label(fact_77_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 98 (all Y_7 all A all X_1 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_7),A),X_1)) <-> Y_7 = X_1 | hBOOL(hAPP_H513860823e_bool(A,X_1)))) # label(fact_78_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 99 (all A_1 all Ba all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),A))) <-> A_1 = Ba | hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)))) # label(fact_79_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 100 (all A_1 all Ba all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),A))) <-> A_1 = Ba | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)))) # label(fact_80_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 101 (all A_1 all Ba all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),A))) <-> A_1 = Ba | hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)))) # label(fact_81_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 102 (all X_1 all Y_7 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_7),A)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_7),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A))) # label(fact_82_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 103 (all X_1 all Y_7 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_7),A)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_7),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A))) # label(fact_83_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 104 (all X_1 all Y_7 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_7),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_7),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A))) # label(fact_84_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 105 (all X_1 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)) # label(fact_85_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 106 (all X_1 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) # label(fact_86_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 107 (all X_1 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)) # label(fact_87_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 108 (all A_1 all Pa hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),collec268032053iple_a(Pa)) = collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fimplies),hAPP_f1591852335a_bool(hAPP_f34030599a_bool(cOMBB_1799513916iple_a,fNot),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1)))),Pa))) # label(fact_88_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 109 (all A_1 all Pa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),collect_nat(Pa)) = collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fimplies),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_1)))),Pa))) # label(fact_89_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 110 (all A_1 all Pa hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_1),collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,fimplies),hAPP_f1246832597l_bool(hAPP_f1164891443l_bool(cOMBB_238756964t_bool,fNot),hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,fequal_fun_nat_bool),A_1)))),Pa))) # label(fact_90_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 111 (all A_1 all Pa hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),collec727977250_state(Pa)) = collec727977250_state(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,fimplies),hAPP_f921536533e_bool(hAPP_f1037965299e_bool(cOMBB_416661851_state,fNot),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1)))),Pa))) # label(fact_91_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 112 (all A_1 all B hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B) = collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fdisj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B)))) # label(fact_92_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 113 (all A_1 all B hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B) = collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_1))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B)))) # label(fact_93_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 114 (all A_1 all B hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_1),B) = collect_fun_nat_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,fdisj),hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,fequal_fun_nat_bool),A_1))),hAPP_f1246832597l_bool(hAPP_f1443436725l_bool(cOMBC_1245412066l_bool,member_fun_nat_bool),B)))) # label(fact_94_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 115 (all A_1 all B hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B) = collec727977250_state(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B)))) # label(fact_95_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 116 (all A_1 all B hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)))) # label(fact_96_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 117 (all A_1 all B hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)))) # label(fact_97_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 118 (all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)))) # label(fact_98_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 119 (all X_2 all Xa hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),Xa) = collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fdisj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),X_2))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),Xa)))) # label(fact_99_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 120 (all X_2 all Xa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),Xa) = collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),Xa)))) # label(fact_100_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.77 121 (all X_2 all Xa hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_2),Xa) = collect_fun_nat_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,fdisj),hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,fequal_fun_nat_bool),X_2))),hAPP_f1246832597l_bool(hAPP_f1443436725l_bool(cOMBC_1245412066l_bool,member_fun_nat_bool),Xa)))) # label(fact_101_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 122 (all X_2 all Xa hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),Xa) = collec727977250_state(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),X_2))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),Xa)))) # label(fact_102_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 123 (all A_1 all Ba (hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),bot_bo1181479936a_bool) -> A_1 = Ba)) # label(fact_103_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 124 (all A_1 all Ba (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool) -> A_1 = Ba)) # label(fact_104_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 125 (all A_1 all Ba (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),bot_bo1055319631e_bool) -> A_1 = Ba)) # label(fact_105_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 126 (all Ba all A_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))) -> Ba = A_1)) # label(fact_106_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 127 (all Ba all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) -> Ba = A_1)) # label(fact_107_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 128 (all Ba all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))) -> Ba = A_1)) # label(fact_108_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 129 (all A_1 all Ba all Ca all D_3 (hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),bot_bo1181479936a_bool)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ca),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,D_3),bot_bo1181479936a_bool)) <-> A_1 = Ca & Ba = D_3 | A_1 = D_3 & Ba = Ca)) # label(fact_109_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 130 (all A_1 all Ba all Ca all D_3 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_3),bot_bot_fun_nat_bool)) <-> A_1 = Ca & Ba = D_3 | A_1 = D_3 & Ba = Ca)) # label(fact_110_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 131 (all A_1 all Ba all Ca all D_3 (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ca),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D_3),bot_bo1055319631e_bool)) <-> A_1 = Ca & Ba = D_3 | A_1 = D_3 & Ba = Ca)) # label(fact_111_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 132 (all Ba all A_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))) <-> Ba = A_1)) # label(fact_112_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 133 (all Ba all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) <-> Ba = A_1)) # label(fact_113_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 134 (all Ba all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))) <-> Ba = A_1)) # label(fact_114_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 135 (all A_1 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) != bot_bo1181479936a_bool) # label(fact_115_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 136 (all A_1 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A) != bot_bot_fun_nat_bool) # label(fact_116_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 137 (all A_1 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) != bot_bo1055319631e_bool) # label(fact_117_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 138 (all A_1 all A bot_bo1181479936a_bool != hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)) # label(fact_118_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 139 (all A_1 all A bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)) # label(fact_119_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 140 (all A_1 all A bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)) # label(fact_120_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 141 (all X_1 hAPP_f124283079iple_a(the_el1436340927iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)) = X_1) # label(fact_121_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 142 (all X_1 hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1) # label(fact_122_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 143 (all X_1 hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = X_1) # label(fact_123_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 144 (all X_1 (hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_124_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 145 (all X_1 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_125_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 146 (all X_1 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_126_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 147 (all X_2 (hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_127_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 148 (all X_2 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_128_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 149 (all X_2 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_129_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 150 (all Ga all Pa hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,skip,Pa)),bot_bo1181479936a_bool)))) # label(fact_130_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 151 (all Ga all Pa hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,skip,Pa)),bot_bo1055319631e_bool)))) # label(fact_131_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 152 (all D_3 all R_1 all Ga all Pa all Ca all Q_1 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_1)),bot_bo1181479936a_bool))) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Q_1,D_3,R_1)),bot_bo1181479936a_bool))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,semi(Ca,D_3),R_1)),bot_bo1181479936a_bool)))))) # label(fact_132_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 153 (all D_3 all R_1 all Ga all Pa all Ca all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_1)),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Q_1,D_3,R_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,semi(Ca,D_3),R_1)),bot_bo1055319631e_bool)))))) # label(fact_133_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 154 (all Y_7 -(all Fun1 all Com_2 all Fun2 Y_7 != hoare_1575745797_state(Fun1,Com_2,Fun2))) # label(fact_134_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 155 (all Y_7 -(all Fun1 all Com_2 all Fun2 Y_7 != hoare_1760757500iple_a(Fun1,Com_2,Fun2))) # label(fact_135_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 156 (all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> -(all B_15 (A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),B_15) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B_15)))))) # label(fact_136_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 157 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> -(all B_15 (A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_15) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_15)))))) # label(fact_137_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 158 (all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> -(all B_15 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B_15) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_15)))))) # label(fact_138_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 159 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> (exists B_15 (A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_15) & -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B_15)))))) # label(fact_139_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 160 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> (exists B_15 (A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_15) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_15)))))) # label(fact_140_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 161 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> (exists B_15 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_15) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B_15)))))) # label(fact_141_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 162 (all A ((all Y_11 -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Y_11),A))) -> A = bot_bo1181479936a_bool)) # label(fact_142_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 163 (all A ((all Y_11 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_11),A))) -> A = bot_bo1055319631e_bool)) # label(fact_143_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 164 (all A ((all Y_11 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_11),A))) -> A = bot_bot_fun_nat_bool)) # label(fact_144_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 165 (all Q_1 all Ga all Ca all Pa ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_7),S_2)) -> (exists P_1 exists Q_2 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(P_1,Ca,Q_2)),bot_bo1181479936a_bool))) & (all S_3 ((all Z_8 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_8),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_8),S_3)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_7),S_3)))))))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,Q_1)),bot_bo1181479936a_bool))))) # label(fact_145_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 166 (all Q_1 all Ga all Ca all Pa ((all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_7),S_2)) -> (exists P_1 exists Q_2 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_1,Ca,Q_2)),bot_bo1055319631e_bool))) & (all S_3 ((all Z_8 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_8),S_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_8),S_3)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_7),S_3)))))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_1)),bot_bo1055319631e_bool))))) # label(fact_146_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 167 (all Com1_2 all Com2_2 semi(Com1_2,Com2_2) != skip) # label(fact_147_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 168 (all Com1_2 all Com2_2 skip != semi(Com1_2,Com2_2)) # label(fact_148_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 169 (all X_35 hAPP_f124283079iple_a(the_el1436340927iple_a,X_35) = hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_f772297704a_bool(hAPP_f390613447a_bool(cOMBB_1501709507iple_a,hAPP_f430043647l_bool(fequal1258664663a_bool,X_35)),hAPP_f1665407592a_bool(hAPP_f549683569a_bool(cOMBC_708118077a_bool,insert873085594iple_a),bot_bo1181479936a_bool)))) # label(fact_149_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 170 (all X_35 hAPP_f22106695ol_nat(the_elem_nat,X_35) = hAPP_f22106695ol_nat(the_nat,hAPP_f158894502t_bool(hAPP_f1777703707t_bool(cOMBB_955900739ol_nat,hAPP_f103356543l_bool(fequal_fun_nat_bool,X_35)),hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,insert_nat),bot_bot_fun_nat_bool)))) # label(fact_150_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 171 (all X_35 hAPP_f2143211163_state(the_el23965208_state,X_35) = hAPP_f2143211163_state(the_Ho10452358_state,hAPP_f1456107715e_bool(hAPP_f1548785833e_bool(cOMBB_1653402815_state,hAPP_f854625363l_bool(fequal1746921144e_bool,X_35)),hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,insert1835143293_state),bot_bo1055319631e_bool)))) # label(fact_151_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 172 (all Com1_1 all Com2_1 all Com1 all Com2 (semi(Com1_1,Com2_1) = semi(Com1,Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_152_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 173 (all A (A != bot_bo1181479936a_bool <-> (exists X_2 exists B_15 (A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),B_15) & -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),B_15)))))) # label(fact_153_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 174 (all A (A != bot_bot_fun_nat_bool <-> (exists X_2 exists B_15 (A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_15) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_15)))))) # label(fact_154_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 175 (all A (A != bot_bo1055319631e_bool <-> (exists X_2 exists B_15 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_15) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_15)))))) # label(fact_155_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 176 (all X_2 (hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X_2)) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),bot_bo1181479936a_bool)))) # label(fact_156_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 177 (all X_2 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),bot_bo1055319631e_bool)))) # label(fact_157_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 178 (all X_2 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),bot_bot_fun_nat_bool)))) # label(fact_158_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 179 (all Ga all Pa all X_35 all A_1 hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(hAPP_f100967412e_bool(hAPP_f1460451647e_bool(cOMBC_524597097e_bool,hAPP_f1406200875e_bool(hAPP_f635443597e_bool(cOMBB_2139825703bool_a,cOMBB_844853809_state),Pa)),hAPP_f871651461_state(hAPP_f851239890_state(cOMBS_777315357_state,hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,update),X_35)),A_1)),ass(X_35,A_1),Pa)),bot_bo1181479936a_bool)))) # label(fact_159_Ass) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 180 (all Ga all Pa all X_35 all A_1 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(hAPP_f1838002347e_bool(hAPP_f1706273077e_bool(cOMBC_867582640e_bool,hAPP_f289738463e_bool(hAPP_f1151843515e_bool(cOMBB_1941618714_state,cOMBB_844853809_state),Pa)),hAPP_f871651461_state(hAPP_f851239890_state(cOMBS_777315357_state,hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,update),X_35)),A_1)),ass(X_35,A_1),Pa)),bot_bo1055319631e_bool)))) # label(fact_160_Ass) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 181 (all Ca all A ((A = bot_bot_fun_nat_bool -> image_1782127643iple_a(hAPP_H1450464520iple_a(cOMBK_1505147640_a_nat,Ca),A) = bot_bo1181479936a_bool) & (A != bot_bot_fun_nat_bool -> image_1782127643iple_a(hAPP_H1450464520iple_a(cOMBK_1505147640_a_nat,Ca),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ca),bot_bo1181479936a_bool)))) # label(fact_161_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 182 (all Ca all A ((A = bot_bo1055319631e_bool -> image_129517430iple_a(hAPP_H377435237iple_a(cOMBK_2022976521_state,Ca),A) = bot_bo1181479936a_bool) & (A != bot_bo1055319631e_bool -> image_129517430iple_a(hAPP_H377435237iple_a(cOMBK_2022976521_state,Ca),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ca),bot_bo1181479936a_bool)))) # label(fact_162_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.46/1.78 183 (all Ca all A ((A = bot_bo1181479936a_bool -> image_194810223_a_nat(hAPP_n1800114674_a_nat(cOMBK_944981412iple_a,Ca),A) = bot_bot_fun_nat_bool) & (A != bot_bo1181479936a_bool -> image_194810223_a_nat(hAPP_n1800114674_a_nat(cOMBK_944981412iple_a,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool)))) # label(fact_163_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 184 (all Ca all A ((A = bot_bo1181479936a_bool -> image_1604514514_state(hAPP_H558669354_state(cOMBK_547979437iple_a,Ca),A) = bot_bo1055319631e_bool) & (A != bot_bo1181479936a_bool -> image_1604514514_state(hAPP_H558669354_state(cOMBK_547979437iple_a,Ca),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ca),bot_bo1055319631e_bool)))) # label(fact_164_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 185 (all Ca all A ((A = bot_bot_fun_nat_bool -> image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,Ca),A) = bot_bot_fun_nat_bool) & (A != bot_bot_fun_nat_bool -> image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool)))) # label(fact_165_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 186 (all Ca all A ((A = bot_bo1055319631e_bool -> image_650584225_state(hAPP_H521649881_state(cOMBK_690957994_state,Ca),A) = bot_bo1055319631e_bool) & (A != bot_bo1055319631e_bool -> image_650584225_state(hAPP_H521649881_state(cOMBK_690957994_state,Ca),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ca),bot_bo1055319631e_bool)))) # label(fact_166_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 187 (all Ca all A ((A = bot_bo1181479936a_bool -> image_306007685iple_a(hAPP_H1455657330iple_a(cOMBK_1824972302iple_a,Ca),A) = bot_bo1181479936a_bool) & (A != bot_bo1181479936a_bool -> image_306007685iple_a(hAPP_H1455657330iple_a(cOMBK_1824972302iple_a,Ca),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ca),bot_bo1181479936a_bool)))) # label(fact_167_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 188 (all Ca all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> image_1782127643iple_a(hAPP_H1450464520iple_a(cOMBK_1505147640_a_nat,Ca),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ca),bot_bo1181479936a_bool))) # label(fact_168_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 189 (all Ca all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> image_306007685iple_a(hAPP_H1455657330iple_a(cOMBK_1824972302iple_a,Ca),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ca),bot_bo1181479936a_bool))) # label(fact_169_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 190 (all Ca all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> image_129517430iple_a(hAPP_H377435237iple_a(cOMBK_2022976521_state,Ca),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ca),bot_bo1181479936a_bool))) # label(fact_170_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 191 (all Ca all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_171_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 192 (all Ca all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> image_194810223_a_nat(hAPP_n1800114674_a_nat(cOMBK_944981412iple_a,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_172_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 193 (all Ca