TSTP Solution File: SWW472+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW472+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 01:17:08 EDT 2022
% Result : Timeout 300.03s 300.23s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SWW472+3 : TPTP v8.1.0. Released v5.3.0.
% 0.09/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.37 % Computer : n017.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Mon Jun 6 06:13:16 EDT 2022
% 0.14/0.37 % CPUTime :
% 1.58/1.95 ============================== Prover9 ===============================
% 1.58/1.95 Prover9 (32) version 2009-11A, November 2009.
% 1.58/1.95 Process 24706 was started by sandbox2 on n017.cluster.edu,
% 1.58/1.95 Mon Jun 6 06:13:17 2022
% 1.58/1.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24553_n017.cluster.edu".
% 1.58/1.95 ============================== end of head ===========================
% 1.58/1.95
% 1.58/1.95 ============================== INPUT =================================
% 1.58/1.95
% 1.58/1.95 % Reading from file /tmp/Prover9_24553_n017.cluster.edu
% 1.58/1.95
% 1.58/1.95 set(prolog_style_variables).
% 1.58/1.95 set(auto2).
% 1.58/1.95 % set(auto2) -> set(auto).
% 1.58/1.95 % set(auto) -> set(auto_inference).
% 1.58/1.95 % set(auto) -> set(auto_setup).
% 1.58/1.95 % set(auto_setup) -> set(predicate_elim).
% 1.58/1.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.58/1.95 % set(auto) -> set(auto_limits).
% 1.58/1.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.58/1.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.58/1.95 % set(auto) -> set(auto_denials).
% 1.58/1.95 % set(auto) -> set(auto_process).
% 1.58/1.95 % set(auto2) -> assign(new_constants, 1).
% 1.58/1.95 % set(auto2) -> assign(fold_denial_max, 3).
% 1.58/1.95 % set(auto2) -> assign(max_weight, "200.000").
% 1.58/1.95 % set(auto2) -> assign(max_hours, 1).
% 1.58/1.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.58/1.95 % set(auto2) -> assign(max_seconds, 0).
% 1.58/1.95 % set(auto2) -> assign(max_minutes, 5).
% 1.58/1.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.58/1.95 % set(auto2) -> set(sort_initial_sos).
% 1.58/1.95 % set(auto2) -> assign(sos_limit, -1).
% 1.58/1.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.58/1.95 % set(auto2) -> assign(max_megs, 400).
% 1.58/1.95 % set(auto2) -> assign(stats, some).
% 1.58/1.95 % set(auto2) -> clear(echo_input).
% 1.58/1.95 % set(auto2) -> set(quiet).
% 1.58/1.95 % set(auto2) -> clear(print_initial_clauses).
% 1.58/1.95 % set(auto2) -> clear(print_given).
% 1.58/1.95 assign(lrs_ticks,-1).
% 1.58/1.95 assign(sos_limit,10000).
% 1.58/1.95 assign(order,kbo).
% 1.58/1.95 set(lex_order_vars).
% 1.58/1.95 clear(print_given).
% 1.58/1.95
% 1.58/1.95 % formulas(sos). % not echoed (1270 formulas)
% 1.58/1.95
% 1.58/1.95 ============================== end of input ==========================
% 1.58/1.95
% 1.58/1.95 % From the command line: assign(max_seconds, 300).
% 1.58/1.95
% 1.58/1.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.58/1.95
% 1.58/1.95 % Formulas that are not ordinary clauses:
% 1.58/1.95 1 (all B_1_1 all B_2_1 is_bool(big_se1212619424_state(B_1_1,B_2_1))) # label(gsy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 2 (all B_1_1 all B_2_1 is_bool(big_se913005884ig_int(B_1_1,B_2_1))) # label(gsy_c_Big__Operators_Osemilattice__big_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 3 (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].
% 1.58/1.95 4 (all B_1_1 is_bool(finite1720675051_state(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 5 (all B_1_1 is_bool(finite1973466193nt_int(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Int__Oint_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 6 (all B_1_1 is_bool(finite2130160977at_nat(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Nat__Onat_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 7 (all B_1_1 is_bool(finite2036162504e_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otri) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 8 (all B_1_1 is_bool(finite58652534t_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mt) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 9 (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].
% 1.58/1.95 10 (all B_1_1 all B_2_1 is_bool(finite683959609_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 11 (all B_1_1 all B_2_1 is_bool(finite1626084323ne_int(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 12 (all B_1_1 all B_2_1 is_bool(finite988810631ne_nat(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 13 (all B_1_1 all B_2_1 is_bool(finite416071164_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 14 (all B_1_1 all B_2_1 is_bool(finite1432773856em_int(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 15 (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].
% 1.58/1.95 16 (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].
% 1.58/1.95 17 (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].
% 1.58/1.95 18 (all B_1_1 all B_2_1 is_bool(hAPP_H242767318e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 19 (all B_1_1 all B_2_1 is_bool(hAPP_int_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 20 (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].
% 1.58/1.95 21 (all B_1_1 all B_2_1 is_bool(hAPP_f1378282496l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O) # label(hypothesis) # label(non_clause). [assumption].
% 1.58/1.95 22 (all B_1_1 all B_2_1 is_bool(hAPP_f448129468l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 23 (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].
% 1.58/1.95 24 (all B_1_1 all B_2_1 is_bool(hAPP_f1410040974l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 25 (all G_1 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),bot_bo784226126e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 26 (all Fun1_2 all Com_1 all Fun2_2 all Fun1_1 all Com all Fun2_1 (hoare_1191504582_state(Fun1_2,Com_1,Fun2_2) = hoare_1191504582_state(Fun1_1,Com,Fun2_1) <-> Fun1_2 = Fun1_1 & Com_1 = Com & Fun2_2 = Fun2_1)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 27 (all G_1 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) -> hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(G_1),Ts)))) # label(fact_2_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 28 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),G_2)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts))))) # label(fact_3_cut) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 29 (all Ts all G_1 all T_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts)))))) # label(fact_4_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 30 (all G_1 all T_1 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool))) & hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)))) # label(fact_5_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 31 (all Qa all G_1 all Pa all Ca all Q_4 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Q_4)),bot_bo784226126e_bool))) -> ((all Z_13 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_4,Z_13),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_13),S_1)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool)))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 32 (all Pa all G_1 all P_1 all Ca all Qa (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(P_1,Ca,Qa)),bot_bo784226126e_bool))) -> ((all Z_13 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_13),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_13),S_1)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool)))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 33 (all A_1 all B_2 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),A_2))) -> (A_1 != B_2 -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2))))) # label(fact_8_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 34 (all A_1 all B_2 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),A_2))) -> (A_1 != B_2 -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2))))) # label(fact_9_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 35 (all A_1 all B_2 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),A_2))) -> (A_1 != B_2 -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2))))) # label(fact_10_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 36 (all B_2 all A_1 all B_29 ((-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_29)) -> A_1 = B_2) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),B_29))))) # label(fact_11_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 37 (all B_2 all A_1 all B_29 ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_29)) -> A_1 = B_2) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),B_29))))) # label(fact_12_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 38 (all B_2 all A_1 all B_29 ((-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_29)) -> A_1 = B_2) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),B_29))))) # label(fact_13_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 39 (all Qa all Pa all G_1 all P_1 all Ca all Q_4 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(P_1,Ca,Q_4)),bot_bo784226126e_bool))) -> ((all Z_13 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_13),S_1)) -> (all S_2 ((all Z_14 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_14),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_4,Z_14),S_2)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_13),S_2)))))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool)))))) # label(fact_14_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 40 (all A_1 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),bot_bot_fun_int_bool))) # label(fact_15_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 41 (all A_1 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),bot_bot_fun_nat_bool))) # label(fact_16_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 42 (all A_1 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),bot_bo784226126e_bool))) # label(fact_17_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 43 (all A_1 all A_2 bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)) # label(fact_18_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 44 (all A_1 all A_2 bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)) # label(fact_19_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 45 (all A_1 all A_2 bot_bo784226126e_bool != hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2)) # label(fact_20_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 46 (all A_1 all A_2 hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2) != bot_bot_fun_int_bool) # label(fact_21_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 47 (all A_1 all A_2 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2) != bot_bot_fun_nat_bool) # label(fact_22_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 48 (all A_1 all A_2 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2) != bot_bo784226126e_bool) # label(fact_23_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 49 (all B_2 all A_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))) <-> B_2 = A_1)) # label(fact_24_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 50 (all B_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) <-> B_2 = A_1)) # label(fact_25_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 51 (all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))) <-> B_2 = A_1)) # label(fact_26_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 52 (all A_1 all B_2 all Ca all D_1 (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ca),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,D_1),bot_bot_fun_int_bool)) <-> A_1 = Ca & B_2 = D_1 | A_1 = D_1 & B_2 = Ca)) # label(fact_27_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 53 (all A_1 all B_2 all Ca all D_1 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_1),bot_bot_fun_nat_bool)) <-> A_1 = Ca & B_2 = D_1 | A_1 = D_1 & B_2 = Ca)) # label(fact_28_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 54 (all A_1 all B_2 all Ca all D_1 (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),bot_bo784226126e_bool)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Ca),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,D_1),bot_bo784226126e_bool)) <-> A_1 = Ca & B_2 = D_1 | A_1 = D_1 & B_2 = Ca)) # label(fact_29_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 55 (all A_1 all A_2 (A_2 = bot_bot_fun_int_bool -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)))) # label(fact_30_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 56 (all A_1 all A_2 (A_2 = bot_bot_fun_nat_bool -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)))) # label(fact_31_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 57 (all A_1 all A_2 (A_2 = bot_bo784226126e_bool -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)))) # label(fact_32_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 58 (all Pa (hAPP_f1805168059t_bool(collect_int,Pa) = bot_bot_fun_int_bool <-> (all X_2 -hBOOL(hAPP_int_bool(Pa,X_2))))) # label(fact_33_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 59 (all Pa (hAPP_f800510211t_bool(collect_nat,Pa) = bot_bot_fun_nat_bool <-> (all X_2 -hBOOL(hAPP_nat_bool(Pa,X_2))))) # label(fact_34_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 60 (all Pa (hAPP_f806699093e_bool(collec637225377_state,Pa) = bot_bo784226126e_bool <-> (all X_2 -hBOOL(hAPP_H242767318e_bool(Pa,X_2))))) # label(fact_35_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 61 (all Ca -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),bot_bot_fun_int_bool))) # label(fact_36_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 62 (all Ca -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_37_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 63 (all Ca -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),bot_bo784226126e_bool))) # label(fact_38_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 64 (all Pa (bot_bot_fun_int_bool = hAPP_f1805168059t_bool(collect_int,Pa) <-> (all X_2 -hBOOL(hAPP_int_bool(Pa,X_2))))) # label(fact_39_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 65 (all Pa (bot_bot_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,Pa) <-> (all X_2 -hBOOL(hAPP_nat_bool(Pa,X_2))))) # label(fact_40_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 66 (all Pa (bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,Pa) <-> (all X_2 -hBOOL(hAPP_H242767318e_bool(Pa,X_2))))) # label(fact_41_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 67 (all A_2 ((exists X_2 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_2))) <-> A_2 != bot_bot_fun_int_bool)) # label(fact_42_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 68 (all A_2 ((exists X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))) <-> A_2 != bot_bot_fun_nat_bool)) # label(fact_43_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 69 (all A_2 ((exists X_2 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_2))) <-> A_2 != bot_bo784226126e_bool)) # label(fact_44_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 70 (all A_2 ((all X_2 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_2))) <-> A_2 = bot_bot_fun_int_bool)) # label(fact_45_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 71 (all A_2 ((all X_2 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))) <-> A_2 = bot_bot_fun_nat_bool)) # label(fact_46_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 72 (all A_2 ((all X_2 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_2))) <-> A_2 = bot_bo784226126e_bool)) # label(fact_47_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 73 (all A_1 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2) = A_2)) # label(fact_51_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 74 (all A_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2) = A_2)) # label(fact_52_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 75 (all A_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2) = A_2)) # label(fact_53_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 76 (all B_2 all A_1 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_29)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),B_29))))) # label(fact_54_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 77 (all B_2 all A_1 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_29)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),B_29))))) # label(fact_55_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 78 (all B_2 all A_1 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_29)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),B_29))))) # label(fact_56_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 79 (all B_29 all X_1 all A_2 (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) -> (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29) <-> A_2 = B_29)))) # label(fact_57_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 80 (all B_29 all X_1 all A_2 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) -> (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29) <-> A_2 = B_29)))) # label(fact_58_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 81 (all B_29 all X_1 all A_2 (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) -> (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29) <-> A_2 = B_29)))) # label(fact_59_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 82 (all Y_1 all A_2 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),A_2),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_int_bool(A_2,X_1)))) # label(fact_60_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 83 (all Y_1 all A_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_2),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_nat_bool(A_2,X_1)))) # label(fact_61_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 84 (all Y_1 all A_2 all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_2),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_H242767318e_bool(A_2,X_1)))) # label(fact_62_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 85 (all A_1 all B_2 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),A_2))) <-> A_1 = B_2 | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)))) # label(fact_63_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 86 (all A_1 all B_2 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),A_2))) <-> A_1 = B_2 | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)))) # label(fact_64_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 87 (all A_1 all B_2 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),A_2))) <-> A_1 = B_2 | hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)))) # label(fact_65_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 88 (all X_1 all Y_1 all A_2 hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2))) # label(fact_66_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 89 (all X_1 all Y_1 all A_2 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2))) # label(fact_67_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 90 (all X_1 all Y_1 all A_2 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2))) # label(fact_68_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 91 (all X_1 all A_2 hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) # label(fact_69_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 92 (all X_1 all A_2 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) # label(fact_70_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 93 (all X_1 all A_2 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) # label(fact_71_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 94 (all A_1 all Pa hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(collect_int,Pa)) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(cOMBS_int_bool_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(fimplies),hAPP_f1805168059t_bool(cOMBB_bool_bool_int(fNot),hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_1)))),Pa))) # label(fact_72_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 95 (all A_1 all Pa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(collect_nat,Pa)) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fimplies),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1)))),Pa))) # label(fact_73_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 96 (all A_1 all Pa hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(collec637225377_state,Pa)) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(cOMBS_865875691l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(fimplies),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_H216526335e_bool(cOMBC_1967329268e_bool(fequal1440809015_state),A_1)))),Pa))) # label(fact_74_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 97 (all A_1 all B_29 hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(cOMBS_int_bool_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(fdisj),hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_1))),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B_29)))) # label(fact_75_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 98 (all A_1 all B_29 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_29)))) # label(fact_76_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 99 (all A_1 all B_29 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(cOMBS_865875691l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(cOMBC_1967329268e_bool(fequal1440809015_state),A_1))),hAPP_f806699093e_bool(cOMBC_538205282l_bool(member1667945571_state),B_29)))) # label(fact_77_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 100 (all A_1 all B_29 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29)))) # label(fact_78_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 101 (all A_1 all B_29 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29)))) # label(fact_79_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 102 (all A_1 all B_29 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29)))) # label(fact_80_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 103 (all A_1 all B_2 (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),bot_bot_fun_int_bool) -> A_1 = B_2)) # label(fact_81_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 104 (all A_1 all B_2 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),bot_bot_fun_nat_bool) -> A_1 = B_2)) # label(fact_82_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 105 (all A_1 all B_2 (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),bot_bo784226126e_bool) -> A_1 = B_2)) # label(fact_83_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 106 (all B_2 all A_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))) -> B_2 = A_1)) # label(fact_84_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 107 (all B_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) -> B_2 = A_1)) # label(fact_85_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 108 (all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))) -> B_2 = A_1)) # label(fact_86_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 109 (all X_1 hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1) # label(fact_87_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 110 (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_88_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 111 (all X_1 hAPP_f718417177_state(the_el2080696983_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1) # label(fact_89_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 112 (all X_1 (hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_90_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 113 (all X_1 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_91_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 114 (all X_1 (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_92_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 115 (all X_2 (hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_93_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 116 (all X_2 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_94_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 117 (all X_2 (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_95_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 118 (all G_1 all Pa hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,skip,Pa)),bot_bo784226126e_bool)))) # label(fact_96_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 119 (all D_1 all R_3 all G_1 all Pa all Ca all Qa (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Qa,D_1,R_3)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,semi(Ca,D_1),R_3)),bot_bo784226126e_bool)))))) # label(fact_97_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 120 (all Y_1 -(all Fun1 all Com_2 all Fun2 Y_1 != hoare_1191504582_state(Fun1,Com_2,Fun2))) # label(fact_98_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 121 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> -(all B_46 (A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_46) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_46)))))) # label(fact_99_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 122 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> -(all B_46 (A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_46) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_46)))))) # label(fact_100_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 123 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> -(all B_46 (A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_46) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_46)))))) # label(fact_101_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 124 (all A_1 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> (exists B_46 (A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_46) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_46)))))) # label(fact_102_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 125 (all A_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> (exists B_46 (A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_46) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_46)))))) # label(fact_103_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 126 (all A_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) -> (exists B_46 (A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_46) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_46)))))) # label(fact_104_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 127 (all A_2 ((all Y_5 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_5),A_2))) -> A_2 = bot_bot_fun_int_bool)) # label(fact_105_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 128 (all A_2 ((all Y_5 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_5),A_2))) -> A_2 = bot_bot_fun_nat_bool)) # label(fact_106_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 129 (all A_2 ((all Y_5 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_5),A_2))) -> A_2 = bot_bo784226126e_bool)) # label(fact_107_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 130 (all Qa all G_1 all Ca all Pa ((all Z_13 all S_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_13),S_1)) -> (exists P_2 exists Q_3 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(P_2,Ca,Q_3)),bot_bo784226126e_bool))) & (all S_2 ((all Z_14 