all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> image_1410872416te_nat(hAPP_n436597305te_nat(cOMBK_1950023923_state,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_173_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 194 (all Ca all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> image_650584225_state(hAPP_H521649881_state(cOMBK_690957994_state,Ca),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ca),bot_bo1055319631e_bool))) # label(fact_174_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 195 (all Ca all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> image_1604514514_state(hAPP_H558669354_state(cOMBK_547979437iple_a,Ca),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ca),bot_bo1055319631e_bool))) # label(fact_175_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 196 (all A all Ba all F_1 all X_1 (Ba = hAPP_H563960305_state(F_1,X_1) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),image_650584225_state(F_1,A)))))) # label(fact_176_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 197 (all A all Ba all F_1 all X_1 (Ba = hAPP_n1126952044_state(F_1,X_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),image_1821565372_state(F_1,A)))))) # label(fact_177_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 198 (all A all Ba all F_1 all X_1 (Ba = hAPP_H928324994_state(F_1,X_1) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),image_1604514514_state(F_1,A)))))) # label(fact_178_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 199 (all A all Ba all F_1 all X_1 (Ba = hAPP_nat_nat(F_1,X_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_nat_nat(F_1,A)))))) # label(fact_179_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 200 (all A all Ba all F_1 all X_1 (Ba = hAPP_H738206399_a_nat(F_1,X_1) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_194810223_a_nat(F_1,A)))))) # label(fact_180_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 201 (all A all Ba all F_1 all X_1 (Ba = hAPP_H716259088te_nat(F_1,X_1) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_1410872416te_nat(F_1,A)))))) # label(fact_181_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 202 (all A all Ba all F_1 all X_1 (Ba = hAPP_H678412245iple_a(F_1,X_1) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),image_306007685iple_a(F_1,A)))))) # label(fact_182_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 203 (all A all Ba all F_1 all X_1 (Ba = hAPP_H1600811558iple_a(F_1,X_1) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),image_129517430iple_a(F_1,A)))))) # label(fact_183_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 204 (all A all Ba all F_1 all X_1 (Ba = hAPP_n178040171iple_a(F_1,X_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),image_1782127643iple_a(F_1,A)))))) # label(fact_184_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 205 (all Y_27 image_nat_nat(cOMBI_nat,Y_27) = Y_27) # label(fact_185_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 206 (all Y_27 image_650584225_state(cOMBI_1367665338_state,Y_27) = Y_27) # label(fact_186_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 207 (all Y_27 image_306007685iple_a(cOMBI_1218222237iple_a,Y_27) = Y_27) # label(fact_187_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 208 (all Vname all Fun_1 all Vname_1 all Fun (is_vname(Vname) & is_vname(Vname_1) -> (ass(Vname,Fun_1) = ass(Vname_1,Fun) <-> Vname = Vname_1 & Fun_1 = Fun))) # label(fact_188_com_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 209 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> (Ba = hAPP_H563960305_state(F_1,X_1) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),image_650584225_state(F_1,A)))))) # label(fact_189_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 210 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (Ba = hAPP_n1126952044_state(F_1,X_1) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),image_1821565372_state(F_1,A)))))) # label(fact_190_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 211 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (Ba = hAPP_H928324994_state(F_1,X_1) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ba),image_1604514514_state(F_1,A)))))) # label(fact_191_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 212 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (Ba = hAPP_nat_nat(F_1,X_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_nat_nat(F_1,A)))))) # label(fact_192_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 213 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (Ba = hAPP_H738206399_a_nat(F_1,X_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_194810223_a_nat(F_1,A)))))) # label(fact_193_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 214 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> (Ba = hAPP_H716259088te_nat(F_1,X_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_1410872416te_nat(F_1,A)))))) # label(fact_194_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 215 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (Ba = hAPP_H678412245iple_a(F_1,X_1) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),image_306007685iple_a(F_1,A)))))) # label(fact_195_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 216 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> (Ba = hAPP_H1600811558iple_a(F_1,X_1) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),image_129517430iple_a(F_1,A)))))) # label(fact_196_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 217 (all Ba all F_1 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (Ba = hAPP_n178040171iple_a(F_1,X_1) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ba),image_1782127643iple_a(F_1,A)))))) # label(fact_197_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 218 (all F_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(F_1,X_1)),image_650584225_state(F_1,A))))) # label(fact_198_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 219 (all F_1 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_n1126952044_state(F_1,X_1)),image_1821565372_state(F_1,A))))) # label(fact_199_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 220 (all F_1 all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H928324994_state(F_1,X_1)),image_1604514514_state(F_1,A))))) # label(fact_200_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 221 (all F_1 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(F_1,X_1)),image_nat_nat(F_1,A))))) # label(fact_201_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 222 (all F_1 all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_H738206399_a_nat(F_1,X_1)),image_194810223_a_nat(F_1,A))))) # label(fact_202_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 223 (all F_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_H716259088te_nat(F_1,X_1)),image_1410872416te_nat(F_1,A))))) # label(fact_203_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 224 (all F_1 all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_H678412245iple_a(F_1,X_1)),image_306007685iple_a(F_1,A))))) # label(fact_204_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 225 (all F_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_H1600811558iple_a(F_1,X_1)),image_129517430iple_a(F_1,A))))) # label(fact_205_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 226 (all F_1 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_n178040171iple_a(F_1,X_1)),image_1782127643iple_a(F_1,A))))) # label(fact_206_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 227 (all Z_2 all F_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Z_2),image_650584225_state(F_1,A))) <-> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A)) & Z_2 = hAPP_H563960305_state(F_1,X_2))))) # label(fact_207_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 228 (all Z_2 all F_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Z_2),image_1604514514_state(F_1,A))) <-> (exists X_2 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) & Z_2 = hAPP_H928324994_state(F_1,X_2))))) # label(fact_208_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 229 (all Z_2 all F_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_2),image_nat_nat(F_1,A))) <-> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & Z_2 = hAPP_nat_nat(F_1,X_2))))) # label(fact_209_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 230 (all Z_2 all F_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_2),image_194810223_a_nat(F_1,A))) <-> (exists X_2 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) & Z_2 = hAPP_H738206399_a_nat(F_1,X_2))))) # label(fact_210_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 231 (all Z_2 all F_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Z_2),image_306007685iple_a(F_1,A))) <-> (exists X_2 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) & Z_2 = hAPP_H678412245iple_a(F_1,X_2))))) # label(fact_211_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 232 (all Z_2 all F_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Z_2),image_129517430iple_a(F_1,A))) <-> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A)) & Z_2 = hAPP_H1600811558iple_a(F_1,X_2))))) # label(fact_212_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 233 (all Z_2 all F_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Z_2),image_1782127643iple_a(F_1,A))) <-> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & Z_2 = hAPP_n178040171iple_a(F_1,X_2))))) # label(fact_213_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 234 (all Vname all Fun_1 all Com1 all Com2 ass(Vname,Fun_1) != semi(Com1,Com2)) # label(fact_214_com_Osimps_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 235 (all Com1 all Com2 all Vname all Fun_1 semi(Com1,Com2) != ass(Vname,Fun_1)) # label(fact_215_com_Osimps_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 236 (all Vname_1 all Fun skip != ass(Vname_1,Fun)) # label(fact_216_com_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 237 (all Vname_1 all Fun ass(Vname_1,Fun) != skip) # label(fact_217_com_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 238 (all F_1 all A (image_129517430iple_a(F_1,A) = bot_bo1181479936a_bool <-> A = bot_bo1055319631e_bool)) # label(fact_218_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 239 (all F_1 all A (image_1782127643iple_a(F_1,A) = bot_bo1181479936a_bool <-> A = bot_bot_fun_nat_bool)) # label(fact_219_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 240 (all F_1 all A (image_1604514514_state(F_1,A) = bot_bo1055319631e_bool <-> A = bot_bo1181479936a_bool)) # label(fact_220_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 241 (all F_1 all A (image_194810223_a_nat(F_1,A) = bot_bot_fun_nat_bool <-> A = bot_bo1181479936a_bool)) # label(fact_221_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 242 (all F_1 image_1604514514_state(F_1,bot_bo1181479936a_bool) = bot_bo1055319631e_bool) # label(fact_222_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 243 (all F_1 image_194810223_a_nat(F_1,bot_bo1181479936a_bool) = bot_bot_fun_nat_bool) # label(fact_223_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 244 (all F_1 image_129517430iple_a(F_1,bot_bo1055319631e_bool) = bot_bo1181479936a_bool) # label(fact_224_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 245 (all F_1 image_1782127643iple_a(F_1,bot_bot_fun_nat_bool) = bot_bo1181479936a_bool) # label(fact_225_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 246 (all F_1 all A (bot_bo1181479936a_bool = image_129517430iple_a(F_1,A) <-> A = bot_bo1055319631e_bool)) # label(fact_226_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 247 (all F_1 all A (bot_bo1181479936a_bool = image_1782127643iple_a(F_1,A) <-> A = bot_bot_fun_nat_bool)) # label(fact_227_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 248 (all F_1 all A (bot_bo1055319631e_bool = image_1604514514_state(F_1,A) <-> A = bot_bo1181479936a_bool)) # label(fact_228_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 249 (all F_1 all A (bot_bot_fun_nat_bool = image_194810223_a_nat(F_1,A) <-> A = bot_bo1181479936a_bool)) # label(fact_229_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 250 (all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) <-> hBOOL(hAPP_H1421470952a_bool(A,X_1)))) # label(fact_230_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 251 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_nat_bool(A,X_1)))) # label(fact_231_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 252 (all Pa collec268032053iple_a(Pa) = Pa) # label(fact_232_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 253 (all Pa collect_nat(Pa) = Pa) # label(fact_233_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.78 254 (all F_1 all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_H678412245iple_a(F_1,X_1)),image_306007685iple_a(F_1,A)) = image_306007685iple_a(F_1,A))) # label(fact_234_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 255 (all F_1 all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_n178040171iple_a(F_1,X_1)),image_1782127643iple_a(F_1,A)) = image_1782127643iple_a(F_1,A))) # label(fact_235_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 256 (all F_1 all A_1 all B image_1604514514_state(F_1,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_H928324994_state(F_1,A_1)),image_1604514514_state(F_1,B))) # label(fact_236_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 257 (all F_1 all A_1 all B image_194810223_a_nat(F_1,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_H738206399_a_nat(F_1,A_1)),image_194810223_a_nat(F_1,B))) # label(fact_237_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 258 (all F_1 all A_1 all B image_129517430iple_a(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_H1600811558iple_a(F_1,A_1)),image_129517430iple_a(F_1,B))) # label(fact_238_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 259 (all F_1 all A_1 all B image_1782127643iple_a(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_n178040171iple_a(F_1,A_1)),image_1782127643iple_a(F_1,B))) # label(fact_239_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 260 (all X_1 hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_H1190454433a_bool(fequal879838495iple_a,X_1)) = X_1) # label(fact_240_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 261 (all A_1 hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1)) = A_1) # label(fact_241_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 262 (all X_1 all Y_7 all Pa ((hBOOL(Pa) -> X_1 = hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_f1591852335a_bool(hAPP_f34030599a_bool(cOMBB_1799513916iple_a,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),X_1)))),hAPP_f1591852335a_bool(hAPP_f34030599a_bool(cOMBB_1799513916iple_a,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),Y_7))))) & (-hBOOL(Pa) -> Y_7 = hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_f1591852335a_bool(hAPP_f34030599a_bool(cOMBB_1799513916iple_a,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),X_1)))),hAPP_f1591852335a_bool(hAPP_f34030599a_bool(cOMBB_1799513916iple_a,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),Y_7))))))) # label(fact_242_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 263 (all F_1 all A_1 all Ba (hBOOL(hAPP_H513860823e_bool(finite9525415_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)),Ba)) <-> A_1 = Ba)) # label(fact_243_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 264 (all F_1 all A_1 all Ba (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)),Ba)) <-> A_1 = Ba)) # label(fact_244_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 265 (all F_1 all A_1 all Ba (hBOOL(hAPP_H1421470952a_bool(finite1537818352iple_a(F_1,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)),Ba)) <-> A_1 = Ba)) # label(fact_245_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 266 (all Pa all A_1 (hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> ((all X_2 (hBOOL(hAPP_H1421470952a_bool(Pa,X_2)) -> X_2 = A_1)) -> hAPP_f124283079iple_a(the_Ho746640593iple_a,Pa) = A_1))) # label(fact_246_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 267 (all X_1 all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = X_1)) # label(fact_247_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 268 (all X_1 all F_1 all F (hBOOL(finite988810631ne_nat(F_1,F)) -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1)) # label(fact_248_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 269 (all X_1 all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)) = X_1)) # label(fact_249_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 270 (all A_1 all Ga all Pa all Ca all Q_1 all X_35 all S_5 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,hAPP_f1838002347e_bool(hAPP_f1706273077e_bool(cOMBC_867582640e_bool,hAPP_f289738463e_bool(hAPP_f1151843515e_bool(cOMBB_1941618714_state,cOMBB_844853809_state),Q_1)),hAPP_n1547241352_state(hAPP_f1848060885_state(cOMBC_1777403949_state,hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,update),loc(X_35))),getlocs(S_5,X_35))))),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(hAPP_f817621513e_bool(hAPP_f512427579e_bool(cOMBB_572666224_state,hAPP_f644196280e_bool(cOMBS_1378840469l_bool,hAPP_f1259673775l_bool(hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj),hAPP_s1806633685e_bool(fequal_state,S_5)))),hAPP_f1838002347e_bool(hAPP_f1706273077e_bool(cOMBC_867582640e_bool,hAPP_f289738463e_bool(hAPP_f1151843515e_bool(cOMBB_1941618714_state,cOMBB_844853809_state),Pa)),hAPP_f871651461_state(hAPP_f851239890_state(cOMBS_777315357_state,hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,update),loc(X_35))),A_1))),local(X_35,A_1,Ca),Q_1)),bot_bo1055319631e_bool))))) # label(fact_250_hoare__derivs_OLocal) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 271 (all A_1 all Ga all Pa all Ca all Q_1 all X_35 all S_5 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(Pa,Ca,hAPP_f100967412e_bool(hAPP_f1460451647e_bool(cOMBC_524597097e_bool,hAPP_f1406200875e_bool(hAPP_f635443597e_bool(cOMBB_2139825703bool_a,cOMBB_844853809_state),Q_1)),hAPP_n1547241352_state(hAPP_f1848060885_state(cOMBC_1777403949_state,hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,update),loc(X_35))),getlocs(S_5,X_35))))),bot_bo1181479936a_bool))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hoare_1760757500iple_a(hAPP_f769584981e_bool(hAPP_f1159960589e_bool(cOMBB_237455441bool_a,hAPP_f644196280e_bool(cOMBS_1378840469l_bool,hAPP_f1259673775l_bool(hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj),hAPP_s1806633685e_bool(fequal_state,S_5)))),hAPP_f100967412e_bool(hAPP_f1460451647e_bool(cOMBC_524597097e_bool,hAPP_f1406200875e_bool(hAPP_f635443597e_bool(cOMBB_2139825703bool_a,cOMBB_844853809_state),Pa)),hAPP_f871651461_state(hAPP_f851239890_state(cOMBS_777315357_state,hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,update),loc(X_35))),A_1))),local(X_35,A_1,Ca),Q_1)),bot_bo1181479936a_bool))))) # label(fact_251_hoare__derivs_OLocal) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 272 (all Loc_3 all Loc_2 (is_loc(Loc_3) & is_loc(Loc_2) -> (loc(Loc_3) = loc(Loc_2) <-> Loc_3 = Loc_2))) # label(fact_252_vname_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 273 (all Loc_3 all Fun_1 all Com_1 all Loc_2 all Fun all Com (is_loc(Loc_3) & is_loc(Loc_2) -> (local(Loc_3,Fun_1,Com_1) = local(Loc_2,Fun,Com) <-> Loc_3 = Loc_2 & Fun_1 = Fun & Com_1 = Com))) # label(fact_253_com_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 274 (all Loc_3 all Fun_1 all Com_1 all Com1 all Com2 local(Loc_3,Fun_1,Com_1) != semi(Com1,Com2)) # label(fact_254_com_Osimps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 275 (all Com1 all Com2 all Loc_3 all Fun_1 all Com_1 semi(Com1,Com2) != local(Loc_3,Fun_1,Com_1)) # label(fact_255_com_Osimps_I35_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 276 (all Loc_2 all Fun all Com all Vname all Fun_1 local(Loc_2,Fun,Com) != ass(Vname,Fun_1)) # label(fact_256_com_Osimps_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 277 (all Vname all Fun_1 all Loc_2 all Fun all Com ass(Vname,Fun_1) != local(Loc_2,Fun,Com)) # label(fact_257_com_Osimps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 278 (all Loc_2 all Fun all Com local(Loc_2,Fun,Com) != skip) # label(fact_258_com_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 279 (all Loc_2 all Fun all Com skip != local(Loc_2,Fun,Com)) # label(fact_259_com_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 280 (all F_1 all X_1 -hBOOL(hAPP_H513860823e_bool(finite9525415_state(F_1,bot_bo1055319631e_bool),X_1))) # label(fact_260_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 281 (all F_1 all X_1 -hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F_1,bot_bot_fun_nat_bool),X_1))) # label(fact_261_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 282 (all F_1 all X_1 -hBOOL(hAPP_H1421470952a_bool(finite1537818352iple_a(F_1,bot_bo1181479936a_bool),X_1))) # label(fact_262_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 283 (all F_1 all A all X_1 (hBOOL(hAPP_H513860823e_bool(finite9525415_state(F_1,A),X_1)) -> A != bot_bo1055319631e_bool)) # label(fact_263_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 284 (all F_1 all A all X_1 (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F_1,A),X_1)) -> A != bot_bot_fun_nat_bool)) # label(fact_264_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 285 (all F_1 all A all X_1 (hBOOL(hAPP_H1421470952a_bool(finite1537818352iple_a(F_1,A),X_1)) -> A != bot_bo1181479936a_bool)) # label(fact_265_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 286 (all Pa all A_1 (hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> ((all X_2 (hBOOL(hAPP_H1421470952a_bool(Pa,X_2)) -> X_2 = A_1)) -> hBOOL(hAPP_H1421470952a_bool(Pa,hAPP_f124283079iple_a(the_Ho746640593iple_a,Pa)))))) # label(fact_266_theI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 287 (all A_1 all Pa ((exists X_2 (hBOOL(hAPP_H1421470952a_bool(Pa,X_2)) & (all Y_11 (hBOOL(hAPP_H1421470952a_bool(Pa,Y_11)) -> Y_11 = X_2)))) -> (hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> hAPP_f124283079iple_a(the_Ho746640593iple_a,Pa) = A_1))) # label(fact_267_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 288 (all Pa ((exists X_2 (hBOOL(hAPP_H1421470952a_bool(Pa,X_2)) & (all Y_11 (hBOOL(hAPP_H1421470952a_bool(Pa,Y_11)) -> Y_11 = X_2)))) -> hBOOL(hAPP_H1421470952a_bool(Pa,hAPP_f124283079iple_a(the_Ho746640593iple_a,Pa))))) # label(fact_268_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 289 (all Ca all S0_1 all Y_27 all A_1 all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(Ca),hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S0_1),loc(Y_27)),hAPP_state_nat(A_1,S0_1))),S1_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(local(Y_27,A_1,Ca)),S0_1),hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S1_2),loc(Y_27)),getlocs(S0_1,Y_27)))))) # label(fact_269_evalc_OLocal) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 290 (all Ca all S0_1 all Y_27 all A_1 all N_3 all S1_2 (hBOOL(evaln(Ca,hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S0_1),loc(Y_27)),hAPP_state_nat(A_1,S0_1)),N_3,S1_2)) -> hBOOL(evaln(local(Y_27,A_1,Ca),S0_1,N_3,hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S1_2),loc(Y_27)),getlocs(S0_1,Y_27)))))) # label(fact_270_evaln_OLocal) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 291 (all F_1 all A_1 all A all X_1 (hBOOL(hAPP_H513860823e_bool(finite1935632226_state(F_1,A_1,A),X_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hBOOL(hAPP_H513860823e_bool(finite9525415_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)),X_1))))) # label(fact_271_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 292 (all F_1 all A_1 all A all X_1 (hBOOL(hAPP_nat_bool(finite929467206at_nat(F_1,A_1,A),X_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)),X_1))))) # label(fact_272_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 293 (all F_1 all A_1 all A all X_1 (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,A_1,A),X_1)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hBOOL(hAPP_H1421470952a_bool(finite1537818352iple_a(F_1,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)),X_1))))) # label(fact_273_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 294 (all C1 all S2 all C0 all S0 all N_2 all S1 (hBOOL(evaln(C0,S0,N_2,S1)) -> (hBOOL(evaln(C1,S1,N_2,S2)) -> hBOOL(evaln(semi(C0,C1),S0,N_2,S2))))) # label(fact_274_evaln_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 295 (all S_1 all N_2 hBOOL(evaln(skip,S_1,N_2,S_1))) # label(fact_275_evaln_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 296 (all S_1 all N_2 all T (hBOOL(evaln(skip,S_1,N_2,T)) -> T = S_1)) # label(fact_276_evaln__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 297 (all C1 all S2 all C0 all S0 all S1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0),S1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1),S2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0,C1)),S0),S2))))) # label(fact_277_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 298 (all S_1 hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_1),S_1))) # label(fact_278_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 299 (all S_1 all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_1),T)) -> T = S_1)) # label(fact_279_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 300 (all X_35 all A_1 all S_4 all N_3 hBOOL(evaln(ass(X_35,A_1),S_4,N_3,hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S_4),X_35),hAPP_state_nat(A_1,S_4))))) # label(fact_280_evaln_OAssign) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 301 (all X_35 all A_1 all S_4 all N_3 all T_1 (hBOOL(evaln(ass(X_35,A_1),S_4,N_3,T_1)) -> T_1 = hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S_4),X_35),hAPP_state_nat(A_1,S_4)))) # label(fact_281_evaln__elim__cases_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 302 (all X_35 all A_1 all S_4 hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(ass(X_35,A_1)),S_4),hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S_4),X_35),hAPP_state_nat(A_1,S_4))))) # label(fact_282_evalc_OAssign) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 303 (all X_35 all A_1 all S_4 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(ass(X_35,A_1)),S_4),T_1)) -> T_1 = hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S_4),X_35),hAPP_state_nat(A_1,S_4)))) # label(fact_283_evalc__elim__cases_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 304 (all Ca all S_4 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(Ca),S_4),T_1)) <-> (exists N_1 hBOOL(evaln(Ca,S_4,N_1,T_1))))) # label(fact_284_eval__eq) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 305 (all U_1 all C_2 all S_1 all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),T)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),U_1)) -> U_1 = T))) # label(fact_285_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 306 (all C_2 all S_1 all N_2 all T (hBOOL(evaln(C_2,S_1,N_2,T)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),T)))) # label(fact_286_evaln__evalc) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 307 (all F_1 all Z_2 all X_1 (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,bot_bo1181479936a_bool),X_1)) -> X_1 = Z_2)) # label(fact_287_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 308 (all F_1 all Z_2 hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,bot_bo1181479936a_bool),Z_2))) # label(fact_288_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 309 (all F_1 all Z_2 all Y_7 all X_1 all A (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),Y_7)) -> hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)),hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_1),Y_7)))))) # label(fact_289_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 310 (all Y_27 all A_1 all Ca all S_4 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(local(Y_27,A_1,Ca)),S_4),T_1)) -> -(all S1_1 (T_1 = hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S1_1),loc(Y_27)),getlocs(S_4,Y_27)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(Ca),hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S_4),loc(Y_27)),hAPP_state_nat(A_1,S_4))),S1_1)))))) # label(fact_290_evalc__elim__cases_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 311 (all Y_27 all A_1 all Ca all S_4 all N_3 all T_1 (hBOOL(evaln(local(Y_27,A_1,Ca),S_4,N_3,T_1)) -> -(all S1_1 (T_1 = hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S1_1),loc(Y_27)),getlocs(S_4,Y_27)) -> -hBOOL(evaln(Ca,hAPP_nat_state(hAPP_v594194232_state(hAPP_s712361723_state(update,S_4),loc(Y_27)),hAPP_state_nat(A_1,S_4)),N_3,S1_1)))))) # label(fact_291_evaln__elim__cases_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 312 (all C1 all C2 all S_1 all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1,C2)),S_1),T)) -> -(all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_1),S1_1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1_1),T)))))) # label(fact_292_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 313 (all C1 all C2 all S_1 all N_2 all T (hBOOL(evaln(semi(C1,C2),S_1,N_2,T)) -> -(all S1_1 (hBOOL(evaln(C1,S_1,N_2,S1_1)) -> -hBOOL(evaln(C2,S1_1,N_2,T)))))) # label(fact_293_evaln__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 314 (all F_1 all A_1 all X_35 all X_1 (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),X_35)),X_1)) -> -(all A_7 all A_19 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),X_35) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_7),A_19) -> (hBOOL(hAPP_nat_bool(finite929467206at_nat(F_1,A_7,A_19),X_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_7),A_19))))))) # label(fact_294_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 315 (all F_1 all A_1 all X_35 all X_1 (hBOOL(hAPP_H513860823e_bool(finite9525415_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),X_35)),X_1)) -> -(all A_7 all A_19 (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),X_35) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_7),A_19) -> (hBOOL(hAPP_H513860823e_bool(finite1935632226_state(F_1,A_7,A_19),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_7),A_19))))))) # label(fact_295_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 316 (all F_1 all A_1 all X_35 all X_1 (hBOOL(hAPP_H1421470952a_bool(finite1537818352iple_a(F_1,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),X_35)),X_1)) -> -(all A_7 all A_19 (hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),X_35) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_7),A_19) -> (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,A_7,A_19),X_1)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_7),A_19))))))) # label(fact_296_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 317 (all Ca hoare_Mirabelle_MGT(Ca) = hoare_1575745797_state(fequal_state,Ca,evalc(Ca))) # label(fact_297_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 318 (all C_2 all S_1 all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),T)) -> (exists N_1 hBOOL(evaln(C_2,S_1,N_1,T))))) # label(fact_298_evalc__evaln) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 319 (all F_1 all A1 all A2 (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F_1,A1),A2)) <-> (exists A_7 exists A_19 exists X_2 (A1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_7),A_19) & A2 = X_2 & hBOOL(hAPP_nat_bool(finite929467206at_nat(F_1,A_7,A_19),X_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_7),A_19)))))) # label(fact_299_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 320 (all F_1 all A1 all A2 (hBOOL(hAPP_H513860823e_bool(finite9525415_state(F_1,A1),A2)) <-> (exists A_7 exists A_19 exists X_2 (A1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_7),A_19) & A2 = X_2 & hBOOL(hAPP_H513860823e_bool(finite1935632226_state(F_1,A_7,A_19),X_2)) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_7),A_19)))))) # label(fact_300_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 321 (all F_1 all A1 all A2 (hBOOL(hAPP_H1421470952a_bool(finite1537818352iple_a(F_1,A1),A2)) <-> (exists A_7 exists A_19 exists X_2 (A1 = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_7),A_19) & A2 = X_2 & hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,A_7,A_19),X_2)) & -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_7),A_19)))))) # label(fact_301_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 322 (all F_1 all Z_2 all A1 all A2 (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A1),A2)) <-> A1 = bot_bo1181479936a_bool & A2 = Z_2 | (exists X_2 exists A_19 exists Y_11 (A1 = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A_19) & A2 = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),Y_11) & -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A_19)) & hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A_19),Y_11)))))) # label(fact_302_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 323 (all C2 all S2 all N2 all T2 all C1 all S1 all N1 all T1 (hBOOL(evaln(C1,S1,N1,T1)) -> (hBOOL(evaln(C2,S2,N2,T2)) -> (exists N_1 (hBOOL(evaln(C1,S1,N_1,T1)) & hBOOL(evaln(C2,S2,N_1,T2))))))) # label(fact_303_evaln__max2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 324 (all N_3 all Pa all Ca all Q_1 (hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_3),hoare_1575745797_state(Pa,Ca,Q_1))) <-> (all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_7),S_2)) -> (all S_3 (hBOOL(evaln(Ca,S_2,N_3,S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_7),S_3)))))))) # label(fact_304_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 325 (all N_3 all Pa all Ca all Q_1 (hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_3),hoare_1760757500iple_a(Pa,Ca,Q_1))) <-> (all Z_7 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_7),S_2)) -> (all S_3 (hBOOL(evaln(Ca,S_2,N_3,S_3)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_7),S_3)))))))) # label(fact_305_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 326 (all X_1 all A all F_1 all F (hBOOL(finite988810631ne_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,X_1),hAPP_f22106695ol_nat(F,A))))))) # label(fact_306_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 327 (all X_1 all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> (A != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_1),hAPP_f2143211163_state(F,A))))))) # label(fact_307_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 328 (all X_1 all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (A != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_1),hAPP_f124283079iple_a(F,A))))))) # label(fact_308_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 329 (all Q_1 all Pa (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,collec268032053iple_a(Pa))) | hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,collec268032053iple_a(Q_1))) -> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),Pa)),Q_1)))))) # label(fact_309_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 330 (all Q_1 all Pa (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),Pa)),Q_1)))))) # label(fact_310_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 331 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A))))) # label(fact_314_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 332 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A))))) # label(fact_315_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 333 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A))))) # label(fact_316_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 334 (all Pa all Q_1 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,collec268032053iple_a(Pa))) & hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,collec268032053iple_a(Q_1))))) # label(fact_317_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 335 (all Pa all Q_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))))) # label(fact_318_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 336 (all Glb_3 all Glb_2 (is_glb(Glb_3) & is_glb(Glb_2) -> (glb(Glb_3) = glb(Glb_2) <-> Glb_3 = Glb_2))) # label(fact_319_vname_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 337 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)))) # label(fact_320_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 338 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)))) # label(fact_321_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 339 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A))) <-> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)))) # label(fact_322_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 340 (all Loc_1 all Glb_1 loc(Loc_1) != glb(Glb_1)) # label(fact_323_vname_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 341 (all Glb_1 all Loc_1 glb(Glb_1) != loc(Loc_1)) # label(fact_324_vname_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 342 (all A all F_1 all F (hBOOL(finite988810631ne_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> ((all X_2 all Y_11 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,X_2),Y_11)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_11),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F,A)),A))))))) # label(fact_325_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 343 (all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> ((all X_2 all Y_11 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_2),Y_11)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_11),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(F,A)),A))))))) # label(fact_326_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.79 344 (all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> ((all X_2 all Y_11 hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),Y_11)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_11),bot_bo1181479936a_bool))))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_f124283079iple_a(F,A)),A))))))) # label(fact_327_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 345 (all F_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> (exists X1 hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F_1,A),X1)))))) # label(fact_328_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 346 (all F_1 all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> (exists X1 hBOOL(hAPP_H1421470952a_bool(finite1537818352iple_a(F_1,A),X1)))))) # label(fact_329_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 347 (all F_1 all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> (exists X1 hBOOL(hAPP_H513860823e_bool(finite9525415_state(F_1,A),X1)))))) # label(fact_330_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 348 (all Pa all F (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F)))))) # label(fact_331_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 349 (all Pa all F (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_2))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F)))))) # label(fact_332_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 350 (all Pa all F (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F)) -> (hBOOL(hAPP_f540970102l_bool(Pa,bot_bo1181479936a_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F_2)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),F_2)) -> (hBOOL(hAPP_f540970102l_bool(Pa,F_2)) -> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),F_2))))))) -> hBOOL(hAPP_f540970102l_bool(Pa,F)))))) # label(fact_333_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 351 (all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) <-> A_1 = bot_bot_fun_nat_bool | (exists A_19 exists A_7 (A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_7),A_19) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_19)))))) # label(fact_334_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 352 (all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) <-> A_1 = bot_bo1055319631e_bool | (exists A_19 exists A_7 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_7),A_19) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_19)))))) # label(fact_335_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 353 (all A_1 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A_1)) <-> A_1 = bot_bo1181479936a_bool | (exists A_19 exists A_7 (A_1 = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_7),A_19) & hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A_19)))))) # label(fact_336_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 354 (all F_1 all Z_2 all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (exists X1 hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),X1))))) # label(fact_337_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 355 (all X_1 all A all F_1 all F (hBOOL(finite795500164em_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,X_1),hAPP_f22106695ol_nat(F,A)))))) # label(fact_338_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 356 (all X_1 all A all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_1),hAPP_f2143211163_state(F,A)))))) # label(fact_339_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 357 (all X_1 all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_1),hAPP_f124283079iple_a(F,A)))))) # label(fact_340_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 358 (all Pa all F (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F)) -> (F != bot_bot_fun_nat_bool -> ((all X_2 hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (F_2 != bot_bot_fun_nat_bool -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F))))))) # label(fact_341_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 359 (all Pa all F (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F)) -> (F != bot_bo1055319631e_bool -> ((all X_2 hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (F_2 != bot_bo1055319631e_bool -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_2)))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F))))))) # label(fact_342_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 360 (all Pa all F (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F)) -> (F != bot_bo1181479936a_bool -> ((all X_2 hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),bot_bo1181479936a_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F_2)) -> (F_2 != bot_bo1181479936a_bool -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),F_2)) -> (hBOOL(hAPP_f540970102l_bool(Pa,F_2)) -> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),F_2)))))))) -> hBOOL(hAPP_f540970102l_bool(Pa,F))))))) # label(fact_343_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 361 (all Y (is_vname(Y) -> ((all Glb (is_glb(Glb) -> Y != glb(Glb))) -> -(all Loc (is_loc(Loc) -> Y != loc(Loc)))))) # label(fact_344_vname_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 362 (all X_1 all A all F_1 all F (hBOOL(finite988810631ne_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F,A) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,X_1),hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))))) # label(fact_345_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 363 (all X_1 all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,A) = X_1) & (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,A) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_1),hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))))))))) # label(fact_346_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 364 (all X_1 all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)) = bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,A) = X_1) & (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)) != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,A) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_1),hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool))))))))) # label(fact_347_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 365 (all X_1 all A all F_1 all F (hBOOL(finite988810631ne_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,X_1),hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_348_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 366 (all X_1 all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)) = X_1) & (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_1),hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))))))) # label(fact_349_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 367 (all X_1 all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)) = bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)) = X_1) & (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)) != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_1),hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)))))))) # label(fact_350_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 368 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B))) -> -(hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B))))) # label(fact_351_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 369 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_352_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 370 (all B all Ca all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B)))))) # label(fact_353_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 371 (all B all Ca all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))))) # label(fact_354_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 372 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_355_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 373 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B))) -> -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)))) # label(fact_356_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 374 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)))) # label(fact_357_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 375 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)))) # label(fact_358_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 376 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)))) # label(fact_359_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 377 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) & -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)))) # label(fact_360_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 378 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)))) # label(fact_361_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 379 (all A all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B) = collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),A))),hAPP_f1591852335a_bool(hAPP_f34030599a_bool(cOMBB_1799513916iple_a,fNot),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B))))) # label(fact_362_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 380 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A))),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B))))) # label(fact_363_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 381 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),A) = bot_bot_fun_nat_bool) # label(fact_364_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 382 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),A) = bot_bo1055319631e_bool) # label(fact_365_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 383 (all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),A) = bot_bo1181479936a_bool) # label(fact_366_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 384 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),bot_bot_fun_nat_bool) = A) # label(fact_367_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 385 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),bot_bo1055319631e_bool) = A) # label(fact_368_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 386 (all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),bot_bo1181479936a_bool) = A) # label(fact_369_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 387 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A) = bot_bot_fun_nat_bool) # label(fact_370_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 388 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,bot_bo1055319631e_bool),A) = bot_bo1055319631e_bool) # label(fact_371_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 389 (all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,bot_bo1181479936a_bool),A) = bot_bo1181479936a_bool) # label(fact_372_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 390 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_373_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 391 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) # label(fact_374_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 392 (all A all X_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),B))) # label(fact_375_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 393 (all A all X_1 all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)),B) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B))) # label(fact_376_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 394 (all A all X_1 all B ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_377_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 395 (all A all X_1 all B ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),B)) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)),B) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),B))))) # label(fact_378_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 396 (all A all X_1 all B ((hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)),B) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B)) & (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)),B) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B))))) # label(fact_379_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 397 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) = A)) # label(fact_380_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 398 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))) = A)) # label(fact_381_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 399 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))) = A)) # label(fact_382_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 400 (all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = A)) # label(fact_383_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 401 (all X_1 all A (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = A)) # label(fact_384_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 402 (all X_1 all A (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool)) = A)) # label(fact_385_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 403 (all A_1 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)) # label(fact_386_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 404 (all A_1 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)) # label(fact_387_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 405 (all A_1 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)) # label(fact_388_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 406 (all A all A_1 all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))),B)) # label(fact_389_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 407 (all A all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))),B)) # label(fact_390_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 408 (all A all A_1 all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))),B)) # label(fact_391_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 409 (all A all A_1 all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) # label(fact_392_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 410 (all A all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),B)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))) # label(fact_393_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 411 (all A all A_1 all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))) # label(fact_394_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 412 (all A all A_1 all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_395_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 413 (all A all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),B))))) # label(fact_396_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 414 (all A all A_1 all B (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)))) <-> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B))))) # label(fact_397_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 415 (all X_1 all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_1),hAPP_f124283079iple_a(F,A)) = hAPP_f124283079iple_a(F,A))))) # label(fact_398_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 416 (all X_1 all A all F_1 all F (hBOOL(finite795500164em_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,X_1),hAPP_f22106695ol_nat(F,A)) = hAPP_f22106695ol_nat(F,A))))) # label(fact_399_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 417 (all N all H all F_1 all F (hBOOL(finite795500164em_nat(F_1,F)) -> ((all X_2 all Y_11 hAPP_nat_nat(H,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,X_2),Y_11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,hAPP_nat_nat(H,X_2)),hAPP_nat_nat(H,Y_11))) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N)) -> (N != bot_bot_fun_nat_bool -> hAPP_nat_nat(H,hAPP_f22106695ol_nat(F,N)) = hAPP_f22106695ol_nat(F,image_nat_nat(H,N))))))) # label(fact_400_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 418 (all N all H all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> ((all X_2 all Y_11 hAPP_H563960305_state(H,hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_2),Y_11)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_H563960305_state(H,X_2)),hAPP_H563960305_state(H,Y_11))) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,N)) -> (N != bot_bo1055319631e_bool -> hAPP_H563960305_state(H,hAPP_f2143211163_state(F,N)) = hAPP_f2143211163_state(F,image_650584225_state(H,N))))))) # label(fact_401_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 419 (all N all H all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> ((all X_2 all Y_11 hAPP_H678412245iple_a(H,hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),Y_11)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_H678412245iple_a(H,X_2)),hAPP_H678412245iple_a(H,Y_11))) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,N)) -> (N != bot_bo1181479936a_bool -> hAPP_H678412245iple_a(H,hAPP_f124283079iple_a(F,N)) = hAPP_f124283079iple_a(F,image_306007685iple_a(H,N))))))) # label(fact_402_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 420 (all Pa all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A)) -> ((all A_7 all A_19 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_19)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_7),A_19)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A_19)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_19),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_7),bot_bot_fun_nat_bool)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)))))) # label(fact_403_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 421 (all Pa all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,A)) -> ((all A_7 all A_19 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_19)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_7),A_19)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,A_19)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_19),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_7),bot_bo1055319631e_bool)))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)))))) # label(fact_404_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 422 (all Pa all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (hBOOL(hAPP_f540970102l_bool(Pa,A)) -> ((all A_7 all A_19 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A_19)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_7),A_19)) -> (hBOOL(hAPP_f540970102l_bool(Pa,A_19)) -> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A_19),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_7),bot_bo1181479936a_bool)))))))) -> hBOOL(hAPP_f540970102l_bool(Pa,bot_bo1181479936a_bool)))))) # label(fact_405_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 423 (all A_1 all Z_2 all A all Y_7 all F_1 (hBOOL(finite1200705745iple_a(F_1)) -> (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),Y_7)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> (exists Y_26 (Y_7 = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,A_1),Y_26) & hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))),Y_26)))))))) # label(fact_409_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 424 (all A_1 all Ba all A all X_1 (hBOOL(hAPP_nat_bool(finite929467206at_nat(times_times_nat,Ba,A),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),A)) -> hBOOL(hAPP_nat_bool(finite929467206at_nat(times_times_nat,A_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)))),X_1)))))) # label(fact_410_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 425 (all Y_7 all Z_2 all A all X_1 all F_1 (hBOOL(finite1200705745iple_a(F_1)) -> (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),X_1)) -> (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),Y_7)) -> Y_7 = X_1)))) # label(fact_414_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 426 (all Z_2 all Ba all A all Y_7 (hBOOL(hAPP_nat_bool(finite929467206at_nat(times_times_nat,Ba,A),Y_7)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),A)) -> hBOOL(hAPP_nat_bool(finite929467206at_nat(times_times_nat,Z_2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),A)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Z_2),Y_7)))))) # label(fact_415_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 427 (all Z_2 all X_1 all A all V all F_1 (hBOOL(finite1200705745iple_a(F_1)) -> (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)),V)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> -(all Y_11 (V = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_1),Y_11) -> -hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),Y_11)))))))) # label(fact_416_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 428 (all X_1 all A (A != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A)))))) # label(fact_417_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 429 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(times_times_nat,A_1),A)))) # label(fact_418_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 430 (all F_1 all A_1 hAPP_f22106695ol_nat(finite_fold1_nat(F_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) = A_1) # label(fact_419_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 431 (all F_1 all A_1 hAPP_f2143211163_state(finite1346402327_state(F_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) = A_1) # label(fact_420_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 432 (all F_1 all A_1 hAPP_f124283079iple_a(finite1382394752iple_a(F_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) = A_1) # label(fact_421_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 433 (all A_1 all G all F_1 (G = finite_fold1_nat(F_1) -> hAPP_f22106695ol_nat(G,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) = A_1)) # label(fact_422_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 434 (all A_1 all G all F_1 (G = finite1346402327_state(F_1) -> hAPP_f2143211163_state(G,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) = A_1)) # label(fact_423_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 435 (all A_1 all G all F_1 (G = finite1382394752iple_a(F_1) -> hAPP_f124283079iple_a(G,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) = A_1)) # label(fact_424_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 436 (all Z_2 all A all Y_7 all F_1 (hBOOL(finite1200705745iple_a(F_1)) -> (hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),Y_7)) -> hAPP_f124283079iple_a(finite978536264iple_a(F_1,Z_2),A) = Y_7))) # label(fact_425_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 437 (all F_1 all Z_2 all A hAPP_f124283079iple_a(finite978536264iple_a(F_1,Z_2),A) = hAPP_f124283079iple_a(the_Ho746640593iple_a,finite2010942150iple_a(F_1,Z_2,A))) # label(fact_426_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 438 (all A all F_1 all F (hBOOL(finite988810631ne_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(F,A) = hAPP_f22106695ol_nat(finite_fold1_nat(F_1),A)))) # label(fact_427_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 439 (all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> hAPP_f124283079iple_a(F,A) = hAPP_f124283079iple_a(finite1382394752iple_a(F_1),A)))) # label(fact_428_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 440 (all X_1 all A all F_1 all F (hBOOL(finite988810631ne_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F_1,X_1),A))))) # label(fact_429_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 441 (all X_1 all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)) = hAPP_f2143211163_state(finite202520804_state(F_1,X_1),A))))) # label(fact_430_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.80 442 (all X_1 all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)) = hAPP_f124283079iple_a(finite978536264iple_a(F_1,X_1),A))))) # label(fact_431_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 443 (all A_1 all A all F_1 all F (hBOOL(finite795500164em_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F_1,A_1),A)))) # label(fact_432_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 444 (all A_1 all A all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)) = hAPP_f2143211163_state(finite202520804_state(F_1,A_1),A)))) # label(fact_433_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 445 (all A_1 all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)) = hAPP_f124283079iple_a(finite978536264iple_a(F_1,A_1),A)))) # label(fact_434_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 446 (all Z_2 all A all F_1 (hBOOL(finite1200705745iple_a(F_1)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> hBOOL(hAPP_H1421470952a_bool(finite2010942150iple_a(F_1,Z_2,A),hAPP_f124283079iple_a(finite978536264iple_a(F_1,Z_2),A)))))) # label(fact_435_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 447 (all F_1 all A hAPP_f124283079iple_a(finite1382394752iple_a(F_1),A) = hAPP_f124283079iple_a(the_Ho746640593iple_a,finite1537818352iple_a(F_1,A))) # label(fact_436_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 448 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),A) = hAPP_f800510211t_bool(finite1578363458t_bool(hAPP_f10625010t_bool(hAPP_f1115950719t_bool(cOMBB_1654519265ol_nat,hAPP_f1311642927t_bool(cOMBC_646315179t_bool,minus_2067140911t_bool)),hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,insert_nat),bot_bot_fun_nat_bool)),B),A))) # label(fact_437_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 449 (all B all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,B),A) = hAPP_f921536533e_bool(finite512563852e_bool(hAPP_f531275309e_bool(hAPP_f1470644835e_bool(cOMBB_946224375_state,hAPP_f2049746453e_bool(cOMBC_872426556e_bool,minus_2076558538e_bool)),hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,insert1835143293_state),bot_bo1055319631e_bool)),B),A))) # label(fact_438_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 450 (all B all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,B),A) = hAPP_f1591852335a_bool(finite1979045230a_bool(hAPP_f485051996a_bool(hAPP_f2085120383a_bool(cOMBB_2080540641iple_a,hAPP_f450029403a_bool(cOMBC_314077933a_bool,minus_469558085a_bool)),hAPP_f1665407592a_bool(hAPP_f549683569a_bool(cOMBC_708118077a_bool,insert873085594iple_a),bot_bo1181479936a_bool)),B),A))) # label(fact_439_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 451 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> ((all X_2 all Y_11 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_2),Y_11)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_11),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A)),A)))))) # label(fact_440_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 452 (all A all F_1 all F (hBOOL(big_se275732192ig_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(F,A) = hAPP_f22106695ol_nat(finite_fold1_nat(F_1),A)))) # label(fact_441_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 453 (all B all A all F_1 all F (hBOOL(finite795500164em_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (B != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,hAPP_f22106695ol_nat(F,B)),hAPP_f22106695ol_nat(F,A)) = hAPP_f22106695ol_nat(F,A)))))) # label(fact_442_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 454 (all B all A all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (B != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A)) -> hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,B)),hAPP_f2143211163_state(F,A)) = hAPP_f2143211163_state(F,A)))))) # label(fact_443_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 455 (all B all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (B != bot_bo1181479936a_bool -> (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,B),A)) -> hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,B)),hAPP_f124283079iple_a(F,A)) = hAPP_f124283079iple_a(F,A)))))) # label(fact_444_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 456 (all X_34 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_34),X_34))) # label(fact_445_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 457 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B))))) # label(fact_446_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 458 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_447_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 459 (all A all Ca all B ((-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B))))) # label(fact_448_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 460 (all A all Ca all B ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B))))) # label(fact_449_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 461 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B))) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B))))) # label(fact_450_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 462 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_451_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 463 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A))) # label(fact_452_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 464 (all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A))) # label(fact_453_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 465 (all A hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,bot_bo1181479936a_bool),A))) # label(fact_454_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 466 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,ord_le1568362934t_bool),A)))))) # label(fact_455_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 467 (all Ba all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_1),Ba)),hAPP_f22106695ol_nat(finite_fold_nat_nat(semila972727038up_nat,Ba),A)))))) # label(fact_456_sup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 468 (all A (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),bot_bot_fun_nat_bool)) <-> A = bot_bot_fun_nat_bool)) # label(fact_457_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 469 (all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool)) <-> A = bot_bo1055319631e_bool)) # label(fact_458_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 470 (all A (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),bot_bo1181479936a_bool)) <-> A = bot_bo1181479936a_bool)) # label(fact_459_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 471 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_460_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 472 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_461_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 473 (all B all A_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)))) # label(fact_462_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 474 (all B all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)))) # label(fact_463_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 475 (all B all A_1 hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,B),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)))) # label(fact_464_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 476 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_465_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.81 477 (all X_1 all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A)),B)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B)))) # label(fact_466_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 478 (all X_1 all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),A)),B)) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B)) & hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B)))) # label(fact_467_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 479 (all B all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))))) # label(fact_468_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 480 (all B all X_1 all A (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B))))) # label(fact_469_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 481 (all B all X_1 all A (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),B))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B))))) # label(fact_470_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 482 (all Ba all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),B))))) # label(fact_471_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 483 (all Ba all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),B))))) # label(fact_472_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 484 (all Ba all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B)) -> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),B))))) # label(fact_473_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 485 (all A_1 all C all D_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),D_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),C)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),D_2))))) # label(fact_474_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 486 (all A_1 all C all D_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),D_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),C)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),D_2))))) # label(fact_475_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 487 (all A_1 all C all D_2 (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,C),D_2)) -> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),C)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),D_2))))) # label(fact_476_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 488 (all A_18 all B_14 all X_33 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_18),B_14)),X_33)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_18),X_33)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_14),X_33))))) # label(fact_477_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 489 (all B_13 all D_1 all A_17 all C_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),C_7)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_13),D_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_17),B_13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,C_7),D_1)))))) # label(fact_478_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 490 (all Z_6 all Y_25 all X_32 