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_14),S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_14),S_2)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_13),S_2)))))))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hoare_1191504582_state(Pa,Ca,Qa)),bot_bo784226126e_bool))))) # label(fact_108_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 131 (all A_2 (A_2 != bot_bot_fun_int_bool <-> (exists X_2 exists B_46 (A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),B_46) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_46)))))) # label(fact_109_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 132 (all A_2 (A_2 != bot_bot_fun_nat_bool <-> (exists X_2 exists B_46 (A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_46) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_46)))))) # label(fact_110_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 133 (all A_2 (A_2 != bot_bo784226126e_bool <-> (exists X_2 exists B_46 (A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_46) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_46)))))) # label(fact_111_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 134 (all X_2 (hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),bot_bot_fun_int_bool)))) # label(fact_112_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 135 (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_113_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.95 136 (all X_2 (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),bot_bo784226126e_bool)))) # label(fact_114_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 137 (all Com1_3 all Com2_3 semi(Com1_3,Com2_3) != skip) # label(fact_115_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 138 (all Com1_3 all Com2_3 skip != semi(Com1_3,Com2_3)) # label(fact_116_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 139 (all Com1 all Com2 all Com1_1 all Com2_1 (semi(Com1,Com2) = semi(Com1_1,Com2_1) <-> Com1 = Com1_1 & Com2 = Com2_1)) # label(fact_117_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 140 (all F all A_1 all B_2 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)),B_2)) <-> A_1 = B_2)) # label(fact_118_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 141 (all F all A_1 all B_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)),B_2)) <-> A_1 = B_2)) # label(fact_119_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 142 (all F all A_1 all B_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)),B_2)) <-> A_1 = B_2)) # label(fact_120_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 143 (all X_1 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1)) # label(fact_121_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 144 (all X_1 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1)) # label(fact_122_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 145 (all X_1 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1)) # label(fact_123_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 146 (all F all A_1 hAPP_f1594865479ol_int(finite_fold1_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)) = A_1) # label(fact_124_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 147 (all F all A_1 hAPP_f22106695ol_nat(finite_fold1_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) = A_1) # label(fact_125_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 148 (all F all A_1 hAPP_f718417177_state(finite1255650454_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)) = A_1) # label(fact_126_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 149 (all A_1 all G all F (G = finite_fold1_int(F) -> hAPP_f1594865479ol_int(G,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)) = A_1)) # label(fact_127_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 150 (all A_1 all G all F (G = finite_fold1_nat(F) -> hAPP_f22106695ol_nat(G,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)) = A_1)) # label(fact_128_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 151 (all A_1 all G all F (G = finite1255650454_state(F) -> hAPP_f718417177_state(G,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool)) = A_1)) # label(fact_129_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 152 (all F all X_1 -hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),bot_bot_fun_int_bool),X_1))) # label(fact_130_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 153 (all F all X_1 -hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),bot_bot_fun_nat_bool),X_1))) # label(fact_131_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 154 (all F all X_1 -hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),bot_bo784226126e_bool),X_1))) # label(fact_132_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 155 (all F all A_2 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),A_2),X_1)) -> A_2 != bot_bot_fun_int_bool)) # label(fact_133_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 156 (all F all A_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),A_2),X_1)) -> A_2 != bot_bot_fun_nat_bool)) # label(fact_134_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 157 (all F all A_2 all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),A_2),X_1)) -> A_2 != bot_bo784226126e_bool)) # label(fact_135_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 158 (all A_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) -> A_2 = bot_bot_fun_int_bool | A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) # label(fact_136_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 159 (all A_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) -> A_2 = bot_bot_fun_nat_bool | A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) # label(fact_137_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 160 (all A_2 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) -> A_2 = bot_bo784226126e_bool | A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) # label(fact_138_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 161 (all X_1 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),X_1))) # label(fact_139_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 162 (all X_36 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_36),X_36))) # label(fact_140_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 163 (all X_36 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_36),X_36))) # label(fact_141_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 164 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)) -> A_2 = B_29))) # label(fact_142_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 165 (all Ca all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29))))) # label(fact_143_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 166 (all Ca all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29))))) # label(fact_144_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 167 (all Ca all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29))))) # label(fact_145_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 168 (all A_2 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_2))) # label(fact_146_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 169 (all A_2 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_2))) # label(fact_147_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 170 (all A_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A_2))) # label(fact_148_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 171 (all X_35 all Y_34 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_35),Y_34)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_34),X_35)))) # label(fact_149_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 172 (all X_35 all Y_34 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_35),Y_34)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_34),X_35)))) # label(fact_150_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 173 (all X_1 all F all G (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))))) # label(fact_151_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 174 (all Z_1 all Y_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z_1),Y_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z_1),X_1))))) # label(fact_152_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 175 (all Z_12 all Y_33 all X_34 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_33),X_34)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_12),Y_33)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_12),X_34))))) # label(fact_153_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 176 (all Z_12 all Y_33 all X_34 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_33),X_34)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_12),Y_33)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_12),X_34))))) # label(fact_154_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 177 (all Y_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) -> X_1 = Y_1))) # label(fact_155_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 178 (all Y_32 all X_33 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_32),X_33)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_33),Y_32)) -> X_33 = Y_32))) # label(fact_156_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 179 (all Y_32 all X_33 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_32),X_33)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_33),Y_32)) -> X_33 = Y_32))) # label(fact_157_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 180 (all Z_1 all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),Z_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z_1))))) # label(fact_158_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 181 (all Z_11 all X_32 all Y_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_32),Y_31)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_31),Z_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_32),Z_11))))) # label(fact_159_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 182 (all Z_11 all X_32 all Y_31 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_32),Y_31)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_31),Z_11)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_32),Z_11))))) # label(fact_160_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 183 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)) -> X_1 = Y_1))) # label(fact_161_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 184 (all X_31 all Y_30 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_31),Y_30)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_30),X_31)) -> X_31 = Y_30))) # label(fact_162_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 185 (all X_31 all Y_30 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_31),Y_30)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_30),X_31)) -> X_31 = Y_30))) # label(fact_163_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 186 (all Ca all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1)) -> (B_2 = Ca -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),A_1))))) # label(fact_164_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 187 (all C_35 all B_45 all A_61 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_45),A_61)) -> (B_45 = C_35 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_35),A_61))))) # label(fact_165_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 188 (all C_35 all B_45 all A_61 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_45),A_61)) -> (B_45 = C_35 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_35),A_61))))) # label(fact_166_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 189 (all Ca all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2)) -> (B_2 = Ca -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),Ca))))) # label(fact_167_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 190 (all C_34 all A_60 all B_44 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_60),B_44)) -> (B_44 = C_34 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_60),C_34))))) # label(fact_168_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 191 (all C_34 all A_60 all B_44 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_60),B_44)) -> (B_44 = C_34 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_60),C_34))))) # label(fact_169_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 192 (all Ca all A_1 all B_2 (A_1 = B_2 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),A_1))))) # label(fact_170_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 193 (all C_33 all A_59 all B_43 (A_59 = B_43 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_33),B_43)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_33),A_59))))) # label(fact_171_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 194 (all C_33 all A_59 all B_43 (A_59 = B_43 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_33),B_43)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_33),A_59))))) # label(fact_172_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 195 (all Ca all A_1 all B_2 (A_1 = B_2 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),Ca))))) # label(fact_173_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 196 (all C_32 all A_58 all B_42 (A_58 = B_42 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_42),C_32)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_58),C_32))))) # label(fact_174_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 197 (all C_32 all A_58 all B_42 (A_58 = B_42 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_42),C_32)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_58),C_32))))) # label(fact_175_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 198 (all X_1 all Pa all Qa (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Pa),Qa)) -> (hBOOL(hAPP_H242767318e_bool(Pa,X_1)) -> hBOOL(hAPP_H242767318e_bool(Qa,X_1))))) # label(fact_176_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 199 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) <-> hBOOL(hAPP_H242767318e_bool(A_2,X_1)))) # label(fact_177_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 200 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) <-> hBOOL(hAPP_int_bool(A_2,X_1)))) # label(fact_178_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 201 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) <-> hBOOL(hAPP_nat_bool(A_2,X_1)))) # label(fact_179_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 202 (all Pa hAPP_f806699093e_bool(collec637225377_state,Pa) = Pa) # label(fact_180_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 203 (all Y_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_181_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 204 (all Y_1 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_182_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 205 (all Y_1 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_183_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 206 (all X_1 all F all G (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))))) # label(fact_184_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 207 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)))) # label(fact_185_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 208 (all X_30 all Y_29 (X_30 = Y_29 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_30),Y_29)))) # label(fact_186_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 209 (all X_30 all Y_29 (X_30 = Y_29 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_30),Y_29)))) # label(fact_187_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 210 (all Qa all Pa all X_1 (hBOOL(hAPP_H242767318e_bool(Pa,X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Pa),Qa)) -> hBOOL(hAPP_H242767318e_bool(Qa,X_1))))) # label(fact_188_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 211 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)))) # label(fact_189_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 212 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)))) # label(fact_190_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 213 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)))) # label(fact_191_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 214 (all X_29 all Y_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_29),Y_28)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_28),X_29)))) # label(fact_192_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 215 (all X_29 all Y_28 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_28)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_28),X_29)))) # label(fact_193_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 216 (all F all G (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2)))))) # label(fact_194_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 217 (all A_2 all B_29 (A_2 = B_29 -> -(hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2))))) # label(fact_195_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 218 (all C_26 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),C_26)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),C_26))))) # label(fact_196_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 219 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))))) # label(fact_197_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 220 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))))) # label(fact_198_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 221 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))))) # label(fact_199_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 222 (all B_29 all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))))) # label(fact_200_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 223 (all B_29 all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))))) # label(fact_201_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 224 (all B_29 all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))))) # label(fact_202_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 225 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29))))) # label(fact_203_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 226 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29))))) # label(fact_204_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 227 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29))))) # label(fact_205_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 228 (all A_2 all B_29 (A_2 = B_29 -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)))) # label(fact_206_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 229 (all A_2 all B_29 (A_2 = B_29 -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)))) # label(fact_207_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 230 (all A_2 all B_29 (A_2 = B_29 <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)))) # label(fact_208_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 231 (all A_2 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),A_2))) # label(fact_209_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 232 (all A_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_1),bot_bot_fun_int_bool)) -> A_1 = bot_bot_fun_int_bool)) # label(fact_210_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 233 (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_211_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 234 (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_212_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 235 (all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),bot_bo784226126e_bool)) -> A_1 = bot_bo784226126e_bool)) # label(fact_213_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 236 (all A_57 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_57),bot_bot_nat)) -> A_57 = bot_bot_nat)) # label(fact_214_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 237 (all A_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_1),bot_bot_fun_int_bool)) <-> A_1 = bot_bot_fun_int_bool)) # label(fact_215_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 238 (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_216_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 239 (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_217_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 240 (all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),bot_bo784226126e_bool)) <-> A_1 = bot_bo784226126e_bool)) # label(fact_218_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 241 (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_219_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 242 (all A_1 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_1))) # label(fact_220_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 243 (all A_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_1))) # label(fact_221_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 244 (all A_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_1))) # label(fact_222_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 245 (all A_1 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A_1))) # label(fact_223_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 246 (all A_56 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_56))) # label(fact_224_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 247 (all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool)) <-> A_2 = bot_bot_fun_int_bool)) # label(fact_225_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 248 (all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool)) <-> A_2 = bot_bot_fun_nat_bool)) # label(fact_226_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 249 (all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),bot_bo784226126e_bool)) <-> A_2 = bot_bo784226126e_bool)) # label(fact_227_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 250 (all A_1 all C_26 all D_10 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_26),D_10)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),C_26)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),D_10))))) # label(fact_228_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 251 (all A_1 all C_26 all D_10 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_26),D_10)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),C_26)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),D_10))))) # label(fact_229_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 252 (all A_1 all C_26 all D_10 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_26),D_10)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),C_26)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),D_10))))) # label(fact_230_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 253 (all B_2 all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),B_29))))) # label(fact_231_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 254 (all B_2 all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),B_29))))) # label(fact_232_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 255 (all B_2 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_2),B_29))))) # label(fact_233_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 256 (all B_29 all X_1 all A_2 (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))))) # label(fact_234_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 257 (all B_29 all X_1 all A_2 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))))) # label(fact_235_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 258 (all B_29 all X_1 all A_2 (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))))) # label(fact_236_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 259 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)))) # label(fact_237_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 260 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)))) # label(fact_238_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 261 (all X_1 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) & hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)))) # label(fact_239_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 262 (all B_29 all A_1 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29)))) # label(fact_240_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 263 (all B_29 all A_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29)))) # label(fact_241_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 264 (all B_29 all A_1 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29)))) # label(fact_242_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 265 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,G_2),G_1)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts))))) # label(fact_243_thin) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 266 (all Ts all G_1 all Ts_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),Ts_1)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts))))) # label(fact_244_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 267 (all Ts all G_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),G_1)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)))) # label(fact_245_asm) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 268 (all B_29 all A_2 ((all X_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_29)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)))) # label(fact_246_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 269 (all B_29 all A_2 ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_29)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)))) # label(fact_247_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 270 (all B_29 all A_2 ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_29)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)))) # label(fact_248_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 271 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)))) # label(fact_249_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 272 (all Qa all Pa ((all X_2 (hBOOL(hAPP_H242767318e_bool(Pa,X_2)) -> hBOOL(hAPP_H242767318e_bool(Qa,X_2)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Pa),Qa)))) # label(fact_250_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 273 (all Qa all Pa ((all X_2 (hBOOL(hAPP_H242767318e_bool(Pa,X_2)) -> hBOOL(hAPP_H242767318e_bool(Qa,X_2)))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(collec637225377_state,Pa)),hAPP_f806699093e_bool(collec637225377_state,Qa))))) # label(fact_251_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 274 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,B_2)),A_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,Y_5)),hAPP_f1676271015ol_nat(F,X_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,Ca)),A_1)))))) # label(fact_252_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 275 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,B_2)),A_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,Y_5)),hAPP_f166061059ol_int(F,X_2))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,Ca)),A_1)))))) # label(fact_253_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 276 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,B_2)),A_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),B_2)) -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,Y_5)),hAPP_n1497837059e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,Ca)),A_1)))))) # label(fact_254_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 277 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,B_2)),A_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),B_2)) -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,Y_5)),hAPP_i468480167e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,Ca)),A_1)))))) # label(fact_255_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 