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_25),X_32)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_6),X_32)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_25),Z_6)),X_32))))) # label(fact_479_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 491 (all B_12 all A_16 all X_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_16),X_31)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_12),X_31)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_16),B_12)),X_31))))) # label(fact_480_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 492 (all Y_24 all X_30 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_24),X_30)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_30),Y_24) = X_30)) # label(fact_481_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 493 (all X_29 all Y_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_29),Y_23)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_29),Y_23) = Y_23)) # label(fact_482_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 494 (all A_15 all X_28 all B_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_28),B_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_28),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_15),B_11))))) # label(fact_483_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 495 (all B_10 all X_27 all A_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_27),A_14)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_27),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_14),B_10))))) # label(fact_484_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 496 (all X_1 all Y_7 all Z_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_1),Y_7)),Z_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),Z_2)))) # label(fact_485_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 497 (all X_1 all Y_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_7)) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_1),Y_7) = Y_7)) # label(fact_486_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 498 (all Y_22 all X_26 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_26),Y_22)))) # label(fact_487_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 499 (all Y_21 all X_25 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_21),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_25),Y_21)))) # label(fact_488_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 500 (all X_24 all Y_20 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_24),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_24),Y_20)))) # label(fact_489_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 501 (all X_23 all Y_19 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_23),Y_19)))) # label(fact_490_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 502 (all X_1 all Y_7 ((hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_7)) <-> hBOOL(bot_bot_bool)) <-> (hBOOL(X_1) <-> hBOOL(bot_bot_bool)) & (hBOOL(Y_7) <-> hBOOL(bot_bot_bool)))) # label(fact_491_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 503 (all X_1 all Y_7 (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_1),Y_7) = bot_bot_fun_nat_bool <-> X_1 = bot_bot_fun_nat_bool & Y_7 = bot_bot_fun_nat_bool)) # label(fact_492_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 504 (all X_1 all Y_7 (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_7) = bot_bo1055319631e_bool <-> X_1 = bot_bo1055319631e_bool & Y_7 = bot_bo1055319631e_bool)) # label(fact_493_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 505 (all X_1 all Y_7 (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_1),Y_7) = bot_bo1181479936a_bool <-> X_1 = bot_bo1181479936a_bool & Y_7 = bot_bo1181479936a_bool)) # label(fact_494_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 506 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),bot_bot_bool)) <-> hBOOL(X_1))) # label(fact_495_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 507 (all X_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_1),bot_bot_fun_nat_bool) = X_1) # label(fact_496_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 508 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),bot_bo1055319631e_bool) = X_1) # label(fact_497_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 509 (all X_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_1),bot_bo1181479936a_bool) = X_1) # label(fact_498_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 510 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,bot_bot_bool),X_1)) <-> hBOOL(X_1))) # label(fact_499_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 511 (all X_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,bot_bot_fun_nat_bool),X_1) = X_1) # label(fact_500_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 512 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),X_1) = X_1) # label(fact_501_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 513 (all X_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,bot_bo1181479936a_bool),X_1) = X_1) # label(fact_502_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 514 (all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,bot_bot_fun_nat_bool),B) = B) # label(fact_503_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 515 (all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),B) = B) # label(fact_504_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 516 (all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,bot_bo1181479936a_bool),B) = B) # label(fact_505_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 517 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),bot_bot_fun_nat_bool) = A) # label(fact_506_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 518 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),bot_bo1055319631e_bool) = A) # label(fact_507_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 519 (all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),bot_bo1181479936a_bool) = A) # label(fact_508_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 520 (all A all B (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B) = bot_bot_fun_nat_bool <-> A = bot_bot_fun_nat_bool & B = bot_bot_fun_nat_bool)) # label(fact_509_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 521 (all A all B (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B) = bot_bo1055319631e_bool <-> A = bot_bo1055319631e_bool & B = bot_bo1055319631e_bool)) # label(fact_510_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 522 (all A all B (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B) = bot_bo1181479936a_bool <-> A = bot_bo1181479936a_bool & B = bot_bo1181479936a_bool)) # label(fact_511_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 523 (all F all Ga (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F),Ga))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)))) # label(fact_512_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 524 (all Ga all F (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F),Ga)))))) # label(fact_513_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 525 (all X_22 all Y_18 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_22),Y_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_22)))) # label(fact_514_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 526 (all Z_5 all Y_17 all X_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_21)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),Y_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),X_21))))) # label(fact_515_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 527 (all Y_16 all X_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),X_20)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),Y_16)) -> X_20 = Y_16))) # label(fact_516_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 528 (all Z_4 all X_19 all Y_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_15)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),Z_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Z_4))))) # label(fact_517_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 529 (all X_18 all Y_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_18),Y_14)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_14),X_18)) -> X_18 = Y_14))) # label(fact_518_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 530 (all C_6 all B_9 all A_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_9),A_13)) -> (B_9 = C_6 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_6),A_13))))) # label(fact_519_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 531 (all C_5 all A_12 all B_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_12),B_8)) -> (B_8 = C_5 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_12),C_5))))) # label(fact_520_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 532 (all C_4 all A_11 all B_7 (A_11 = B_7 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_4),B_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_4),A_11))))) # label(fact_521_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 533 (all C_3 all A_10 all B_6 (A_10 = B_6 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_6),C_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),C_3))))) # label(fact_522_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 534 (all Y_7 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_7)) <-> X_1 = Y_7))) # label(fact_523_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 535 (all X_17 all Y_13 (X_17 = Y_13 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_17),Y_13)))) # label(fact_524_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 536 (all X_1 all Y_7 (X_1 = Y_7 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_7)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_1)))) # label(fact_525_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 537 (all X_16 all Y_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Y_12)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_12),X_16)))) # label(fact_526_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 538 (all Pa all Q_1 collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fdisj),Pa)),Q_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,collec268032053iple_a(Pa)),collec268032053iple_a(Q_1))) # label(fact_527_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 539 (all Pa all Q_1 collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),Pa)),Q_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,collect_nat(Pa)),collect_nat(Q_1))) # label(fact_528_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 540 (all X_1 all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B))))) # label(fact_529_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 541 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_530_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 542 (all B all X_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B))))) # label(fact_531_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 543 (all B all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_532_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 544 (all X_1 all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),B))))) # label(fact_533_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 545 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_534_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 546 (all A all Ca all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B))))) # label(fact_535_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 547 (all A all Ca all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B))))) # label(fact_536_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 548 (all B all Ca all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B))))) # label(fact_537_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 549 (all B all Ca all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B))))) # label(fact_538_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 550 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) | hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)))) # label(fact_539_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 551 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)))) # label(fact_540_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 552 (all A all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B) = collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fdisj),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),A))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B)))) # label(fact_541_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 553 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B) = collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B)))) # label(fact_542_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 554 (all R_1 all S (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),R_1)),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),S))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,R_1),S)))) # label(fact_543_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 555 (all R_1 all S (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S)))) # label(fact_544_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 556 (all R_1 all S all X_2 (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),R_1)),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),S)),X_2)) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,R_1),S))))) # label(fact_545_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 557 (all R_1 all S all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S)),X_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,R_1),S))))) # label(fact_546_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 558 (all A_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_1))) # label(fact_547_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 559 (all A_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_1))) # label(fact_548_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 560 (all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A_1))) # label(fact_549_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 561 (all A_1 hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,bot_bo1181479936a_bool),A_1))) # label(fact_550_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 562 (all A_9 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_9))) # label(fact_551_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 563 (all A_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_1),bot_bot_bool)) <-> (hBOOL(A_1) <-> hBOOL(bot_bot_bool)))) # label(fact_552_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 564 (all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool)) <-> A_1 = bot_bot_fun_nat_bool)) # label(fact_553_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 565 (all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),bot_bo1055319631e_bool)) <-> A_1 = bot_bo1055319631e_bool)) # label(fact_554_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 566 (all A_1 (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A_1),bot_bo1181479936a_bool)) <-> A_1 = bot_bo1181479936a_bool)) # label(fact_555_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 567 (all A_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),bot_bot_nat)) <-> A_1 = bot_bot_nat)) # label(fact_556_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 568 (all A_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_1),bot_bot_bool)) -> (hBOOL(A_1) <-> hBOOL(bot_bot_bool)))) # label(fact_557_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 569 (all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool)) -> A_1 = bot_bot_fun_nat_bool)) # label(fact_558_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 570 (all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),bot_bo1055319631e_bool)) -> A_1 = bot_bo1055319631e_bool)) # label(fact_559_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 571 (all A_1 (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A_1),bot_bo1181479936a_bool)) -> A_1 = bot_bo1181479936a_bool)) # label(fact_560_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.81 572 (all A_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),bot_bot_nat)) -> A_8 = bot_bot_nat)) # label(fact_561_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 573 (all A all A_1 all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B))) # label(fact_562_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 574 (all A all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B))) # label(fact_563_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 575 (all A all A_1 all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B))) # label(fact_564_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 576 (all A_1 all B all C hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)),C) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B),C))) # label(fact_565_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 577 (all A_1 all B all C hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)),C) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C))) # label(fact_566_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 578 (all A_1 all B all C hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)),C) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),C))) # label(fact_567_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 579 (all Ts all Ga all Ts_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),Ts_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts))))) # label(fact_568_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 580 (all Ts all Ga all Ts_1 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts_1)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,Ts),Ts_1)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts))))) # label(fact_569_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 581 (all Ts all Ga (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),Ga)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts)))) # label(fact_570_asm) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 582 (all Ts all Ga (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,Ts),Ga)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts)))) # label(fact_571_asm) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 583 (all A_1 all B hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_1))),B)) # label(fact_572_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 584 (all A_1 all B hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,collec727977250_state(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),B)) # label(fact_573_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 585 (all A_1 all B hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,collec268032053iple_a(hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),B)) # label(fact_574_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 586 (all A_1 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)),A)) # label(fact_575_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 587 (all A_1 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)),A)) # label(fact_576_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 588 (all A_1 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)),A)) # label(fact_577_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 589 (all Ba all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(semila972727038up_nat,Ba),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(semila972727038up_nat,Ba),A)))) # label(fact_578_fold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 590 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B) = hAPP_f800510211t_bool(finite1578363458t_bool(insert_nat,B),A))) # label(fact_579_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 591 (all B all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B) = hAPP_f921536533e_bool(finite512563852e_bool(insert1835143293_state,B),A))) # label(fact_580_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 592 (all B all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B) = hAPP_f1591852335a_bool(finite1979045230a_bool(insert873085594iple_a,B),A))) # label(fact_581_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 593 (all A all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) -> A = bot_bot_fun_nat_bool | A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) # label(fact_582_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 594 (all A all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))) -> A = bot_bo1055319631e_bool | A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))) # label(fact_583_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 595 (all A all X_1 (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool))) -> A = bot_bo1181479936a_bool | A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool))) # label(fact_584_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 596 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)))))) # label(fact_585_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 597 (all A all X_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B)))))) # label(fact_586_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 598 (all A all X_1 all B (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool))),B)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),B)))))) # label(fact_587_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 599 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) <-> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))))) # label(fact_588_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 600 (all A all X_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B))) <-> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))),B))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B))))) # label(fact_589_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 601 (all A all X_1 all B (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),B))) <-> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_1),bot_bo1181479936a_bool))),B))) & (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B))))) # label(fact_590_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 602 (all B all A all F_1 all F (hBOOL(finite795500164em_nat(F_1,F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (B != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F_1,hAPP_f22106695ol_nat(F,A)),hAPP_f22106695ol_nat(F,B)))))))) # label(fact_591_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 603 (all B all A all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (B != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,A)),hAPP_f2143211163_state(F,B)))))))) # label(fact_592_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 604 (all B all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,B)) -> (B != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,A)),hAPP_f124283079iple_a(F,B)))))))) # label(fact_593_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 605 (all Ca all Ba all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Ba)))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_fold_nat_nat(semila972727038up_nat,Ca),A)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Ba),Ca)))))) # label(fact_594_fold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 606 (all Pa all A all F (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),A)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all A_7 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_7),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_7),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_7),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F))))))) # label(fact_595_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 607 (all Pa all A all F (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),A)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)) -> ((all A_7 all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_7),A)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_7),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_7),F_2)))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F))))))) # label(fact_596_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 608 (all Pa all A all F (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,F),A)) -> (hBOOL(hAPP_f540970102l_bool(Pa,bot_bo1181479936a_bool)) -> ((all A_7 all F_2 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F_2)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_7),A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_7),F_2)) -> (hBOOL(hAPP_f540970102l_bool(Pa,F_2)) -> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_7),F_2)))))))) -> hBOOL(hAPP_f540970102l_bool(Pa,F))))))) # label(fact_597_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 609 (all B all A ((all X_2 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),B)))) -> hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),B)))) # label(fact_598_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 610 (all B all A ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_599_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 611 (all M_1 all C_2 all S_1 all N_2 all T (hBOOL(evaln(C_2,S_1,N_2,T)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_1)) -> hBOOL(evaln(C_2,S_1,M_1,T))))) # label(fact_600_evaln__nonstrict) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 612 (all K hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K))))) # label(fact_601_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 613 (all A all Ba ((hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),bot_bo1181479936a_bool))) -> hAPP_f124283079iple_a(partia1866111638iple_a(Ba),A) = Ba) & (-hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(ord_le1908022732a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),bot_bo1181479936a_bool))) -> hAPP_f124283079iple_a(partia1866111638iple_a(Ba),A) = hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Ba),bot_bo1181479936a_bool))))))) # label(fact_602_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 614 (all A all Ba ((hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool))) -> hAPP_f22106695ol_nat(partial_flat_lub_nat(Ba),A) = Ba) & (-hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool))) -> hAPP_f22106695ol_nat(partial_flat_lub_nat(Ba),A) = hAPP_f22106695ol_nat(the_nat,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool))))))) # label(fact_603_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 615 (all A all Ba ((hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),bot_bo1055319631e_bool))) -> hAPP_f2143211163_state(partia415982977_state(Ba),A) = Ba) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),bot_bo1055319631e_bool))) -> hAPP_f2143211163_state(partia415982977_state(Ba),A) = hAPP_f2143211163_state(the_Ho10452358_state,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ba),bot_bo1055319631e_bool))))))) # label(fact_604_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 616 (all N (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N)) <-> (exists M all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),M)))))) # label(fact_605_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 617 (all U all F_1 ((all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F_1,N_1)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,ord_less_eq_nat),F_1)),U)))))) # label(fact_606_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 618 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,A) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_1),hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_607_Sup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 619 (all X_1 hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1) # label(fact_608_Sup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 620 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_1),hAPP_f22106695ol_nat(big_la43341705in_nat,A)) = hAPP_f22106695ol_nat(big_la43341705in_nat,A)))) # label(fact_609_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 621 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(big_la43341705in_nat,A) = hAPP_f22106695ol_nat(finite_fold1_nat(semila972727038up_nat),A))) # label(fact_610_Sup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 622 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_1),hAPP_f22106695ol_nat(big_la43341705in_nat,A))))) # label(fact_611_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 623 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_1),hAPP_f22106695ol_nat(big_la43341705in_nat,A)))))) # label(fact_612_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 624 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (B != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_f22106695ol_nat(big_la43341705in_nat,B)),hAPP_f22106695ol_nat(big_la43341705in_nat,A)) = hAPP_f22106695ol_nat(big_la43341705in_nat,A))))) # label(fact_613_Sup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 625 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (B != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_f22106695ol_nat(big_la43341705in_nat,A)),hAPP_f22106695ol_nat(big_la43341705in_nat,B))))))) # label(fact_614_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 626 (all A_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(semila972727038up_nat,A_1),A))) # label(fact_615_Sup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 627 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(semila972727038up_nat,X_1),A)))) # label(fact_616_Sup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 628 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_1),hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_617_Sup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 629 (all N all H ((all X_2 all Y_11 hAPP_nat_nat(H,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_2),Y_11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(H,X_2)),hAPP_nat_nat(H,Y_11))) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N)) -> (N != bot_bot_fun_nat_bool -> hAPP_nat_nat(H,hAPP_f22106695ol_nat(big_la43341705in_nat,N)) = hAPP_f22106695ol_nat(big_la43341705in_nat,image_nat_nat(H,N)))))) # label(fact_618_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 630 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> ((all X_2 all Y_11 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_2),Y_11)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_11),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(big_la43341705in_nat,A)),A)))))) # label(fact_619_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 631 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (B != bot_bot_fun_nat_bool -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_f22106695ol_nat(big_la43341705in_nat,A)),hAPP_f22106695ol_nat(big_la43341705in_nat,B)))))))) # label(fact_620_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 632 (all B all Ca all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B)))))) # label(fact_621_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 633 (all B all Ca all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B)))))) # label(fact_622_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 634 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B))) -> -(hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) -> -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B))))) # label(fact_623_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 635 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_624_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 636 (all Ga all F (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F)) | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,F),Ga))))) # label(fact_625_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 637 (all X_15 all A_6 all B_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_6),B_5))) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),A_6)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),B_5))))) # label(fact_626_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 638 (all B_4 all D all A_5 all C_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_5),C_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_4),D)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_5),B_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,C_1),D)))))) # label(fact_627_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 639 (all Z_3 all X_14 all Y_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Z_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_10),Z_3)))))) # label(fact_628_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 640 (all B_3 all X_13 all A_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),A_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),B_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_4),B_3)))))) # label(fact_629_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 641 (all Y_9 all X_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_12)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_12),Y_9) = Y_9)) # label(fact_630_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 642 (all X_11 all Y_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),Y_8)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_11),Y_8) = X_11)) # label(fact_631_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 643 (all A_3 all B_2 all X_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),X_10)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_3),B_2)),X_10)))) # label(fact_632_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 644 (all B_1 all A_2 all X_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),X_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_2),B_1)),X_9)))) # label(fact_633_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 645 (all X_1 all Y_7 all Z_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_7),Z_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_7)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z_2)))) # label(fact_634_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 646 (all X_1 all Y_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_7)) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_1),Y_7) = X_1)) # label(fact_635_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 647 (all X_8 all Y_6 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_8),Y_6)),Y_6))) # label(fact_636_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 648 (all X_7 all Y_5 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_7),Y_5)),Y_5))) # label(fact_637_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 649 (all X_6 all Y_4 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_6),Y_4)),X_6))) # label(fact_638_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 650 (all X_5 all Y_3 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_5),Y_3)),X_5))) # label(fact_639_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 651 (all X_4 all Y_2 all Z_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_2),Z_1))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_4),Y_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_4),Z_1))))) # label(fact_640_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 652 (all X_3 all Y_1 all Z hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_3),Y_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_3),Z))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_1),Z))))) # label(fact_641_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 653 (all B all A_1 all C (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),C)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)),C) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B),C)))) # label(fact_642_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.82 654 (all B all A_1 all C (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)),C) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C)))) # label(fact_643_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 655 (all B all A_1 all C (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)),C) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,B),C)))) # label(fact_644_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 656 (all B all A_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B)))) # label(fact_645_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 657 (all B all A_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B)))) # label(fact_646_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 658 (all B all A_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B)))) # label(fact_647_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 659 (all B all A_1 all C (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),C)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)),C) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B),C))) # label(fact_648_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 660 (all B all A_1 all C (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)),C) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C))) # label(fact_649_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 661 (all B all A_1 all C (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)),C) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,B),C))) # label(fact_650_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 662 (all B all A_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B))) # label(fact_651_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 663 (all B all A_1 all A (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B))) # label(fact_652_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 664 (all B all A_1 all A (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B))) # label(fact_653_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 665 (all A_1 all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B))) # label(fact_654_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 666 (all A_1 all A all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B))) # label(fact_655_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 667 (all A_1 all A all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B))) # label(fact_656_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 668 (all B all A_1 all C ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),C)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)),C) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B),C))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),C)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)),C) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B),C)))) # label(fact_657_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 669 (all B all A_1 all C ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)),C) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)),C) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C)))) # label(fact_658_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 670 (all B all A_1 all C ((hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)),C) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,B),C))) & (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)),C) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,B),C)))) # label(fact_659_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 671 (all B all A_1 all A ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B)))) # label(fact_660_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 672 (all B all A_1 all A ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B)))) # label(fact_661_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 673 (all B all A_1 all A ((hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B))) & (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B)))) # label(fact_662_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 674 (all R_1 all S all X_2 (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),R_1)),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),S)),X_2)) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,R_1),S))))) # label(fact_663_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 675 (all R_1 all S all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S)),X_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,R_1),S))))) # label(fact_664_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.82 676 (all Pa all Q_1 collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),Pa)),Q_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,collec268032053iple_a(Pa)),collec268032053iple_a(Q_1))) # label(fact_665_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 677 (all Pa all Q_1 collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),Pa)),Q_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,collect_nat(Pa)),collect_nat(Q_1))) # label(fact_666_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 678 (all X_1 all A all Pa (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),collec268032053iple_a(Pa)))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_1),A)) & hBOOL(hAPP_H1421470952a_bool(Pa,X_1)))) # label(fact_667_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 679 (all X_1 all A all Pa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),collect_nat(Pa)))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) & hBOOL(hAPP_nat_bool(Pa,X_1)))) # label(fact_668_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 680 (all A all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B) = collec268032053iple_a(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,fconj),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),A))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B)))) # label(fact_669_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 681 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B) = collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B)))) # label(fact_670_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 682 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)) & hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)))) # label(fact_671_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 683 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)))) # label(fact_672_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 684 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),A)))) # label(fact_673_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 685 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)))) # label(fact_674_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 686 (all Ca all A all B (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Ca),B)))) # label(fact_675_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 687 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)))) # label(fact_676_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 688 (all A all B (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B) = bot_bot_fun_nat_bool <-> (all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),B)) -> X_2 != Xa)))))) # label(fact_677_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 689 (all A all B (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B) = bot_bo1055319631e_bool <-> (all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A)) -> (all Xa (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Xa),B)) -> X_2 != Xa)))))) # label(fact_678_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 690 (all A all B (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B) = bot_bo1181479936a_bool <-> (all X_2 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> (all Xa (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Xa),B)) -> X_2 != Xa)))))) # label(fact_679_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 691 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),bot_bot_fun_nat_bool) = bot_bot_fun_nat_bool) # label(fact_680_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 692 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),bot_bo1055319631e_bool) = bot_bo1055319631e_bool) # label(fact_681_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 693 (all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),bot_bo1181479936a_bool) = bot_bo1181479936a_bool) # label(fact_682_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 694 (all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,bot_bot_fun_nat_bool),B) = bot_bot_fun_nat_bool) # label(fact_683_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 695 (all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),B) = bot_bo1055319631e_bool) # label(fact_684_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 696 (all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,bot_bo1181479936a_bool),B) = bot_bo1181479936a_bool) # label(fact_685_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 697 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,bot_bot_bool),X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_686_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 698 (all X_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,bot_bot_fun_nat_bool),X_1) = bot_bot_fun_nat_bool) # label(fact_687_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 699 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),X_1) = bot_bo1055319631e_bool) # label(fact_688_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 700 (all X_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,bot_bo1181479936a_bool),X_1) = bot_bo1181479936a_bool) # label(fact_689_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 701 (all X_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),bot_bot_bool)) <-> hBOOL(bot_bot_bool))) # label(fact_690_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 702 (all X_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_1),bot_bot_fun_nat_bool) = bot_bot_fun_nat_bool) # label(fact_691_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 703 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),bot_bo1055319631e_bool) = bot_bo1055319631e_bool) # label(fact_692_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 704 (all X_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,X_1),bot_bo1181479936a_bool) = bot_bo1181479936a_bool) # label(fact_693_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 705 (all A all B (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),B) = bot_bot_fun_nat_bool -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = A)) # label(fact_694_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 706 (all A all B (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B) = bot_bo1055319631e_bool -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A),B) = A)) # label(fact_695_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 707 (all A all B (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),B) = bot_bo1181479936a_bool -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,A),B) = A)) # label(fact_696_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 708 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),A)) = bot_bot_fun_nat_bool) # label(fact_697_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 709 (all A all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,B),A)) = bot_bo1055319631e_bool) # label(fact_698_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 710 (all A all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila671163144a_bool,A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(minus_469558085a_bool,B),A)) = bot_bo1181479936a_bool) # label(fact_699_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 711 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 712 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 713 (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].