278 (all Ca all A_1 all F all B_2 (A_1 = hAPP_f806699093e_bool(F,B_2) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),B_2)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_5)),hAPP_f806699093e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Ca)),A_1)))))) # label(fact_256_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 279 (all Ca all A_1 all F all B_2 (A_1 = hAPP_nat_nat(F,B_2) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),B_2)) -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Y_5)),hAPP_nat_nat(F,X_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Ca)),A_1)))))) # label(fact_257_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 280 (all Ca all A_1 all F all B_2 (A_1 = hAPP_int_int(F,B_2) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),B_2)) -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(F,Y_5)),hAPP_int_int(F,X_2))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(F,Ca)),A_1)))))) # label(fact_258_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 281 (all Ca all A_1 all F all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),hAPP_f1676271015ol_nat(F,B_2))) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),hAPP_f1676271015ol_nat(F,Ca))))))) # label(fact_259_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 282 (all Ca all A_1 all F all B_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),hAPP_f166061059ol_int(F,B_2))) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),hAPP_f166061059ol_int(F,Ca))))))) # label(fact_260_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 283 (all Ca all A_1 all F all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_n1497837059e_bool(F,B_2))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_n1497837059e_bool(F,Ca))))))) # label(fact_261_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 284 (all Ca all A_1 all F all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_i468480167e_bool(F,B_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_i468480167e_bool(F,Ca))))))) # label(fact_262_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 285 (all Ca all A_1 all F all B_2 (A_1 = hAPP_n1497837059e_bool(F,B_2) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_n1497837059e_bool(F,Ca))))))) # label(fact_263_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 286 (all Ca all A_1 all F all B_2 (A_1 = hAPP_i468480167e_bool(F,B_2) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),hAPP_i468480167e_bool(F,Ca))))))) # label(fact_264_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 287 (all Ca all A_1 all F all B_2 (A_1 = hAPP_f1676271015ol_nat(F,B_2) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),hAPP_f1676271015ol_nat(F,Ca))))))) # label(fact_265_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 288 (all Ca all A_1 all F all B_2 (A_1 = hAPP_f166061059ol_int(F,B_2) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),hAPP_f166061059ol_int(F,Ca))))))) # label(fact_266_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 289 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,B_2)),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,A_1)),Ca)))))) # label(fact_267_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 290 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,B_2)),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,A_1)),Ca)))))) # label(fact_268_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 291 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,B_2)),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,A_1)),Ca)))))) # label(fact_269_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 292 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,B_2)),Ca)) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,A_1)),Ca)))))) # label(fact_270_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 293 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2)) -> (hAPP_n1497837059e_bool(F,B_2) = Ca -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,X_2)),hAPP_n1497837059e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,A_1)),Ca)))))) # label(fact_271_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 294 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2)) -> (hAPP_i468480167e_bool(F,B_2) = Ca -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_5)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,X_2)),hAPP_i468480167e_bool(F,Y_5))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,A_1)),Ca)))))) # label(fact_272_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 295 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2)) -> (hAPP_f1676271015ol_nat(F,B_2) = Ca -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,X_2)),hAPP_f1676271015ol_nat(F,Y_5))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,A_1)),Ca)))))) # label(fact_273_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 296 (all F all Ca all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2)) -> (hAPP_f166061059ol_int(F,B_2) = Ca -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),Y_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,X_2)),hAPP_f166061059ol_int(F,Y_5))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,A_1)),Ca)))))) # label(fact_274_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 297 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),A_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_n1497837059e_bool(F,B_2))) -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_n1497837059e_bool(F,Y_5)),hAPP_n1497837059e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_n1497837059e_bool(F,A_1))))))) # label(fact_275_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 298 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_i468480167e_bool(F,B_2))) -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_i468480167e_bool(F,Y_5)),hAPP_i468480167e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_i468480167e_bool(F,A_1))))))) # label(fact_276_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 299 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f1676271015ol_nat(F,B_2))) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(F,Y_5)),hAPP_f1676271015ol_nat(F,X_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f1676271015ol_nat(F,A_1))))))) # label(fact_277_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 300 (all Ca all F all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_f166061059ol_int(F,B_2))) -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f166061059ol_int(F,Y_5)),hAPP_f166061059ol_int(F,X_2))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_f166061059ol_int(F,A_1))))))) # label(fact_278_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 301 (all F all Ca all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1)) -> (hAPP_f806699093e_bool(F,B_2) = Ca -> ((all X_2 all Y_5 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_5),X_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_5)),hAPP_f806699093e_bool(F,X_2))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ca),hAPP_f806699093e_bool(F,A_1))))))) # label(fact_279_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 302 (all F all Ca all B_2 all A_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),A_1)) -> (hAPP_nat_nat(F,B_2) = Ca -> ((all X_2 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Y_5)),hAPP_nat_nat(F,X_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_nat_nat(F,A_1))))))) # label(fact_280_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 303 (all F all Ca all B_2 all A_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_1)) -> (hAPP_int_int(F,B_2) = Ca -> ((all X_2 all Y_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(F,Y_5)),hAPP_int_int(F,X_2))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_int_int(F,A_1))))))) # label(fact_281_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 304 (all F all A_1 all A_2 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,A_1),A_2),X_1)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)),X_1))))) # label(fact_282_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 305 (all F all A_1 all A_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,A_1),A_2),X_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)),X_1))))) # label(fact_283_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 306 (all F all A_1 all A_2 all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,A_1),A_2),X_1)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2)),X_1))))) # label(fact_284_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 307 (all X_1 all A_2 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> (A_2 != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A_2))))))) # label(fact_285_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 308 (all X_1 all A_2 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> (A_2 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A_2))))))) # label(fact_286_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 309 (all X_1 all A_2 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> (A_2 != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,A_2))))))) # label(fact_287_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 310 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,powp_H1405539888_state(A_2)),powp_H1405539888_state(B_29))))) # label(fact_288_Powp__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 311 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29))) <-> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B_29))) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29))))) # label(fact_289_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 312 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29))) <-> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B_29))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29))))) # label(fact_290_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 313 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29))) <-> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B_29))) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29))))) # label(fact_291_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 314 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29)))))) # label(fact_292_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 315 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29)))))) # label(fact_293_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 316 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29)))))) # label(fact_294_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 317 (all A_2 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hAPP_f1594865479ol_int(F_1,A_2) = hAPP_f1594865479ol_int(finite_fold1_int(F),A_2)))) # label(fact_295_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 318 (all A_2 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hAPP_f22106695ol_nat(F_1,A_2) = hAPP_f22106695ol_nat(finite_fold1_nat(F),A_2)))) # label(fact_296_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 319 (all A_2 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hAPP_f718417177_state(F_1,A_2) = hAPP_f718417177_state(finite1255650454_state(F),A_2)))) # label(fact_297_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 320 (all A_2 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (A_2 != bot_bot_fun_int_bool -> ((all X_2 all Y_5 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_5)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_5),bot_bot_fun_int_bool))))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(F_1,A_2)),A_2))))))) # label(fact_298_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 321 (all A_2 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (A_2 != bot_bot_fun_nat_bool -> ((all X_2 all Y_5 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_5)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_5),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A_2)),A_2))))))) # label(fact_299_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 322 (all A_2 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (A_2 != bot_bo784226126e_bool -> ((all X_2 all Y_5 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_5)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_5),bot_bo784226126e_bool))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_f718417177_state(F_1,A_2)),A_2))))))) # label(fact_300_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 323 (all Ca all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) -> -(hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29))))) # label(fact_301_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 324 (all Ca all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) -> -(hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29))))) # label(fact_302_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 325 (all Ca all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29))))) # label(fact_303_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 326 (all B_29 all Ca all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))))) # label(fact_304_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 327 (all B_29 all Ca all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))))) # label(fact_305_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 328 (all B_29 all Ca all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))))) # label(fact_306_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 329 (all A_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2))))) # label(fact_310_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 330 (all A_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2))))) # label(fact_311_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 331 (all A_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2))))) # label(fact_312_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 332 (all B_29 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))))) # label(fact_313_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 333 (all B_29 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))))) # label(fact_314_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 334 (all B_29 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))))) # label(fact_315_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 335 (all A_2 all A_1 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29)))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))))) # label(fact_316_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 336 (all A_2 all A_1 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))))) # label(fact_317_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 337 (all A_2 all A_1 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29)))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))))) # label(fact_318_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 338 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))))) # label(fact_319_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 339 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))))) # label(fact_320_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.96 340 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))))) # label(fact_321_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 341 (all Ca all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)))) # label(fact_322_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 342 (all Ca all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)))) # label(fact_323_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 343 (all Ca all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)))) # label(fact_324_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 344 (all Ca all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2)))) # label(fact_325_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 345 (all Ca all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2)))) # label(fact_326_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 346 (all Ca all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2)))) # label(fact_327_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 347 (all A_2 all B_29 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),B_29) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)) # label(fact_328_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 348 (all A_2 all B_29 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),B_29) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)) # label(fact_329_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 349 (all A_2 all B_29 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),B_29) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)) # label(fact_330_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 350 (all Ca all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2)) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29)))) # label(fact_331_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 351 (all Ca all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2)) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29)))) # label(fact_332_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 352 (all Ca all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29)))) # label(fact_333_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 353 (all A_2 all B_29 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(cOMBS_865875691l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(cOMBC_538205282l_bool(member1667945571_state),A_2))),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_f806699093e_bool(cOMBC_538205282l_bool(member1667945571_state),B_29))))) # label(fact_334_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 354 (all A_2 all B_29 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(cOMBS_int_bool_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(fconj),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A_2))),hAPP_f1805168059t_bool(cOMBB_bool_bool_int(fNot),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B_29))))) # label(fact_335_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 355 (all A_2 all B_29 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A_2))),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_29))))) # label(fact_336_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 356 (all A_2 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),A_2) = bot_bot_fun_int_bool) # label(fact_337_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 357 (all A_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),A_2) = bot_bot_fun_nat_bool) # label(fact_338_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 358 (all A_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),A_2) = bot_bo784226126e_bool) # label(fact_339_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 359 (all A_2 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),bot_bot_fun_int_bool) = A_2) # label(fact_340_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 360 (all A_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),bot_bot_fun_nat_bool) = A_2) # label(fact_341_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 361 (all A_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),bot_bo784226126e_bool) = A_2) # label(fact_342_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 362 (all A_2 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),A_2) = bot_bot_fun_int_bool) # label(fact_343_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 363 (all A_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A_2) = bot_bot_fun_nat_bool) # label(fact_344_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 364 (all A_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,bot_bo784226126e_bool),A_2) = bot_bo784226126e_bool) # label(fact_345_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 365 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))) # label(fact_346_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 366 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))) # label(fact_347_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 367 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))) # label(fact_348_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 368 (all A_2 all X_1 all B_29 ((hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),B_29) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))))) # label(fact_349_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 369 (all A_2 all X_1 all B_29 ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),B_29) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))))) # label(fact_350_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 370 (all A_2 all X_1 all B_29 ((hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),B_29) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))))) # label(fact_351_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 371 (all C_26 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),C_26)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B_29),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_26),A_2)) = A_2))) # label(fact_352_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 372 (all C_26 all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),C_26)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B_29),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_26),A_2)) = A_2))) # label(fact_353_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 373 (all C_26 all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),C_26)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B_29),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_26),A_2)) = A_2))) # label(fact_354_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 374 (all D_10 all B_29 all A_2 all C_26 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),C_26)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,D_10),B_29)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_26),D_10)))))) # label(fact_355_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 375 (all D_10 all B_29 all A_2 all C_26 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_26)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,D_10),B_29)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_26),D_10)))))) # label(fact_356_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 376 (all D_10 all B_29 all A_2 all C_26 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_26)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,D_10),B_29)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_26),D_10)))))) # label(fact_357_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 377 (all A_2 all B_29 hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),A_2))) # label(fact_358_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 378 (all A_2 all B_29 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),A_2))) # label(fact_359_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 379 (all A_2 all B_29 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),A_2))) # label(fact_360_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 380 (all A_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)))) # label(fact_361_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 381 (all A_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)))) # label(fact_362_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 382 (all A_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)))) # label(fact_363_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 383 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))))) # label(fact_364_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 384 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))))) # label(fact_365_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 385 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))))) # label(fact_366_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 386 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))))) # label(fact_367_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 387 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))))) # label(fact_368_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 388 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))))) # label(fact_369_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 389 (all F all Z_1 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),bot_bot_fun_int_bool),X_1)) -> X_1 = Z_1)) # label(fact_370_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 390 (all F all Z_1 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),bot_bot_fun_nat_bool),X_1)) -> X_1 = Z_1)) # label(fact_371_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 391 (all F all Z_1 all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),bot_bo784226126e_bool),X_1)) -> X_1 = Z_1)) # label(fact_372_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 392 (all F all Z_1 hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),bot_bot_fun_int_bool),Z_1))) # label(fact_373_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 393 (all F all Z_1 hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),bot_bot_fun_nat_bool),Z_1))) # label(fact_374_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 394 (all F all Z_1 hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),bot_bo784226126e_bool),Z_1))) # label(fact_375_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 395 (all F all Z_1 all Y_1 all X_1 all A_2 (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Y_1)))))) # label(fact_376_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 396 (all F all Z_1 all Y_1 all X_1 all A_2 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Y_1)))))) # label(fact_377_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 397 (all F all Z_1 all Y_1 all X_1 all A_2 (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1)) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),Y_1)))))) # label(fact_378_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 398 (all X_1 all A_2 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,A_2) = X_1) & (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,A_2) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))))) # label(fact_379_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 399 (all X_1 all A_2 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,A_2) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))))) # label(fact_380_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 400 (all X_1 all A_2 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,A_2) = X_1) & (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,A_2) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))))))))) # label(fact_381_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 401 (all X_1 all A_2 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = X_1) & (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))))) # label(fact_382_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 402 (all X_1 all A_2 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_383_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 403 (all X_1 all A_2 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = X_1) & (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))))))) # label(fact_384_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 404 (all A_1 all