% 1.59/1.83 714 (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].
% 1.59/1.83 715 (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].
% 1.59/1.83 716 (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].
% 1.59/1.83 717 (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].
% 1.59/1.83 718 (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].
% 1.59/1.83 719 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 720 (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].
% 1.59/1.83 721 (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].
% 1.59/1.83 722 (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].
% 1.59/1.83 723 (all P hAPP_nat_nat(cOMBI_nat,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 724 (all X all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 725 (all X all Y (X != Y | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 726 (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].
% 1.59/1.83 727 (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].
% 1.59/1.83 728 (all P all Q hAPP_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 729 (all P all Q (is_bool(P) -> hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 730 (all P all Q (is_bool(P) -> hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 731 (all X all Y (-hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 732 (all X all Y (X != Y | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 733 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 734 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 735 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 736 (all P all Q hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 737 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f2073279419e_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].
% 1.59/1.83 738 (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].
% 1.59/1.83 739 (all P all Q all R hAPP_state_state(hAPP_n1547241352_state(hAPP_f1848060885_state(cOMBC_1777403949_state,P),Q),R) = hAPP_nat_state(hAPP_s1892499976_state(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Nat__Onat_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 740 (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].
% 1.59/1.83 741 (all P all Q all R hAPP_state_state(hAPP_f871651461_state(hAPP_f851239890_state(cOMBS_777315357_state,P),Q),R) = hAPP_nat_state(hAPP_s1892499976_state(P,R),hAPP_state_nat(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__Nat__Onat_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 742 (all P all Q all R hAPP_state_bool(hAPP_f746301080e_bool(hAPP_f162060345e_bool(cOMBB_844853809_state,P),Q),R) = hAPP_state_bool(P,hAPP_state_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Ostate_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 743 (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].
% 1.59/1.83 744 (all P hAPP_H678412245iple_a(cOMBI_1218222237iple_a,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_U) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 745 (all X all Y (-hBOOL(hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(fequal879838495iple_a,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 746 (all X all Y (X != Y | hBOOL(hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(fequal879838495iple_a,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 747 (all P all Q (is_bool(P) -> hAPP_f54304608l_bool(hAPP_b1630757474l_bool(cOMBK_1994329625t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 748 (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].
% 1.59/1.83 749 (all P hAPP_H563960305_state(cOMBI_1367665338_state,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 750 (all X all Y (-hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 751 (all X all Y (X != Y | hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 752 (all P all Q all R hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 753 (all P all Q hAPP_n178040171iple_a(hAPP_H1450464520iple_a(cOMBK_1505147640_a_nat,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 754 (all P all Q hAPP_H738206399_a_nat(hAPP_n1800114674_a_nat(cOMBK_944981412iple_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 755 (all P all Q (is_bool(P) -> hAPP_H1421470952a_bool(hAPP_b119575286a_bool(cOMBK_151824839iple_a,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 756 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 757 (all P all Q all R hAPP_nat_bool(hAPP_f158894502t_bool(hAPP_f1777703707t_bool(cOMBB_955900739ol_nat,P),Q),R) = hAPP_f54304608l_bool(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 758 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 759 (all P all Q all R hAPP_f54304608l_bool(hAPP_f1246832597l_bool(hAPP_f1164891443l_bool(cOMBB_238756964t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f54304608l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 760 (all P all Q all R hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 761 (all P all Q all R hAPP_f54304608l_bool(hAPP_f1246832597l_bool(hAPP_f1743029098l_bool(cOMBS_1187019125l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1748468828l_bool(P,R),hAPP_f54304608l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 762 (all P all Q all R hAPP_s58564346l_bool(hAPP_f1259673775l_bool(hAPP_f1561913689l_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_004) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 763 (all P all Q all R hAPP_s1892499976_state(hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,P),Q),R) = hAPP_v594194232_state(hAPP_s712361723_state(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ovname_000tc__fun_Itc__Nat__) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 764 (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].
% 1.59/1.83 765 (all P all Q hAPP_H716259088te_nat(hAPP_n436597305te_nat(cOMBK_1950023923_state,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Hoare____Mirabelle____ddpglwnxwg__O_005) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 766 (all X all Y (-hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(fequal1258664663a_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 767 (all X all Y (X != Y | hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(fequal1258664663a_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 768 (all P all Q (is_bool(P) -> hAPP_H513860823e_bool(hAPP_b1245957081e_bool(cOMBK_1079618832_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg___006) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 769 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f34030599a_bool(cOMBB_1799513916iple_a,P),Q),R) = hAPP_bool_bool(P,hAPP_H1421470952a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 770 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1017515220l_bool(P,R),hAPP_H1421470952a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 771 (all X all Y (-hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_007) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 772 (all X all Y (X != Y | hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_008) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 773 (all P all Q all R hAPP_a2036067514e_bool(hAPP_f769584981e_bool(hAPP_f1159960589e_bool(cOMBB_237455441bool_a,P),Q),R) = hAPP_f1759915619e_bool(P,hAPP_a2036067514e_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].
% 1.59/1.83 774 (all P all Q all R hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 775 (all P all Q all R hAPP_a2036067514e_bool(hAPP_f100967412e_bool(hAPP_f1460451647e_bool(cOMBC_524597097e_bool,P),Q),R) = hAPP_f746301080e_bool(hAPP_a1224971408e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__Com__Ostate_J_000t) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 776 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1037965299e_bool(cOMBB_416661851_state,P),Q),R) = hAPP_bool_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel_009) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 777 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 778 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,P),Q),R) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__010) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 779 (all P all Q all R hAPP_f54304608l_bool(hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 780 (all P all Q all R hAPP_f1748468828l_bool(hAPP_f1974927549l_bool(hAPP_f857404385l_bool(cOMBB_444170502t_bool,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f54304608l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 781 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f817621513e_bool(hAPP_f512427579e_bool(cOMBB_572666224_state,P),Q),R) = hAPP_f1759915619e_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_012) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 782 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f1838002347e_bool(hAPP_f1706273077e_bool(cOMBC_867582640e_bool,P),Q),R) = hAPP_f746301080e_bool(hAPP_s286259371e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__Com__Os) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 783 (all P all Q hAPP_H678412245iple_a(hAPP_H1455657330iple_a(cOMBK_1824972302iple_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_013) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 784 (all P all Q all R hAPP_H1017515220l_bool(hAPP_f997599971l_bool(hAPP_f439164429l_bool(cOMBB_1782929690iple_a,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1421470952a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_014) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 785 (all P all Q hAPP_H1600811558iple_a(hAPP_H377435237iple_a(cOMBK_2022976521_state,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_015) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 786 (all P all Q hAPP_H928324994_state(hAPP_H558669354_state(cOMBK_547979437iple_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 787 (all P all Q all R hAPP_a849909144l_bool(hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_a2036067514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_016) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 788 (all P all Q all R hAPP_H226398757l_bool(hAPP_f1558728829l_bool(hAPP_f1442918689l_bool(cOMBB_1382207997_state,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_017) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 789 (all P all Q all R hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,P),Q),R) = hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 790 (all P all Q all R hAPP_f800510211t_bool(hAPP_f1730770594t_bool(hAPP_f1311642927t_bool(cOMBC_646315179t_bool,P),Q),R) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__018) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 791 (all P all Q all R hAPP_f54304608l_bool(hAPP_f1246832597l_bool(hAPP_f1443436725l_bool(cOMBC_1245412066l_bool,P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__019) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 792 (all P all Q hAPP_H563960305_state(hAPP_H521649881_state(cOMBK_690957994_state,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___020) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 793 (all P all Q all R hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(hAPP_f1345202233l_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_021) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 794 (all P all Q all R hAPP_a723219176e_bool(hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,P),Q),R) = hAPP_f167292325e_bool(P,hAPP_a849909144l_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].
% 1.59/1.83 795 (all P all Q all R hAPP_H513860823e_bool(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 796 (all P all Q all R hAPP_a1224971408e_bool(hAPP_f1406200875e_bool(hAPP_f635443597e_bool(cOMBB_2139825703bool_a,P),Q),R) = hAPP_f162060345e_bool(P,hAPP_a2036067514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_022) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 797 (all P all Q all R hAPP_n1512601776t_bool(hAPP_f10625010t_bool(hAPP_f1115950719t_bool(cOMBB_1654519265ol_nat,P),Q),R) = hAPP_f1730770594t_bool(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 798 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f772297704a_bool(hAPP_f390613447a_bool(cOMBB_1501709507iple_a,P),Q),R) = hAPP_f540970102l_bool(P,hAPP_H1190454433a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 799 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,P),Q),R) = hAPP_f540970102l_bool(hAPP_H1840393229l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_023) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 800 (all P all Q all R hAPP_s1874344717e_bool(hAPP_f873506917e_bool(hAPP_f1398071125e_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_024) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 801 (all P all Q all R hAPP_s286259371e_bool(hAPP_f289738463e_bool(hAPP_f1151843515e_bool(cOMBB_1941618714_state,P),Q),R) = hAPP_f162060345e_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_025) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 802 (all P all Q all R hAPP_H513860823e_bool(hAPP_f1456107715e_bool(hAPP_f1548785833e_bool(cOMBB_1653402815_state,P),Q),R) = hAPP_f1760790145l_bool(P,hAPP_H1645666623e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_026) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 803 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___027) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 804 (all P all Q all R hAPP_a1200519163e_bool(hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,P),Q),R) = hAPP_f644196280e_bool(P,hAPP_a849909144l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_028) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 805 (all P all Q all R hAPP_H1190454433a_bool(hAPP_f1665407592a_bool(hAPP_f549683569a_bool(cOMBC_708118077a_bool,P),Q),R) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_029) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 806 (all P all Q all R hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(hAPP_f450029403a_bool(cOMBC_314077933a_bool,P),Q),R) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 807 (all P all Q all R hAPP_H1645666623e_bool(hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___030) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 808 (all P all Q all R hAPP_f921536533e_bool(hAPP_f1583986009e_bool(hAPP_f2049746453e_bool(cOMBC_872426556e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_031) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.83 809 (all P all Q all R hAPP_H1641355846a_bool(hAPP_f485051996a_bool(hAPP_f2085120383a_bool(cOMBB_2080540641iple_a,P),Q),R) = hAPP_f1026156344a_bool(P,hAPP_H1190454433a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_032) # label(axiom) # label(non_clause). [assumption].
% 2.18/2.43 810 (all P all Q all R hAPP_H727730819e_bool(hAPP_f531275309e_bool(hAPP_f1470644835e_bool(cOMBB_946224375_state,P),Q),R) = hAPP_f1583986009e_bool(P,hAPP_H1645666623e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_033) # label(axiom) # label(non_clause). [assumption].
% 2.18/2.43
% 2.18/2.43 ============================== end of process non-clausal formulas ===
% 2.18/2.43
% 2.18/2.43 ============================== PROCESS INITIAL CLAUSES ===============
% 2.18/2.43
% 2.18/2.43 ============================== PREDICATE ELIMINATION =================
% 2.18/2.43
% 2.18/2.43 ============================== end predicate elimination =============
% 2.18/2.43
% 2.18/2.43 Auto_denials: (non-Horn, no changes).
% 2.18/2.43
% 2.18/2.43 Term ordering decisions:
% 2.18/2.43 Function symbol KB weights: bot_bo1181479936a_bool=1. insert873085594iple_a=1. bot_bo1055319631e_bool=1. insert1835143293_state=1. bot_bot_fun_nat_bool=1. member_nat=1. member1713797107iple_a=1. insert_nat=1. finite_finite_nat=1. ord_less_eq_nat=1. member1758697444_state=1. finite1655202547iple_a=1. ord_le1568362934t_bool=1. finite784854244_state=1. minus_2067140911t_bool=1. ord_le1908022732a_bool=1. semila840543986t_bool=1. semila972727038up_nat=1. minus_469558085a_bool=1. ord_le1720872323e_bool=1. bot_bot_bool=1. semila671163144a_bool=1. minus_2076558538e_bool=1. semila465093516t_bool=1. fconj=1. semila1498788770a_bool=1. big_la43341705in_nat=1. semila2145357127e_bool=1. semila80283416nf_nat=1. cOMBC_1552014468l_bool=1. cOMBC_226598744l_bool=1. fdisj=1. cOMBB_1782929690iple_a=1. cOMBS_1148211387l_bool=1. cOMBB_1015721476ol_nat=1. cOMBS_nat_bool_bool=1. fequal879838495iple_a=1. semila447562797e_bool=1. update=1. the_Ho746640593iple_a=1. cOMBC_839220826a_bool=1. fequal1531560888_state=1. fequal_fun_nat_bool=1. fequal_nat=1. times_times_nat=1. fimplies=1. cOMBC_nat_nat_bool=1. semila1168014441p_bool=1. bot_bo1701429464l_bool=1. fNot=1. cOMBB_1382207997_state=1. cOMBB_444170502t_bool=1. cOMBC_1424981238e_bool=1. cOMBC_1693257480l_bool=1. cOMBS_1187019125l_bool=1. cOMBS_1248383340l_bool=1. bot_bot_nat=1. cOMBB_1799513916iple_a=1. cOMBB_188601460_state=1. cOMBB_844853809_state=1. cOMBC_1193272608_state=1. fequal_state=1. insert_fun_nat_bool=1. ord_less_eq_bool=1. fFalse=1. skip=1. cOMBC_231445413l_bool=1. cOMBS_777315357_state=1. cOMBB_1941618714_state=1. cOMBB_2139825703bool_a=1. cOMBC_178881787t_bool=1. cOMBC_488258100e_bool=1. cOMBC_524597097e_bool=1. cOMBC_708118077a_bool=1. cOMBC_764456866l_bool=1. cOMBC_867582640e_bool=1. cOMBK_1505147640_a_nat=1. cOMBK_1824972302iple_a=1. cOMBK_2022976521_state=1. cOMBK_547979437iple_a=1. cOMBK_690957994_state=1. cOMBK_944981412iple_a=1. cOMBK_nat_nat=1. semila310582991f_bool=1. cOMBB_1348041619bool_a=1. cOMBB_1355796797bool_a=1. cOMBB_1654519265ol_nat=1. cOMBB_1757942702_state=1. cOMBB_1759179140_state=1. cOMBB_2080540641iple_a=1. cOMBB_946224375_state=1. cOMBB_bool_bool_nat=1. cOMBC_1245412066l_bool=1. cOMBC_1777403949_state=1. cOMBC_2027030106e_bool=1. cOMBC_314077933a_bool=1. cOMBC_41962815e_bool=1. cOMBC_471052088e_bool=1. cOMBC_646315179t_bool=1. cOMBC_872426556e_bool=1. cOMBK_1458035955bool_a=1. cOMBK_631994958_state=1. cOMBS_1378840469l_bool=1. fequal1258664663a_bool=1. fequal1746921144e_bool=1. cOMBB_1501709507iple_a=1. cOMBB_1653402815_state=1. cOMBB_237455441bool_a=1. cOMBB_238756964t_bool=1. cOMBB_416661851_state=1. cOMBB_572666224_state=1. cOMBB_800536526ol_nat=1. cOMBB_955900739ol_nat=1. cOMBI_1218222237iple_a=1. cOMBI_1367665338_state=1. cOMBI_nat=1. cOMBK_1079618832_state=1. cOMBK_151824839iple_a=1. cOMBK_1950023923_state=1. cOMBK_1994329625t_bool=1. cOMBK_bool_nat=1. fTrue=1. member_fun_nat_bool=1. the_Ho10452358_state=1. the_el1436340927iple_a=1. the_el23965208_state=1. the_elem_nat=1. the_nat=1. cOMBB_145932198bool_a=1. cOMBB_160679318_state=1. cOMBC_892787026e_bool=1. cOMBK_bool_state=1. finite2012431853t_bool=1. glb_1=1. loc_1=1. b=1. c=1. g=1. p=1. hAPP_f54304608l_bool=1. hAPP_f540970102l_bool=1. hAPP_f1591852335a_bool=1. hAPP_f800510211t_bool=1. hAPP_f921536533e_bool=1. hAPP_f1760790145l_bool=1. hAPP_H1641355846a_bool=1. hAPP_H727730819e_bool=1. hAPP_n1512601776t_bool=1. hAPP_n215258509l_bool=1. hAPP_H1840393229l_bool=1. hAPP_nat_bool=1. hAPP_f1730770594t_bool=1. hAPP_n1699378549t_bool=1. hAPP_f1026156344a_bool=1. hAPP_H1421470952a_bool=1. hAPP_H248360617l_bool=1. hAPP_nat_nat=1. hAPP_f1583986009e_bool=1. hAPP_nat_fun_nat_nat=1. hAPP_f22106695ol_nat=1. hAPP_f103356543l_bool=1. hAPP_state_bool=1. hAPP_f430043647l_bool=1. hAPP_s1806633685e_bool=1. hAPP_f124283079iple_a=1. hAPP_H513860823e_bool=1. hAPP_f854625363l_bool=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. hAPP_f2143211163_state=1. hAPP_H678412245iple_a=1. hAPP_a2036067514e_bool=1. hAPP_H1190454433a_bool=1. hAPP_f1722879237t_bool=1. hAPP_f672239281a_bool=1. hAPP_H1455657330iple_a=1. hAPP_H563960305_state=1. hAPP_f1203760810a_bool=1. hAPP_f1246832597l_bool=1. hAPP_f439164429l_bool=1. hAPP_f997599971l_bool=1. hAPP_f1080886329l_bool=1. hAPP_f1146629647l_bool=1. hAPP_f561022312t_bool=1. image_1782127643iple_a=1. hAPP_H1645666623e_bool=1. image_129517430iple_a=1. image_1604514514_state=1. image_194810223_a_nat=1. hAPP_nat_state=1. semi=1. hAPP_H521649881_state=1. hAPP_f1371755681a_bool=1. hAPP_s712361723_state=1. hAPP_v594194232_state=1. image_306007685iple_a=1. ass=1. image_nat_nat=1. finite1537818352iple_a=1. image_650584225_state=1. finite1669978781iple_a=1. finite9525415_state=1. finite988810631ne_nat=1. finite_fold1Set_nat=1. finite_fold_nat_nat=1. hAPP_f229349961t_bool=1. finite774711482_state=1. hAPP_state_nat=1. hAPP_f1442918689l_bool=1. hAPP_f1558728829l_bool=1. hAPP_f1743029098l_bool=1. hAPP_f1974927549l_bool=1. hAPP_f262880489e_bool=1. hAPP_f643944041l_bool=1. hAPP_f760664097e_bool=1. hAPP_f857404385l_bool=1. hAPP_n178040171iple_a=1. finite795500164em_nat=1. finite950012314iple_a=1. hAPP_H1600811558iple_a=1. hAPP_H738206399_a_nat=1. hAPP_H928324994_state=1. hAPP_f1542232213_state=1. hAPP_f1561913689l_bool=1. hAPP_f34030599a_bool=1. hAPP_f633452666l_bool=1. hAPP_v365393659_state=1. finite506823037_state=1. getlocs=1. finite978536264iple_a=1. hAPP_f1259673775l_bool=1. hAPP_f1759915619e_bool=1. hAPP_f817621513e_bool=1. hAPP_f851239890_state=1. hAPP_f871651461_state=1. hAPP_H1450464520iple_a=1. hAPP_H377435237iple_a=1. hAPP_H558669354_state=1. hAPP_H716259088te_nat=1. hAPP_b2019457360e_bool=1. hAPP_f100967412e_bool=1. hAPP_f1151843515e_bool=1. hAPP_f1262649863e_bool=1. hAPP_f1406200875e_bool=1. hAPP_f1460451647e_bool=1. hAPP_f1570313510t_bool=1. hAPP_f1665407592a_bool=1. hAPP_f1706273077e_bool=1. hAPP_f1838002347e_bool=1. hAPP_f289738463e_bool=1. hAPP_f549683569a_bool=1. hAPP_f635443597e_bool=1. hAPP_f644196280e_bool=1. hAPP_f688831301t_bool=1. hAPP_f762269719e_bool=1. hAPP_f762886889e_bool=1. hAPP_f964290431e_bool=1. hAPP_n1800114674_a_nat=1. image_1410872416te_nat=1. hAPP_a849909144l_bool=1. hAPP_b1095269219e_bool=1. hAPP_b540892988e_bool=1. hAPP_f1006724181e_bool=1. hAPP_f10625010t_bool=1. hAPP_f1115950719t_bool=1. hAPP_f1178339559l_bool=1. hAPP_f1283379615l_bool=1. hAPP_f1311642927t_bool=1. hAPP_f1345202233l_bool=1. hAPP_f1398071125e_bool=1. hAPP_f1443436725l_bool=1. hAPP_f1470644835e_bool=1. hAPP_f1509969235l_bool=1. hAPP_f162060345e_bool=1. hAPP_f1637334154l_bool=1. hAPP_f167292325e_bool=1. hAPP_f1824947087e_bool=1. hAPP_f1848060885_state=1. hAPP_f1863945078e_bool=1. hAPP_f2049746453e_bool=1. hAPP_f2085120383a_bool=1. hAPP_f340725611e_bool=1. hAPP_f450029403a_bool=1. hAPP_f485051996a_bool=1. hAPP_f531275309e_bool=1. hAPP_f701449317e_bool=1. hAPP_f746301080e_bool=1. hAPP_f873506917e_bool=1. hAPP_f894608603t_bool=1. hAPP_n1126952044_state=1. hAPP_n1547241352_state=1. hAPP_s1892499976_state=1. hAPP_s58564346l_bool=1. hAPP_state_state=1. image_1821565372_state=1. big_se275732192ig_nat=1. finite1578363458t_bool=1. finite1979045230a_bool=1. finite202520804_state=1. finite512563852e_bool=1. hAPP_H1017515220l_bool=1. hAPP_H226398757l_bool=1. hAPP_a1200519163e_bool=1. hAPP_a1224971408e_bool=1. hAPP_a723219176e_bool=1. hAPP_b1013836512t_bool=1. hAPP_b119575286a_bool=1. hAPP_b1245957081e_bool=1. hAPP_b1630757474l_bool=1. hAPP_f1037965299e_bool=1. hAPP_f1159960589e_bool=1. hAPP_f1164891443l_bool=1. hAPP_f1456107715e_bool=1. hAPP_f1505651103t_bool=1. hAPP_f1548785833e_bool=1. hAPP_f158894502t_bool=1. hAPP_f1748468828l_bool=1. hAPP_f1777703707t_bool=1. hAPP_f390613447a_bool=1. hAPP_f512427579e_bool=1. hAPP_f618557131t_bool=1. hAPP_f769584981e_bool=1. hAPP_f772297704a_bool=1. hAPP_n1006566506l_bool=1. hAPP_n436597305te_nat=1. hAPP_s1874344717e_bool=1. hAPP_s2001034685l_bool=1. hAPP_s286259371e_bool=1. hAPP_f1261923407e_bool=1. hAPP_f1951378235l_bool=1. hAPP_f2073279419e_bool=1. hAPP_f375255701e_bool=1. hAPP_f963367678e_bool=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f67=1. f68=1. f70=1. f108=1. f109=1. f110=1. f111=1. f112=1. f113=1. f114=1. f115=1. f116=1. f124=1. f125=1. f126=1. f127=1. f128=1. f129=1. f130=1. f131=1. f132=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f158=1. f159=1. f161=1. f162=1. f163=1. f164=1. f167=1. f168=1. f169=1. f170=1. f171=1. f172=1. hoare_606018542rivs_a=1. hoare_659004819_state=1. collect_nat=1. collec268032053iple_a=1. evalc=1. loc=1. collec727977250_state=1. collect_fun_nat_bool=1. finite_fold1_nat=1. finite1200705745iple_a=1. glb=1. finite1382394752iple_a=1. hoare_560051114alid_a=1. hoare_592710359_state=1. finite1317819144e_bool=1. finite1956789438t_bool=1. finite419198954a_bool=1. finite1346402327_state=1. partia1866111638iple_a=1. partia415982977_state=1. partial_flat_lub_nat=1. hoare_Mirabelle_MGT=1. undefined_glb=1. undefined_loc=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f45=1. f46=1. f47=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f117=1. f118=1. f119=1. f120=1. f121=1. f122=1. f133=1. f134=1. f149=1. f150=1. f160=1. f165=1. f166=1. hoare_1575745797_state=1. hoare_1760757500iple_a=1. finite2010942150iple_a=1. local=1. finite929467206at_nat=1. finite1935632226_state=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f69=1. f71=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f123=1. f151=1. f152=1. f153=1. f154=1. f155=1. f156=1. f157=1. evaln=1. f1=1. f2=1. f3=1. f4=1. f48=1. f49=1. f51=1. f52=1. f74=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f92=1. f93=1. f94=1. f96=1. f97=1. f98=1. f99=1. f100=1. f101=1. f135=1. f136=1. f137=1. f138=1. f139=1. f140=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f72=1. f75=1. f147=1. f148=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f50=1. f53=1. f73=1. f95=1.
% 8.76/9.01
% 8.76/9.01 ============================== end of process initial clauses ========
% 8.76/9.01
% 8.76/9.01 ============================== CLAUSES FOR SEARCH ====================
% 8.76/9.01
% 8.76/9.01 ============================== end of clauses for search =============
% 8.76/9.01
% 8.76/9.01 ============================== SEARCH ================================
% 8.76/9.01
% 8.76/9.01 % Starting search at 0.77 seconds.
% 8.76/9.01
% 8.76/9.01 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 1.70 sec).
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=38.000, iters=3340
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=37.000, iters=3383
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=36.000, iters=3419
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=34.000, iters=3350
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=33.000, iters=3366
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=32.000, iters=3344
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=31.000, iters=3373
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=30.000, iters=3410
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=29.000, iters=3612
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=28.000, iters=3877
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=26.000, iters=3470
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=24.000, iters=3336
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=23.000, iters=3476
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=22.000, iters=3358
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=21.000, iters=3347
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=20.000, iters=3397
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=19.000, iters=3359
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=18.000, iters=3341
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=17.000, iters=3339
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=16.000, iters=3354
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=15.000, iters=3346
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=14.000, iters=3362
% 8.76/9.01
% 8.76/9.01 Low Water (keep): wt=13.000, iters=3341
% 8.76/9.01
% 8.76/9.01 Low Water (displace): id=3704, wt=84.000
% 8.76/9.01
% 8.76/9.01 Low Water (displace): id=3740, wt=82.000
% 8.76/9.01
% 8.76/9.01 Low Water (displace): id=3272, wt=80.000
% 8.76/9.01
% 8.76/9.01 Low Water (displace): id=3815, wt=79.000
% 8.76/9.01
% 8.76/9.01 Low Water (displace): id=3851, wt=76Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------