A_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))) = A_2)) # label(fact_385_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 405 (all A_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) = A_2)) # label(fact_386_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 406 (all A_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))) = A_2)) # label(fact_387_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 407 (all X_1 all A_2 (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = A_2)) # label(fact_388_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 408 (all X_1 all A_2 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = A_2)) # label(fact_389_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 409 (all X_1 all A_2 (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = A_2)) # label(fact_390_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 410 (all A_1 all A_2 hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)) # label(fact_391_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 411 (all A_1 all A_2 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),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_2)) # label(fact_392_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 412 (all A_1 all A_2 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2)) # label(fact_393_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 413 (all A_2 all A_1 all B_29 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))),B_29)) # label(fact_394_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 414 (all A_2 all A_1 all B_29 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))),B_29)) # label(fact_395_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 415 (all A_2 all A_1 all B_29 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))),B_29)) # label(fact_396_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 416 (all A_2 all A_1 all B_29 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))) # label(fact_397_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 417 (all A_2 all A_1 all B_29 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))) # label(fact_398_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 418 (all A_2 all A_1 all B_29 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))) # label(fact_399_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 419 (all Pa all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,A_2)) -> ((all A_55 all A_42 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_42)) -> (hBOOL(hAPP_f448129468l_bool(Pa,A_42)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_42),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),bot_bot_fun_int_bool)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)))))) # label(fact_400_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 420 (all Pa all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A_2)) -> ((all A_55 all A_42 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_42)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A_42)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_42),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),bot_bot_fun_nat_bool)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)))))) # label(fact_401_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 421 (all Pa all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,A_2)) -> ((all A_55 all A_42 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_42)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_42)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,A_42)) -> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_42),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),bot_bo784226126e_bool)))))))) -> hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool)))))) # label(fact_402_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 422 (all Pa all A_2 all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F_1),A_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) -> ((all A_55 all F_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),F_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,F_2)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),F_2)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,F_1))))))) # label(fact_403_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 423 (all Pa all A_2 all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F_1),A_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all A_55 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1))))))) # label(fact_404_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 424 (all Pa all A_2 all F_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F_1),A_2)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool)) -> ((all A_55 all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,F_2)) -> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),F_2)))))))) -> hBOOL(hAPP_f1378282496l_bool(Pa,F_1))))))) # label(fact_405_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 425 (all F all A_1 all X_28 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),X_28)),X_1)) -> -(all A_55 all A_42 (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),X_28) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),A_42) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,A_55),A_42),X_1)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_42))))))) # label(fact_406_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 426 (all F all A_1 all X_28 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),X_28)),X_1)) -> -(all A_55 all A_42 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),X_28) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),A_42) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,A_55),A_42),X_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_42))))))) # label(fact_407_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 427 (all F all A_1 all X_28 all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),X_28)),X_1)) -> -(all A_55 all A_42 (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),X_28) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),A_42) -> (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,A_55),A_42),X_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_42))))))) # label(fact_408_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 428 (all F all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (A_2 != bot_bot_fun_int_bool -> (exists X1 hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),A_2),X1)))))) # label(fact_409_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 429 (all F all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (A_2 != bot_bot_fun_nat_bool -> (exists X1 hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),A_2),X1)))))) # label(fact_410_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 430 (all F all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (A_2 != bot_bo784226126e_bool -> (exists X1 hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),A_2),X1)))))) # label(fact_411_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 431 (all Pa all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> (hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,F_2)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,F_1)))))) # label(fact_412_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 432 (all Pa all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1)))))) # label(fact_413_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 433 (all Pa all F_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,F_2)) -> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2))))))) -> hBOOL(hAPP_f1378282496l_bool(Pa,F_1)))))) # label(fact_414_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 434 (all A_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_1)) <-> A_1 = bot_bot_fun_int_bool | (exists A_42 exists A_55 (A_1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),A_42) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42)))))) # label(fact_415_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 435 (all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) <-> A_1 = bot_bot_fun_nat_bool | (exists A_42 exists A_55 (A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),A_42) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42)))))) # label(fact_416_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 436 (all A_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) <-> A_1 = bot_bo784226126e_bool | (exists A_42 exists A_55 (A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),A_42) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_42)))))) # label(fact_417_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 437 (all F all Z_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (exists X1 hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),X1))))) # label(fact_418_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 438 (all F all Z_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (exists X1 hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),X1))))) # label(fact_419_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 439 (all F all Z_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (exists X1 hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),X1))))) # label(fact_420_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 440 (all F all A1 all A2 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite_fold1Set_int(F),A1),A2)) <-> (exists A_55 exists A_42 exists X_2 (A1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_55),A_42) & A2 = X_2 & hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,A_55),A_42),X_2)) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_55),A_42)))))) # label(fact_421_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 441 (all F all A1 all A2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite_fold1Set_nat(F),A1),A2)) <-> (exists A_55 exists A_42 exists X_2 (A1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_55),A_42) & A2 = X_2 & hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,A_55),A_42),X_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_55),A_42)))))) # label(fact_422_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 442 (all F all A1 all A2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite2066257190_state(F),A1),A2)) <-> (exists A_55 exists A_42 exists X_2 (A1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_55),A_42) & A2 = X_2 & hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,A_55),A_42),X_2)) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_55),A_42)))))) # label(fact_423_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 443 (all A_2 all B_29 all X_1 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H242767318e_bool(A_2,X_1)),hAPP_H242767318e_bool(B_29,X_1))))) # label(fact_424_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 444 (all A_2 all B_29 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_int_bool(A_2,X_1)),hAPP_int_bool(B_29,X_1))))) # label(fact_425_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 445 (all A_2 all B_29 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A_2,X_1)),hAPP_nat_bool(B_29,X_1))))) # label(fact_426_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 446 (all A_2 all B_29 all X_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H242767318e_bool(A_2,X_2)),hAPP_H242767318e_bool(B_29,X_2))))) # label(fact_427_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 447 (all A_2 all B_29 all X_2 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_int_bool(A_2,X_2)),hAPP_int_bool(B_29,X_2))))) # label(fact_428_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 448 (all A_2 all B_29 all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A_2,X_2)),hAPP_nat_bool(B_29,X_2))))) # label(fact_429_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 449 (all A_1 all B_2 all Ca all D_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ca),D_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),D_1))))) # label(fact_430_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 450 (all F all Z_1 all A1 all A2 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A1),A2)) <-> A1 = bot_bot_fun_int_bool & A2 = Z_1 | (exists X_2 exists A_42 exists Y_5 (A1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),A_42) & A2 = hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_5) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_42)) & hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_42),Y_5)))))) # label(fact_431_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 451 (all F all Z_1 all A1 all A2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A1),A2)) <-> A1 = bot_bot_fun_nat_bool & A2 = Z_1 | (exists X_2 exists A_42 exists Y_5 (A1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_42) & A2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_5) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_42)) & hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_42),Y_5)))))) # label(fact_432_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 452 (all F all Z_1 all A1 all A2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A1),A2)) <-> A1 = bot_bo784226126e_bool & A2 = Z_1 | (exists X_2 exists A_42 exists Y_5 (A1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_42) & A2 = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_5) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_42)) & hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_42),Y_5)))))) # label(fact_433_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 453 (all B_29 all A_2 all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (B_29 != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),A_2)) -> hAPP_int_int(hAPP_int_fun_int_int(F,hAPP_f1594865479ol_int(F_1,B_29)),hAPP_f1594865479ol_int(F_1,A_2)) = hAPP_f1594865479ol_int(F_1,A_2)))))) # label(fact_434_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 454 (all B_29 all A_2 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (B_29 != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),A_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,B_29)),hAPP_f22106695ol_nat(F_1,A_2)) = hAPP_f22106695ol_nat(F_1,A_2)))))) # label(fact_435_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 455 (all B_29 all A_2 all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (B_29 != bot_bo784226126e_bool -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)) -> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,B_29)),hAPP_f718417177_state(F_1,A_2)) = hAPP_f718417177_state(F_1,A_2)))))) # label(fact_436_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 456 (all X_1 all A_2 all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (A_2 != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A_2)))))) # label(fact_437_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 457 (all X_1 all A_2 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (A_2 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A_2)))))) # label(fact_438_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 458 (all X_1 all A_2 all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (A_2 != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,A_2)))))) # label(fact_439_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 459 (all Pa all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> (F_1 != bot_bot_fun_int_bool -> ((all X_2 hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),bot_bot_fun_int_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) -> (F_2 != bot_bot_fun_int_bool -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,F_2)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,F_1))))))) # label(fact_440_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 460 (all Pa all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (F_1 != bot_bot_fun_nat_bool -> ((all X_2 hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (F_2 != bot_bot_fun_nat_bool -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1))))))) # label(fact_441_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 461 (all Pa all F_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1)) -> (F_1 != bot_bo784226126e_bool -> ((all X_2 hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (F_2 != bot_bo784226126e_bool -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,F_2)) -> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2)))))))) -> hBOOL(hAPP_f1378282496l_bool(Pa,F_1))))))) # label(fact_442_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 462 (all X_1 all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),X_1) = X_1)) # label(fact_443_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 463 (all X_1 all A_2 all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(F_1,A_2)) = hAPP_f718417177_state(F_1,A_2))))) # label(fact_444_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 464 (all X_1 all A_2 all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A_2)) = hAPP_f1594865479ol_int(F_1,A_2))))) # label(fact_445_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 465 (all X_1 all A_2 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A_2)) = hAPP_f22106695ol_nat(F_1,A_2))))) # label(fact_446_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 466 (all A_1 all B_2 all Ca all D_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ca),D_1) -> (A_1 = B_2 <-> Ca = D_1))) # label(fact_447_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 467 (all A_1 all Z_1 all A_2 all Y_1 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> (exists Y_27 (Y_1 = hAPP_int_int(hAPP_int_fun_int_int(F,A_1),Y_27) & hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool))),Y_27)))))))) # label(fact_448_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 468 (all A_1 all Z_1 all A_2 all Y_1 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> (exists Y_27 (Y_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,A_1),Y_27) & hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool))),Y_27)))))))) # label(fact_449_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 469 (all A_1 all Z_1 all A_2 all Y_1 all F (hBOOL(finite1720675051_state(F)) -> (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) -> (exists Y_27 (Y_1 = hAPP_H574424047_state(hAPP_H280516760_state(F,A_1),Y_27) & hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),bot_bo784226126e_bool))),Y_27)))))))) # label(fact_450_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 470 (all A_2 all F all F_1 (hBOOL(big_se913005884ig_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hAPP_f1594865479ol_int(F_1,A_2) = hAPP_f1594865479ol_int(finite_fold1_int(F),A_2)))) # label(fact_451_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 471 (all A_2 all F all F_1 (hBOOL(big_se275732192ig_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hAPP_f22106695ol_nat(F_1,A_2) = hAPP_f22106695ol_nat(finite_fold1_nat(F),A_2)))) # label(fact_452_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 472 (all A_2 all F all F_1 (hBOOL(big_se1212619424_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hAPP_f718417177_state(F_1,A_2) = hAPP_f718417177_state(finite1255650454_state(F),A_2)))) # label(fact_453_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 473 (all A_1 all B_2 all A_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,B_2),A_2),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),bot_bot_fun_nat_bool)))),X_1)))))) # label(fact_454_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 474 (all A_1 all B_2 all A_2 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,B_2),A_2),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),A_2)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,A_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),bot_bot_fun_int_bool)))),X_1)))))) # label(fact_455_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 475 (all X_1 all A_2 (A_2 != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A_2)))))) # label(fact_456_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 476 (all X_1 all A_2 (A_2 != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),A_2)))))) # label(fact_457_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 477 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_29))) <-> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29))) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B_29))) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)))))) # label(fact_458_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 478 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_29))) <-> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B_29))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)))))) # label(fact_459_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 479 (all A_2 all X_1 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_29))) <-> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29))) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B_29))) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)))))) # label(fact_460_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 480 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A_2))))) # label(fact_461_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 481 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A_2))))) # label(fact_462_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 482 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))),hAPP_f1676271015ol_nat(finite1401757860_state,A_2))))) # label(fact_463_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 483 (all A_54 all B_41 all C_31 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_54),B_41)),C_31) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_54),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_41),C_31))) # label(fact_464_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 484 (all A_54 all B_41 all C_31 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_54),B_41)),C_31) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_54),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_41),C_31))) # label(fact_465_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 485 (all Ca all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),A_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Ca),B_29))))) # label(fact_466_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 486 (all Ca all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B_29))))) # label(fact_467_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 487 (all Ca all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B_29))))) # label(fact_468_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 488 (all C_26 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_29),C_26)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),C_26))))) # label(fact_469_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 489 (all X_1 -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),X_1))) # label(fact_472_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 490 (all X_27 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),X_27))) # label(fact_473_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 491 (all X_27 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_27),X_27))) # label(fact_474_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 492 (all X_1 all Y_1 (X_1 != Y_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)))) # label(fact_475_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 493 (all X_1 all Y_1 (X_1 != Y_1 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)))) # label(fact_476_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 494 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) | X_1 = Y_1)) # label(fact_477_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 495 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) | X_1 = Y_1)) # label(fact_478_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 496 (all X_26 all Y_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_26)) | X_26 = Y_26 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_26),X_26)))) # label(fact_479_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 497 (all X_26 all Y_26 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_26),Y_26)) | X_26 = Y_26 | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_26),X_26)))) # label(fact_480_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 498 (all X_1 all Y_1 all Z_1 all F (hBOOL(finite1973466193nt_int(F)) -> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_int_int(hAPP_int_fun_int_int(F,Y_1),Z_1)) = hAPP_int_int(hAPP_int_fun_int_int(F,Y_1),hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)))) # label(fact_481_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 499 (all X_1 all Y_1 all Z_1 all F (hBOOL(finite2130160977at_nat(F)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,Y_1),Z_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,Y_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)))) # label(fact_482_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 500 (all Y_1 all X_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_483_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 501 (all Y_1 all X_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_484_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 502 (all X_25 all Y_25 (X_25 != Y_25 -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_25)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_25),X_25))))) # label(fact_485_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 503 (all X_25 all Y_25 (X_25 != Y_25 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_25),Y_25)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_25),X_25))))) # label(fact_486_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 504 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> X_1 != Y_1)) # label(fact_487_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 505 (all X_24 all Y_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_24)) -> X_24 != Y_24)) # label(fact_488_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 506 (all X_24 all Y_24 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_24),Y_24)) -> X_24 != Y_24)) # label(fact_489_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.97 507 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)))) # label(fact_490_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 508 (all X_23 all Y_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_23)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_23)))) # label(fact_491_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 509 (all X_23 all Y_23 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_23),Y_23)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_23),X_23)))) # label(fact_492_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 510 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)))) # label(fact_493_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 511 (all X_22 all Y_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_22)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_22),X_22)))) # label(fact_494_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 512 (all X_22 all Y_22 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_22),Y_22)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_22),X_22)))) # label(fact_495_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 513 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> X_1 != Y_1)) # label(fact_496_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 514 (all X_21 all Y_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),Y_21)) -> X_21 != Y_21)) # label(fact_497_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 515 (all X_21 all Y_21 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_21),Y_21)) -> X_21 != Y_21)) # label(fact_498_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 516 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> Y_1 != X_1)) # label(fact_499_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 517 (all X_20 all Y_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_20),Y_20)) -> Y_20 != X_20)) # label(fact_500_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 518 (all X_20 all Y_20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_20)) -> Y_20 != X_20)) # label(fact_501_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 519 (all Pa all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)) -> hBOOL(Pa)))) # label(fact_502_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 520 (all Pa all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) -> hBOOL(Pa)))) # label(fact_503_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 521 (all Pa all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) -> hBOOL(Pa)))) # label(fact_504_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 522 (all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1)))) # label(fact_505_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 523 (all A_53 all B_40 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_53),B_40)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_40),A_53)))) # label(fact_506_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 524 (all A_53 all B_40 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_53),B_40)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_40),A_53)))) # label(fact_507_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 525 (all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2)))) # label(fact_508_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 526 (all B_39 all A_52 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_39),A_52)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_52),B_39)))) # label(fact_509_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 527 (all B_39 all A_52 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_39),A_52)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_52),B_39)))) # label(fact_510_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 528 (all Ca all A_1 all B_2 (A_1 = B_2 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),Ca)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),Ca))))) # label(fact_511_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 529 (all C_30 all A_51 all B_38 (A_51 = B_38 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_38),C_30)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_51),C_30))))) # label(fact_512_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 530 (all C_30 all A_51 all B_38 (A_51 = B_38 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_38),C_30)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_51),C_30))))) # label(fact_513_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 531 (all Ca all A_1 all B_2 (A_1 = B_2 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Ca),B_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Ca),A_1))))) # label(fact_514_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 532 (all C_29 all A_50 all B_37 (A_50 = B_37 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_29),B_37)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_29),A_50))))) # label(fact_515_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 533 (all C_29 all A_50 all B_37 (A_50 = B_37 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_29),B_37)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_29),A_50))))) # label(fact_516_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 534 (all Ca all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2)) -> (B_2 = Ca -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),Ca))))) # label(fact_517_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 535 (all C_28 all A_49 all B_36 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_49),B_36)) -> (B_36 = C_28 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_49),C_28))))) # label(fact_518_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 536 (all C_28 all A_49 all B_36 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_49),B_36)) -> (B_36 = C_28 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_49),C_28))))) # label(fact_519_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 537 (all Ca all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1)) -> (B_2 = Ca -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Ca),A_1))))) # label(fact_520_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 538 (all C_27 all B_35 all A_48 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_35),A_48)) -> (B_35 = C_27 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_27),A_48))))) # label(fact_521_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 539 (all C_27 all B_35 all A_48 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_35),A_48)) -> (B_35 = C_27 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_27),A_48))))) # label(fact_522_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 540 (all Z_1 all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),Z_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Z_1))))) # label(fact_523_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 541 (all Z_10 all X_19 all Y_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_19),Y_19)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_19),Z_10)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_19),Z_10))))) # label(fact_524_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 542 (all Z_10 all X_19 all Y_19 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_19),Y_19)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_19),Z_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_19),Z_10))))) # label(fact_525_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 543 (all Z_1 all Y_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),Y_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),X_1))))) # label(fact_526_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 544 (all Z_9 all Y_18 all X_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_18),X_18)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_18))))) # label(fact_527_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 545 (all Z_9 all Y_18 all X_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_18),X_18)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_9),Y_18)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_9),X_18))))) # label(fact_528_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 546 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)))) # label(fact_529_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 547 (all X_17 all Y_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_17),Y_17)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_17),X_17)))) # label(fact_530_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 548 (all X_17 all Y_17 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_17),Y_17)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_17),X_17)))) # label(fact_531_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 549 (all X_16 all Y_16 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_16),Y_16)) -> (X_16 != Y_16 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_16),X_16))))) # label(fact_532_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 550 (all X_16 all Y_16 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_16),Y_16)) -> (X_16 != Y_16 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_16),X_16))))) # label(fact_533_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 551 (all F all G (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,F),G)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) & -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,G),F)))) # label(fact_534_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 552 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)))) # label(fact_535_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 553 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)))) # label(fact_536_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 554 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)))) # label(fact_537_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 555 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)))) # label(fact_538_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 556 (all X_15 all Y_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_15),X_15)))) # label(fact_539_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 557 (all X_15 all Y_15 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_15),Y_15)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_15),X_15)))) # label(fact_540_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 558 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) & X_1 != Y_1)) # label(fact_541_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 559 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) & X_1 != Y_1)) # label(fact_542_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 560 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) & X_1 != Y_1)) # label(fact_543_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 561 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) & -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)))) # label(fact_544_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 562 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)))) # label(fact_545_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 563 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) & -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)))) # label(fact_546_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 564 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) | X_1 = Y_1)) # label(fact_547_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 565 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) | X_1 = Y_1)) # label(fact_548_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 566 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) | X_1 = Y_1)) # label(fact_549_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 567 (all X_14 all Y_14 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_14),Y_14)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_14),X_14)))) # label(fact_550_leI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 568 (all X_14 all Y_14 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_14),Y_14)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_14),X_14)))) # label(fact_551_leI) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 569 (all Y_13 all X_13 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_13)))) # label(fact_552_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 570 (all Y_13 all X_13 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_13),X_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_13),Y_13)))) # label(fact_553_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 571 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_554_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 572 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_555_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 573 (all A_1 all B_2 (A_1 != B_2 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2))))) # label(fact_556_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 574 (all A_47 all B_34 (A_47 != B_34 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_47),B_34)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_47),B_34))))) # label(fact_557_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 575 (all A_47 all B_34 (A_47 != B_34 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_47),B_34)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_47),B_34))))) # label(fact_558_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 576 (all A_1 all B_2 (A_1 != B_2 -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1))))) # label(fact_559_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 577 (all A_46 all B_33 (A_46 != B_33 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_33),A_46)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_33),A_46))))) # label(fact_560_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 578 (all A_46 all B_33 (A_46 != B_33 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_33),A_46)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_33),A_46))))) # label(fact_561_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 579 (all Y_12 all X_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_12),X_12)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_12),Y_12)))) # label(fact_562_leD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 580 (all Y_12 all X_12 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_12),X_12)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_12),Y_12)))) # label(fact_563_leD) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 581 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)))) # label(fact_564_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 582 (all X_11 all Y_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),Y_11)))) # label(fact_565_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 583 (all X_11 all Y_11 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_11),Y_11)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),Y_11)))) # label(fact_566_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 584 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_567_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 585 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_568_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 586 (all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) | X_1 = Y_1)) # label(fact_569_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 587 (all X_10 all Y_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),Y_10)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10)) | X_10 = Y_10)) # label(fact_570_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 588 (all X_10 all Y_10 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_10),Y_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_10),Y_10)) | X_10 = Y_10)) # label(fact_571_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 589 (all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),B_2)) -> (A_1 != B_2 -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),B_2))))) # label(fact_572_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 590 (all A_45 all B_32 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_45),B_32)) -> (A_45 != B_32 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_45),B_32))))) # label(fact_573_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 591 (all A_45 all B_32 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_45),B_32)) -> (A_45 != B_32 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_45),B_32))))) # label(fact_574_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 592 (all B_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_2),A_1)) -> (A_1 != B_2 -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_2),A_1))))) # label(fact_575_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 593 (all B_31 all A_44 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_31),A_44)) -> (A_44 != B_31 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_44))))) # label(fact_576_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 594 (all B_31 all A_44 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_31),A_44)) -> (A_44 != B_31 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_31),A_44))))) # label(fact_577_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 595 (all Z_1 all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),Z_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Z_1))))) # label(fact_578_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 596 (all Z_8 all X_9 all Y_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),Z_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Z_8))))) # label(fact_579_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 597 (all Z_8 all X_9 all Y_9 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Y_9)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_9),Z_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Z_8))))) # label(fact_580_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 598 (all Z_1 all Y_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z_1),Y_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),X_1))))) # label(fact_581_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 599 (all Z_7 all Y_8 all X_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_8),X_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_7),X_8))))) # label(fact_582_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 600 (all Z_7 all Y_8 all X_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_8),X_8)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_7),Y_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_7),X_8))))) # label(fact_583_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 601 (all Z_1 all X_1 all Y_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Y_1),Z_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,X_1),Z_1))))) # label(fact_584_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 602 (all Z_6 all X_7 all Y_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_7),Z_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Z_6))))) # label(fact_585_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 603 (all Z_6 all X_7 all Y_7 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Y_7)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_7),Z_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_7),Z_6))))) # label(fact_586_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 604 (all Z_1 all Y_1 all X_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),Y_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,Z_1),X_1))))) # label(fact_587_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 605 (all Z_5 all Y_6 all X_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),X_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_5),Y_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_5),X_6))))) # label(fact_588_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 606 (all Z_5 all Y_6 all X_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_6),X_6)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_5),Y_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_5),X_6))))) # label(fact_589_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 607 (all A_1 -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_1),bot_bot_fun_int_bool))) # label(fact_590_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 608 (all A_1 -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_1),bot_bot_fun_nat_bool))) # label(fact_591_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 609 (all A_1 -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,A_1),bot_bot_bool))) # label(fact_592_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 610 (all A_1 -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_1),bot_bo784226126e_bool))) # label(fact_593_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 611 (all A_43 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_43),bot_bot_nat))) # label(fact_594_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 612 (all A_1 (A_1 != bot_bot_fun_int_bool <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,bot_bot_fun_int_bool),A_1)))) # label(fact_595_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 613 (all A_1 (A_1 != bot_bot_fun_nat_bool <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,bot_bot_fun_nat_bool),A_1)))) # label(fact_596_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 614 (all A_1 (-(hBOOL(A_1) <-> hBOOL(bot_bot_bool)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,bot_bot_bool),A_1)))) # label(fact_597_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 615 (all A_1 (A_1 != bot_bo784226126e_bool <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,bot_bo784226126e_bool),A_1)))) # label(fact_598_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 616 (all A_1 (A_1 != bot_bot_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,bot_bot_nat),A_1)))) # label(fact_599_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 617 (all A_2 -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),bot_bot_fun_int_bool))) # label(fact_600_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 618 (all A_2 -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),bot_bot_fun_nat_bool))) # label(fact_601_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 619 (all A_2 -hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),bot_bo784226126e_bool))) # label(fact_602_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 620 (all A_1 all B_2 all Ca all D_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ca),D_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),B_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ca),D_1))))) # label(fact_603_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 621 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) & A_2 != B_29)) # label(fact_604_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 622 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) | A_2 = B_29)) # label(fact_605_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 623 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)))) # label(fact_606_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 624 (all C_26 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),C_26)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),C_26))))) # label(fact_607_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 625 (all C_26 all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,B_29),C_26)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),C_26))))) # label(fact_608_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 626 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)))))) # label(fact_609_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 627 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)))))) # label(fact_610_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 628 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)))))) # label(fact_611_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 629 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29)))))) # label(fact_612_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 630 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29)))))) # label(fact_613_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 631 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29)))))) # label(fact_614_card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 632 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1676271015ol_nat(finite1401757860_state,B_29)),hAPP_f1676271015ol_nat(finite1401757860_state,A_2))) -> A_2 = B_29)))) # label(fact_615_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 633 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,B_29)),hAPP_f957591787ol_nat(finite_card_int,A_2))) -> A_2 = B_29)))) # label(fact_616_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 634 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B_29)),hAPP_f22106695ol_nat(finite_card_nat,A_2))) -> A_2 = B_29)))) # label(fact_617_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 635 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29))),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)))))) # label(fact_618_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 636 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)))))) # label(fact_619_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 637 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)))))) # label(fact_620_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 638 (all Y_1 all Z_1 all A_2 all X_1 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),X_1)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1)) -> Y_1 = X_1)))) # label(fact_621_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 639 (all Y_1 all Z_1 all A_2 all X_1 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1)) -> Y_1 = X_1)))) # label(fact_622_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 640 (all Y_1 all Z_1 all A_2 all X_1 all F (hBOOL(finite1720675051_state(F)) -> (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),X_1)) -> (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1)) -> Y_1 = X_1)))) # label(fact_623_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 641 (all Z_1 all B_2 all A_2 all Y_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,B_2),A_2),Y_1)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_2),A_2)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(times_times_int,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_2),A_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),Y_1)))))) # label(fact_624_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 642 (all Z_1 all B_2 all A_2 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,B_2),A_2),Y_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_2),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(times_times_nat,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_2),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Z_1),Y_1)))))) # label(fact_625_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 643 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_29),A_2)) -> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29))))) # label(fact_626_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 644 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_29),A_2)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29))))) # label(fact_627_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 645 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_29),A_2)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29))))) # label(fact_628_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 646 (all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (A_2 != bot_bot_fun_int_bool -> ((all X_2 all Y_5 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_2),Y_5)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_5),bot_bot_fun_int_bool))))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),A_2)),A_2)))))) # label(fact_629_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 647 (all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (A_2 != bot_bot_fun_nat_bool -> ((all X_2 all Y_5 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_2),Y_5)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_5),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A_2)),A_2)))))) # label(fact_630_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 648 (all Z_1 all X_1 all A_2 all V_2 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)),V_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> -(all Y_5 (V_2 = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Y_5) -> -hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_5)))))))) # label(fact_631_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 649 (all Z_1 all X_1 all A_2 all V_2 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)),V_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> -(all Y_5 (V_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Y_5) -> -hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_5)))))))) # label(fact_632_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 650 (all Z_1 all X_1 all A_2 all V_2 all F (hBOOL(finite1720675051_state(F)) -> (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)),V_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> -(all Y_5 (V_2 = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),Y_5) -> -hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_5)))))))) # label(fact_633_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 651 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) -> (exists B_30 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_30),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B_29),A_2)))))) # label(fact_634_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 652 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29)) -> (exists B_30 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_30),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B_29),A_2)))))) # label(fact_635_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 653 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29)) -> (exists B_30 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_30),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B_29),A_2)))))) # label(fact_636_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 654 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29)))))) # label(fact_637_psubset__card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 655 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29)))))) # label(fact_638_psubset__card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 656 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29)))))) # label(fact_639_psubset__card__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 657 (all A_2 all B_29 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_29)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_2),B_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),hAPP_f1676271015ol_nat(finite1401757860_state,B_29))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le2137177998e_bool,A_2),B_29)))))) # label(fact_640_card__psubset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 658 (all A_2 all B_29 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B_29)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),hAPP_f957591787ol_nat(finite_card_int,B_29))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A_2),B_29)))))) # label(fact_641_card__psubset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 659 (all A_2 all B_29 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_29)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),hAPP_f22106695ol_nat(finite_card_nat,B_29))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A_2),B_29)))))) # label(fact_642_card__psubset) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 660 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A_2)))))) # label(fact_643_card__Diff1__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 661 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A_2)))))) # label(fact_644_card__Diff1__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 662 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))),hAPP_f1676271015ol_nat(finite1401757860_state,A_2)))))) # label(fact_645_card__Diff1__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 663 (all Y_1 all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A_2))))))) # label(fact_646_card__Diff2__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 664 (all Y_1 all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A_2))))))) # label(fact_647_card__Diff2__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 665 (all Y_1 all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),bot_bo784226126e_bool)))),hAPP_f1676271015ol_nat(finite1401757860_state,A_2))))))) # label(fact_648_card__Diff2__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 666 (all Pa all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) -> ((all B_30 all A_42 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42)) -> ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_42)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),B_30)))) -> (hBOOL(hAPP_f448129468l_bool(Pa,A_42)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_30),A_42))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,A_2)))))) # label(fact_649_finite__linorder__max__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 667 (all Pa all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all B_30 all A_42 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42)) -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_42)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),B_30)))) -> (hBOOL(hAPP_f54304608l_bool(Pa,A_42)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_30),A_42))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,A_2)))))) # label(fact_650_finite__linorder__max__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 668 (all C_25 all A all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_25),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A),C_25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_1),C_25)))))) # label(fact_651_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 669 (all N all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))))) # label(fact_652_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 670 (all Pa all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) -> ((all B_30 all A_42 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_42)) -> ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_42)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_30),X_2)))) -> (hBOOL(hAPP_f448129468l_bool(Pa,A_42)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_30),A_42))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,A_2)))))) # label(fact_653_finite__linorder__min__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 671 (all Pa all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all B_30 all A_42 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_42)) -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_42)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_30),X_2)))) -> (hBOOL(hAPP_f54304608l_bool(Pa,A_42)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_30),A_42))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,A_2)))))) # label(fact_654_finite__linorder__min__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 672 (all N all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))))) # label(fact_655_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 673 (all N_1 all K_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)))) # label(fact_656_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 674 (all N all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K) <-> M = N)))) # label(fact_657_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 675 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_658_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 676 (all M all N (M != N <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)))) # label(fact_659_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 677 (all X all Y (X != Y -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X))))) # label(fact_660_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 678 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_661_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 679 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> M_1 != N_1)) # label(fact_662_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 680 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_663_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 681 (all Pa all M all N ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M))) -> ((M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)))))) # label(fact_664_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 682 (all K_1 all L_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),L_1)))))) # label(fact_665_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 683 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> M_1 = N_1))) # label(fact_666_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 684 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))))) # label(fact_667_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 685 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J))))) # label(fact_668_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 686 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1))))) # label(fact_669_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 687 (all M_1 all N_1 (M_1 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_670_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 688 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)))) # label(fact_671_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 689 (all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1))))) # label(fact_672_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 690 (all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1)))) # label(fact_673_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 691 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1))) # label(fact_674_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 692 (all M_1 all N_1 all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1))) # label(fact_675_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 693 (all K_1 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1))) # label(fact_676_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 694 (all I_1 all J all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),K_1)),J)) # label(fact_677_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 695 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) & M != N)) # label(fact_678_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 696 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | M = N)) # label(fact_679_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 697 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_680_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 698 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> (M_1 != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))))) # label(fact_681_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 699 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) | M_1 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_682_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 700 (all L_1 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1)))))) # label(fact_683_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 701 (all N_1 all J all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N_1)),K_1)))) # label(fact_684_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 702 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),M_1))) # label(fact_685_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 703 (all L_1 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1))))) # label(fact_686_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 704 (all L_1 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),L_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),L_1))))) # label(fact_687_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 705 (all I_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),I_1)) = I_1)) # label(fact_688_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 706 (all I_2 all J_2 all F ((all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_2)))))) # label(fact_689_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 707 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)))) # label(fact_690_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 708 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),one_one_nat)) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,A_2)))) # label(fact_691_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 709 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),one_one_nat)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,A_2)))) # label(fact_692_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 710 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),one_one_nat)) & (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) = hAPP_f1676271015ol_nat(finite1401757860_state,A_2)))) # label(fact_693_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 711 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A_2)),one_one_nat)))) # label(fact_694_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 712 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A_2)),one_one_nat)))) # label(fact_695_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 713 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,A_2)),one_one_nat)))) # label(fact_696_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 714 (all B_29 all A_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),B_29)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),B_29))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),B_29))),one_one_nat))))) # label(fact_697_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 715 (all B_29 all A_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B_29)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),B_29))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),B_29))),one_one_nat))))) # label(fact_698_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.98 716 (all B_29 all A_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),A_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_1),B_29)) -> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),B_29))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),B_29))),one_one_nat))))) # label(fact_699_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 717 (all Z_1 all X_1 all A_2 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_700_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 718 (all Z_1 all X_1 all A_2 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_701_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 719 (all M_1 all N_1 all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1))) # label(fact_702_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 720 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = one_one_nat <-> M = one_one_nat & N = one_one_nat)) # label(fact_703_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 721 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),M_1)) # label(fact_704_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 722 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),one_one_nat) = N_1) # label(fact_705_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 723 (all M all N (one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) <-> M = one_one_nat & N = one_one_nat)) # label(fact_706_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 724 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N_1) = N_1) # label(fact_707_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 725 (all X_1 (one_one_int = X_1 <-> X_1 = one_one_int)) # label(fact_708_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 726 (all X_1 (one_one_nat = X_1 <-> X_1 = one_one_nat)) # label(fact_709_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 727 (all A_41 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_41) = A_41) # label(fact_710_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 728 (all A_41 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_41) = A_41) # label(fact_711_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 729 (all A_40 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_40) = A_40) # label(fact_712_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 730 (all A_40 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_40) = A_40) # label(fact_713_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 731 (all A_39 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_39),one_one_int) = A_39) # label(fact_714_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 732 (all A_39 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_39),one_one_nat) = A_39) # label(fact_715_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 733 (all A_38 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_38),one_one_int) = A_38) # label(fact_716_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 734 (all A_38 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_38),one_one_nat) = A_38) # label(fact_717_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 735 (all X_1 all Z_1 all A_2 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)),A_2)))) # label(fact_718_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 736 (all X_1 all Z_1 all A_2 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)),A_2)))) # label(fact_719_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 737 (all Z_1 all A_2 all Y_1 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),Y_1)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2) = Y_1))) # label(fact_720_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 738 (all Z_1 all A_2 all Y_1 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),Y_1)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2) = Y_1))) # label(fact_721_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 739 (all Z_1 all A_2 all Y_1 all F (hBOOL(finite1720675051_state(F)) -> (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),Y_1)) -> hAPP_f718417177_state(finite212984546_state(F,Z_1),A_2) = Y_1))) # label(fact_722_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 740 (all Z_1 all X_1 all A_2 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)),A_2))))) # label(fact_723_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 741 (all Z_1 all X_1 all A_2 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)),A_2))))) # label(fact_724_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 742 (all Z_1 all X_1 all A_2 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2)))))) # label(fact_725_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 743 (all Z_1 all X_1 all A_2 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2)))))) # label(fact_726_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 744 (all X_1 all A_2 all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,X_1),A_2))))) # label(fact_727_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 745 (all X_1 all A_2 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,X_1),A_2))))) # label(fact_728_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 746 (all X_1 all A_2 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_f718417177_state(finite212984546_state(F,X_1),A_2))))) # label(fact_729_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 747 (all A_1 all A_2 all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,A_1),A_2)))) # label(fact_730_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 748 (all A_1 all A_2 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,A_1),A_2)))) # label(fact_731_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 749 (all A_1 all A_2 all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_1),A_2)) = hAPP_f718417177_state(finite212984546_state(F,A_1),A_2)))) # label(fact_732_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 750 (all Z_1 all A_2 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(finite772772422nt_int(F,Z_1),A_2),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2)))))) # label(fact_733_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 751 (all Z_1 all A_2 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(finite929467206at_nat(F,Z_1),A_2),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2)))))) # label(fact_734_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 752 (all Z_1 all A_2 all F (hBOOL(finite1720675051_state(F)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(finite1946095968_state(F,Z_1),A_2),hAPP_f718417177_state(finite212984546_state(F,Z_1),A_2)))))) # label(fact_735_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 753 (all A_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_1),A_2)) -> hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_1),A_2)) = hAPP_f1594865479ol_int(finite_fold_int_int(times_times_int,A_1),A_2)))) # label(fact_736_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 754 (all A_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A_2)) -> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_1),A_2)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(times_times_nat,A_1),A_2)))) # label(fact_737_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 755 (all Z_1 all X_1 all A_2 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A_2) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))))) # label(fact_738_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 756 (all Z_1 all X_1 all A_2 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_739_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 757 (all N_3 all M_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M_8)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),N_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_8),N_3)))))) # label(fact_740_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 758 (all N_3 all M_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),M_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_8),N_3)))))) # label(fact_741_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 759 (all A_37 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_37) = A_37) # label(fact_742_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 760 (all A_37 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_37) = A_37) # label(fact_743_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 761 (all A_36 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_36),one_one_int) = A_36) # label(fact_744_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 762 (all A_36 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_36),one_one_nat) = A_36) # label(fact_745_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 763 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f957591787ol_nat(finite_card_int,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_746_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 764 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_card_nat,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_747_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 765 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_f1676271015ol_nat(finite1401757860_state,A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))))))) # label(fact_748_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 766 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))) # label(fact_749_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 767 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))) # label(fact_750_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 768 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))))) # label(fact_751_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 769 (all X_5 all Y_4 all Z_4 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_5),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y_4),Z_4)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_5),Y_4)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_5),Z_4))) # label(fact_752_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 770 (all X_5 all Y_4 all Z_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_4),Z_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_5),Y_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_5),Z_4))) # label(fact_753_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 771 (all Ca all D_1 all A_1 all B_2 (A_1 != B_2 & Ca != D_1 <-> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Ca)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),D_1)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),D_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Ca)))) # label(fact_754_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 772 (all Ca all D_1 all A_1 all B_2 (A_1 != B_2 & Ca != D_1 <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_1),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_2),D_1)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_1),D_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_2),Ca)))) # label(fact_755_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 773 (all A_35 all B_28 all C_24 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_35),B_28)),C_24) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_35),C_24)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_28),C_24))) # label(fact_756_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 774 (all A_35 all B_28 all C_24 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_35),B_28)),C_24) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_35),C_24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_28),C_24))) # label(fact_757_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 775 (all A_34 all B_27 all C_23 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_34),B_27)),C_23) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_34),C_23)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_27),C_23))) # label(fact_758_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 776 (all A_34 all B_27 all C_23 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_34),B_27)),C_23) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_34),C_23)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_27),C_23))) # label(fact_759_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 777 (all A_33 all M_7 all B_26 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_33),M_7)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_26),M_7)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_33),B_26)),M_7)) # label(fact_760_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 778 (all A_33 all M_7 all B_26 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_33),M_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_26),M_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_33),B_26)),M_7)) # label(fact_761_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 779 (all A_32 all E_1 all B_25 all C_22 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_32),E_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_25),E_1)),C_22)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_32),B_25)),E_1)),C_22)) # label(fact_762_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 780 (all A_32 all E_1 all B_25 all C_22 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_32),E_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_25),E_1)),C_22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_32),B_25)),E_1)),C_22)) # label(fact_763_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 781 (all W all Y_1 all X_1 all Z_1 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Y_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Z_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_1)) <-> W = X_1 | Y_1 = Z_1)) # label(fact_764_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 782 (all W all Y_1 all X_1 all Z_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,W),Y_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),Z_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,W),Z_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),Y_1)) <-> W = X_1 | Y_1 = Z_1)) # label(fact_765_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 783 (all A_31 all C_21 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_31),C_21) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_21),A_31)) # label(fact_766_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 784 (all A_31 all C_21 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_31),C_21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_21),A_31)) # label(fact_767_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 785 (all A_30 all C_20 all D_9 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_30),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_20),D_9)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_20),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_30),D_9))) # label(fact_768_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 786 (all A_30 all C_20 all D_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_30),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_20),D_9)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_20),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_30),D_9))) # label(fact_769_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 787 (all A_29 all C_19 all D_8 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_29),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_19),D_8)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_29),C_19)),D_8)) # label(fact_770_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 788 (all A_29 all C_19 all D_8 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_29),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_19),D_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_29),C_19)),D_8)) # label(fact_771_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 789 (all A_28 all B_24 all C_18 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_28),B_24)),C_18) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_28),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_24),C_18))) # label(fact_772_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 790 (all A_28 all B_24 all C_18 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_28),B_24)),C_18) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_28),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_24),C_18))) # label(fact_773_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 791 (all A_27 all B_23 all C_17 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_27),B_23)),C_17) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_27),C_17)),B_23)) # label(fact_774_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 792 (all A_27 all B_23 all C_17 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_27),B_23)),C_17) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_27),C_17)),B_23)) # label(fact_775_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 793 (all A_26 all B_22 all C_16 all D_7 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_26),B_22)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_16),D_7)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_26),C_16)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_22),D_7))) # label(fact_776_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 794 (all A_26 all B_22 all C_16 all D_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_26),B_22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_16),D_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_26),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_22),D_7))) # label(fact_777_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 795 (all B_21 all A_25 all C_15 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_21),A_25) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_15),A_25) -> B_21 = C_15)) # label(fact_778_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 796 (all B_21 all A_25 all C_15 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_21),A_25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_15),A_25) -> B_21 = C_15)) # label(fact_779_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 797 (all A_24 all B_20 all C_14 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_24),B_20) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_24),C_14) -> B_20 = C_14)) # label(fact_780_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 798 (all A_24 all B_20 all C_14 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_24),B_20) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_24),C_14) -> B_20 = C_14)) # label(fact_781_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 799 (all A_23 all B_19 all C_13 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_23),B_19) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_23),C_13) -> B_19 = C_13)) # label(fact_782_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 800 (all A_23 all B_19 all C_13 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_23),B_19) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_23),C_13) -> B_19 = C_13)) # label(fact_783_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 801 (all B_2 all A_1 all Ca (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_2),A_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_1) <-> B_2 = Ca)) # label(fact_784_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 802 (all B_2 all A_1 all Ca (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),A_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_1) <-> B_2 = Ca)) # label(fact_785_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 803 (all A_1 all B_2 all Ca (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),B_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),Ca) <-> B_2 = Ca)) # label(fact_786_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 804 (all A_1 all B_2 all Ca (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),B_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),Ca) <-> B_2 = Ca)) # label(fact_787_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 805 (all A_22 all B_18 all C_12 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_22),B_18)),C_12) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_22),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_18),C_12))) # label(fact_788_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 806 (all A_22 all B_18 all C_12 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_22),B_18)),C_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_18),C_12))) # label(fact_789_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 807 (all M all K all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K) <-> M = N)) # label(fact_790_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 808 (all K all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N) <-> M = N)) # label(fact_791_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 809 (all M_1 all N_1 all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1))) # label(fact_792_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 810 (all X all Y all Z hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z))) # label(fact_793_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 811 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)) # label(fact_794_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 812 (all A_1 all Ca all B_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_2),Ca))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2)))) # label(fact_795_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 813 (all A_1 all Ca all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),Ca))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2)))) # label(fact_796_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 814 (all Ca all A_1 all B_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),B_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),B_2)))) # label(fact_797_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 815 (all Ca all A_1 all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),B_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),B_2)))) # label(fact_798_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 816 (all C_11 all A_21 all B_17 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_21),B_17)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_21),C_11)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_17),C_11))))) # label(fact_799_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 817 (all C_11 all A_21 all B_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_21),C_11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_17),C_11))))) # label(fact_800_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 818 (all C_10 all A_20 all B_16 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_20),B_16)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_10),A_20)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_10),B_16))))) # label(fact_801_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 819 (all C_10 all A_20 all B_16 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_16)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_20)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_16))))) # label(fact_802_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 820 (all C_9 all D_6 all A_19 all B_15 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),B_15)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_9),D_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_19),C_9)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_15),D_6)))))) # label(fact_803_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 821 (all C_9 all D_6 all A_19 all B_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),B_15)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_9),D_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_6)))))) # label(fact_804_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 822 (all A_18 all C_8 all B_14 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_18),C_8)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_14),C_8))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_18),B_14)))) # label(fact_805_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 823 (all A_18 all C_8 all B_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),C_8))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_18),B_14)))) # label(fact_806_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 824 (all C_7 all A_17 all B_13 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_7),A_17)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_7),B_13))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_17),B_13)))) # label(fact_807_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 825 (all C_7 all A_17 all B_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_17)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_13))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),B_13)))) # label(fact_808_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 826 (all C_6 all A_16 all B_12 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_16)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),B_12))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_16),B_12)))) # label(fact_809_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 827 (all C_6 all A_16 all B_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),B_12))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_16),B_12)))) # label(fact_810_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 828 (all A_15 all C_5 all B_11 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_15),C_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_11),C_5))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_15),B_11)))) # label(fact_811_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 829 (all A_15 all C_5 all B_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_15),C_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_5))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_15),B_11)))) # label(fact_812_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 830 (all C_4 all D_5 all A_14 all B_10 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_14),B_10)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_4),D_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_14),C_4)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_10),D_5)))))) # label(fact_813_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 831 (all C_4 all D_5 all A_14 all B_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_14),B_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_4),D_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_10),D_5)))))) # label(fact_814_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 832 (all C_3 all A_13 all B_9 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_13),B_9)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_3),A_13)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_3),B_9))))) # label(fact_815_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 833 (all C_3 all A_13 all B_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_13),B_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_3),A_13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_3),B_9))))) # label(fact_816_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 834 (all C_2 all A_12 all B_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_12),B_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),C_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_8),C_2))))) # label(fact_817_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 835 (all C_2 all A_12 all B_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_12),B_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),C_2))))) # label(fact_818_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 836 (all Ca all A_1 all B_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),B_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),B_2)))) # label(fact_819_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 837 (all Ca all A_1 all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),B_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)))) # label(fact_820_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 838 (all A_1 all Ca all B_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_2),Ca))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),B_2)))) # label(fact_821_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 839 (all A_1 all Ca all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),Ca))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)))) # label(fact_822_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 840 (all A_11 all B_7 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),B_7)),B_7) = A_11) # label(fact_823_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 841 (all A_10 all B_6 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_10),B_6)),B_6) = A_10) # label(fact_824_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 842 (all I_1 all J all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)))) # label(fact_825_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 843 (all M_1 all N_1 all K_1 all L_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),L_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))))) # label(fact_826_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 844 (all K_1 all L_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))))) # label(fact_827_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 845 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))))) # label(fact_828_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 846 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))))) # label(fact_829_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 847 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))))) # label(fact_830_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 848 (all K all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_831_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 849 (all J all I_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),I_1))) # label(fact_832_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 850 (all I_1 all J -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),I_1))) # label(fact_833_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 851 (all Y all X all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_834_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 852 (all Z all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_835_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 853 (all N_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)))) # label(fact_836_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 854 (all N_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)))) # label(fact_837_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 855 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) <-> (exists K_2 N = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2)))) # label(fact_838_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 856 (all K all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_839_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 857 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))))) # label(fact_840_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 858 (all M_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))))) # label(fact_841_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 859 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))))) # label(fact_842_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 860 (all K_1 all L_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))))) # label(fact_843_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 861 (all M_1 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)))) # label(fact_844_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 862 (all M_1 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_845_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 863 (all M_1 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N_1)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))))) # label(fact_846_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 864 (all Z all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_847_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 865 (all Y all X all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_848_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 866 (all M_1 all K_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) # label(fact_849_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 867 (all K_1 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) # label(fact_850_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 868 (all I_1 all J all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) # label(fact_851_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 869 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)),N_1) = M_1) # label(fact_852_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 870 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),N_1) = M_1) # label(fact_853_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 871 (all K_1 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1))) # label(fact_854_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 872 (all M_1 all N_1 all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1))) # label(fact_855_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 873 (all A_9 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_9),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_9),one_one_int)))) # label(fact_856_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 874 (all A_9 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),one_one_nat)))) # label(fact_857_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 875 (all A_1 all E all Ca all B_2 all D_1 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1) <-> Ca = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_2),A_1)),E)),D_1))) # label(fact_858_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 876 (all A_1 all E all Ca all B_2 all D_1 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1) <-> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2)),E)),Ca) = D_1)) # label(fact_859_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 877 (all A_8 all M_6 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_8),M_6)),M_6) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_8),one_one_int)),M_6)) # label(fact_860_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 878 (all A_8 all M_6 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_8),M_6)),M_6) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_8),one_one_nat)),M_6)) # label(fact_861_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 879 (all M_5 all A_7 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_5),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_7),M_5)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_7),one_one_int)),M_5)) # label(fact_862_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 880 (all M_5 all A_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_7),M_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),one_one_nat)),M_5)) # label(fact_863_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 881 (all M_4 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_4),M_4) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_4)) # label(fact_864_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 882 (all M_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),M_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),M_4)) # label(fact_865_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 883 (all C_1 all D_4 all A_6 all B_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_6),B_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_1),D_4)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_6),C_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_5),D_4)))))) # label(fact_869_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 884 (all C_1 all D_4 all A_6 all B_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_1),D_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_5),D_4)))))) # label(fact_870_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 885 (all C all D_3 all A_5 all B_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_5),B_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),D_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_5),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_4),D_3)))))) # label(fact_871_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 886 (all C all D_3 all A_5 all B_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_5),B_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C),D_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_5),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),D_3)))))) # label(fact_872_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 887 (all A_1 all E all Ca all B_2 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_2),A_1)),E)),D_1))))) # label(fact_873_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 888 (all A_1 all E all Ca all B_2 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2)),E)),Ca)),D_1)))) # label(fact_874_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 889 (all A_1 all E all Ca all B_2 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ca),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_2),A_1)),E)),D_1))))) # label(fact_875_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 890 (all A_1 all E all Ca all B_2 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),E)),D_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),B_2)),E)),Ca)),D_1)))) # label(fact_876_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 891 (all I_2 all J_2 all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_2)))) # label(fact_877_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 892 (all M_1 all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = M_1)) # label(fact_878_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 893 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1))) # label(fact_879_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 894 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1))) # label(fact_880_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 895 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)))) # label(fact_881_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 896 (all K all I_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2) = K <-> J_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),I_2)))) # label(fact_882_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 897 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1) = M_1)) # label(fact_883_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 898 (all I_2 all K all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_2))))) # label(fact_884_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 899 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1))) # label(fact_885_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 900 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = M_1)) # label(fact_886_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 901 (all M_1 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)),K_1))))) # label(fact_887_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 902 (all J_2 all K all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K)),I_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K))))) # label(fact_888_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 903 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J))) # label(fact_889_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 904 (all X_4 all Y_3 (X_4 != Y_3 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_4),Y_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_3),X_4))))) # label(fact_890_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 905 (all A_4 all B_3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_4),B_3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_3),A_4)) # label(fact_891_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 906 (all A_4 all B_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_4),B_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_3),A_4)) # label(fact_892_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 907 (all Lx_6 all Rx_6 all Ry_4 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_6),Ry_4)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_6),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),Ry_4))) # label(fact_893_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 908 (all Lx_6 all Rx_6 all Ry_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_6),Ry_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),Ry_4))) # label(fact_894_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 909 (all Lx_5 all Rx_5 all Ry_3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_5),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_5),Ry_3)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_5),Rx_5)),Ry_3)) # label(fact_895_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 910 (all Lx_5 all Rx_5 all Ry_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_5),Ry_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_5),Rx_5)),Ry_3)) # label(fact_896_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 911 (all Lx_4 all Ly_4 all Rx_4 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_4),Ly_4)),Rx_4) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly_4),Rx_4))) # label(fact_897_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 912 (all Lx_4 all Ly_4 all Rx_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_4),Ly_4)),Rx_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly_4),Rx_4))) # label(fact_898_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 913 (all Lx_3 all Ly_3 all Rx_3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_3),Ly_3)),Rx_3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_3),Rx_3)),Ly_3)) # label(fact_899_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 914 (all Lx_3 all Ly_3 all Rx_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_3),Ly_3)),Rx_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_3),Rx_3)),Ly_3)) # label(fact_900_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 915 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_2),Ly_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_2),Ry_2)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_2),Ry_2)))) # label(fact_901_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 916 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_2),Ly_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_2),Ry_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_2),Ry_2)))) # label(fact_902_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 917 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_1),Ly_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_1),Ry_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_1),Ly_1)),Ry_1))) # label(fact_903_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 918 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_1),Ly_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_1),Ry_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_1),Ly_1)),Ry_1))) # label(fact_904_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 919 (all Lx all Ly all Rx all Ry hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),Ly)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx),Ry)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),Rx)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly),Ry))) # label(fact_905_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 920 (all Lx all Ly all Rx all Ry hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),Ly)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx),Ry)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),Rx)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly),Ry))) # label(fact_906_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 921 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,A_2))))) # label(fact_907_card_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 922 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,A_2))))) # label(fact_908_card_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.99 923 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f1676271015ol_nat(finite1401757860_state,A_2))))) # label(fact_909_card_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 924 (all U_1 all M all N all J_2 all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_2)),U_1)),M)),N))))) # label(fact_910_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 925 (all U_1 all M all N all I_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2)),U_1)),N)))))) # label(fact_911_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 926 (all U_1 all M all N all J_2 all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_2)),U_1)),M)),N))))) # label(fact_912_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 927 (all U_2 all M_1 all N_1 all J all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_2)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_2)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U_2)),M_1)),N_1))) # label(fact_913_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 928 (all U_1 all M all N all J_2 all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_2)),U_1)),M) = N))) # label(fact_914_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 929 (all I_1 all U_2 all J all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_2)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),U_2)),K_1)) # label(fact_915_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 930 (all U_1 all M all N all I_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N) <-> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2)),U_1)),N)))) # label(fact_916_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 931 (all U_2 all M_1 all N_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_2)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_2)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U_2)),N_1)))) # label(fact_917_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 932 (all U_1 all M all N all I_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_2)),U_1)),N)))))) # label(fact_918_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 933 (all M all K all F ((all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)))))) # label(fact_919_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 934 (all V_1 all U all Y_2 all X_3 all A_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_3),A_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_2),A_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_1)) -> (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U),V_1) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U),X_3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_1),Y_2))),A_3)))))))) # label(fact_920_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 935 (all X_1 all A_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A_2)) -> hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,A_2)))) # label(fact_921_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 936 (all X_1 all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,A_2)))) # label(fact_922_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 937 (all X_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) -> (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A_2)) -> hAPP_nat_nat(suc,hAPP_f1676271015ol_nat(finite1401757860_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) = hAPP_f1676271015ol_nat(finite1401757860_state,A_2)))) # label(fact_923_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 938 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_924_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 939 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_925_le0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 940 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1)))) # label(fact_926_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 941 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1))))) # label(fact_927_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 942 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1)))) # label(fact_928_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 943 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N = zero_zero_nat | M = zero_zero_nat & N = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_929_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 944 (all M all N (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N = zero_zero_nat | M = zero_zero_nat & N = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_930_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 945 (all K all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N) <-> K = zero_zero_nat | M = N)) # label(fact_931_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 946 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))))) # label(fact_932_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 947 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | M = N)) # label(fact_933_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 948 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_934_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 949 (all N all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) <-> N = M))) # label(fact_935_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 950 (all N_1 all M_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_1))) -> M_1 = N_1))) # label(fact_936_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 951 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))))) # label(fact_937_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 952 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> (hAPP_nat_nat(suc,M_1) != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N_1))))) # label(fact_938_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 953 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1))))) # label(fact_939_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 954 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> M_1 = N_1))) # label(fact_940_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 955 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_941_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 956 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_942_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 957 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) # label(fact_943_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 958 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) # label(fact_944_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 959 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N_1))) # label(fact_945_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 960 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_946_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 961 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> M_1 = hAPP_nat_nat(suc,N_1)))) # label(fact_947_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 962 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_1))))) # label(fact_948_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 963 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),hAPP_nat_nat(suc,M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)))) # label(fact_949_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 964 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) | M = hAPP_nat_nat(suc,N))) # label(fact_950_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 965 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M)))) # label(fact_951_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 966 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1))) # label(fact_952_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 967 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) # label(fact_953_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 968 (all M_1 all N_1 all K_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),K_1)) # label(fact_954_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 969 (all K all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),N) <-> M = N)) # label(fact_955_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 970 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_956_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 971 (all N (N != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_957_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 972 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_958_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 973 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> N_1 != zero_zero_nat)) # label(fact_959_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 974 (all N_1 (N_1 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_960_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 975 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1) # label(fact_961_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 976 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),zero_zero_nat) = M_1) # label(fact_962_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 977 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = zero_zero_nat <-> M = zero_zero_nat & N = zero_zero_nat)) # label(fact_963_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 978 (all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = M_1 -> N_1 = zero_zero_nat)) # label(fact_964_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 979 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),zero_zero_nat)) <-> N = zero_zero_nat)) # label(fact_965_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 980 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_966_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 981 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N_1) = zero_zero_nat) # label(fact_967_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 982 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),zero_zero_nat) = M_1) # label(fact_968_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 983 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),M_1) = zero_zero_nat) # label(fact_969_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 984 (all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) = zero_zero_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M_1) = zero_zero_nat -> M_1 = N_1))) # label(fact_970_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 985 (all M all K all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K) <-> M = N | K = zero_zero_nat)) # label(fact_971_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 986 (all K all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N) <-> M = N | K = zero_zero_nat)) # label(fact_972_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 987 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = zero_zero_nat <-> M = zero_zero_nat | N = zero_zero_nat)) # label(fact_973_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 988 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),zero_zero_nat) = zero_zero_nat) # label(fact_974_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 989 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N_1) = zero_zero_nat) # label(fact_975_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 990 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_976_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 991 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_977_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 992 (all M_1 hAPP_nat_nat(suc,M_1) != zero_zero_nat) # label(fact_978_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 993 (all M_1 zero_zero_nat != hAPP_nat_nat(suc,M_1)) # label(fact_979_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 994 (all Nat_4 all Nat_3 (hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3) <-> Nat_4 = Nat_3)) # label(fact_980_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 995 (all N_1 hAPP_nat_nat(suc,N_1) != N_1) # label(fact_981_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 996 (all Nat_2 hAPP_nat_nat(suc,Nat_2) != zero_zero_nat) # label(fact_982_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 997 (all M_1 hAPP_nat_nat(suc,M_1) != zero_zero_nat) # label(fact_983_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 998 (all N_1 N_1 != hAPP_nat_nat(suc,N_1)) # label(fact_984_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 999 (all Nat_1 zero_zero_nat != hAPP_nat_nat(suc,Nat_1)) # label(fact_985_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1000 (all M_1 zero_zero_nat != hAPP_nat_nat(suc,M_1)) # label(fact_986_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1001 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) <-> (exists M_2 N = hAPP_nat_nat(suc,M_2)))) # label(fact_987_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1002 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,zero_zero_nat))) <-> N = zero_zero_nat)) # label(fact_988_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1003 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) <-> M = zero_zero_nat | (exists J_1 (M = hAPP_nat_nat(suc,J_1) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),N)))))) # label(fact_989_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1004 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)))) # label(fact_990_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1005 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)))))) # label(fact_991_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1006 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),M_1)))))) # label(fact_992_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1007 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)))))) # label(fact_993_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1008 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(suc,zero_zero_nat))) = N_1)) # label(fact_994_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1009 (all I_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(suc,I_1))),N_1)))) # label(fact_995_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1010 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)) = N_1)) # label(fact_997_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1011 (all I_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),M_1))))) # label(fact_998_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1012 (all I_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),I_1))))) # label(fact_999_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1013 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) <-> (exists K_2 N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2))))) # label(fact_1000_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1014 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_1001_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1015 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) <-> N = M))) # label(fact_1002_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1016 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)))) # label(fact_1003_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1017 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))))) # label(fact_1004_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1018 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1005_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1019 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1006_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1020 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M)))) # label(fact_1007_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1021 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),hAPP_nat_nat(suc,M_1)))) # label(fact_1008_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1022 (all K all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1009_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1023 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) # label(fact_1010_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1024 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) # label(fact_1011_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1025 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)))) # label(fact_1012_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1026 (all K all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1013_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1027 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N_1)),one_one_nat) = N_1) # label(fact_1014_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1028 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_1015_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1029 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1016_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1030 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),M_1))))) # label(fact_1017_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1031 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J)))))) # label(fact_1018_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1032 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1)))))) # label(fact_1019_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1033 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1020_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1034 (all K all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1021_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1035 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_1022_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1036 (all M all N all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_1023_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1037 (all M all N all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N) <-> M = N))) # label(fact_1024_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1038 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)) = zero_zero_nat) # label(fact_1025_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1039 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) = zero_zero_nat)) # label(fact_1026_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1040 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1027_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1041 (all M_1 all N_1 (M_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) -> N_1 = one_one_nat | M_1 = zero_zero_nat)) # label(fact_1028_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1042 (all M_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(suc,J)))) # label(fact_1029_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1043 (all M_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)))) # label(fact_1030_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1044 (all Pa all A_1 all B_2 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),B_2))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))) & (all D_2 (A_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),D_2) -> hBOOL(hAPP_nat_bool(Pa,D_2)))))) # label(fact_1031_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1045 (all Pa all A_1 all B_2 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),B_2))) <-> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)) & -hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) | (exists D_2 (A_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_2),D_2) & -hBOOL(hAPP_nat_bool(Pa,D_2))))))) # label(fact_1032_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1046 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))))) # label(fact_1033_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1047 (all K all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))))) # label(fact_1034_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1048 (all M all N all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))))) # label(fact_1035_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1049 (all N all Pa (-hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(Pa,N)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),N)) & (all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2)) -> -hBOOL(hAPP_nat_bool(Pa,I)))) & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat)))))))) # label(fact_1036_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1050 (all N_1 all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = zero_zero_nat) & (M_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1))))) # label(fact_1037_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1051 (all N_1 all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = N_1) & (M_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1))))) # label(fact_1038_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1052 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1)) # label(fact_1040_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1053 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)) # label(fact_1041_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1054 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1)) # label(fact_1042_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1055 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)))) # label(fact_1043_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1056 (all Pa all I_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) -> (hBOOL(hAPP_nat_bool(Pa,J_2)) -> ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I))) -> hBOOL(hAPP_nat_bool(Pa,I))))) -> hBOOL(hAPP_nat_bool(Pa,I_2)))))) # label(fact_1044_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1057 (all N all Pa (-hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(Pa,N)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) & (all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)) -> -hBOOL(hAPP_nat_bool(Pa,I)))) & hBOOL(hAPP_nat_bool(Pa,K_2))))))) # label(fact_1045_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1058 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> (exists K_2 N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2))))) # label(fact_1046_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1059 (all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) & hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_2) = J)))) # label(fact_1047_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1060 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (exists M_2 N_1 = hAPP_nat_nat(suc,M_2)))) # label(fact_1048_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1061 (all I_2 all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N_2 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))) -> hBOOL(hAPP_nat_bool(Pa,N_2)))) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K),I_2)))))) # label(fact_1049_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1062 (all N_1 all M_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_3)) -> (exists M_2 M_3 = hAPP_nat_nat(suc,M_2)))) # label(fact_1050_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1063 (all I_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)) -> (K_1 != hAPP_nat_nat(suc,I_1) -> -(all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) -> K_1 != hAPP_nat_nat(suc,J_1)))))) # label(fact_1051_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1064 (all I_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1)) -> -(all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) -> K_1 != hAPP_nat_nat(suc,J_1))))) # label(fact_1052_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1065 (all N_1 (N_1 != zero_zero_nat -> (exists M_2 N_1 = hAPP_nat_nat(suc,M_2)))) # label(fact_1053_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1066 (all Y (Y != zero_zero_nat -> -(all Nat Y != hAPP_nat_nat(suc,Nat)))) # label(fact_1054_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1067 (all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N_2 (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))) -> hBOOL(hAPP_nat_bool(Pa,N_2)))) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))))) # label(fact_1055_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1068 (all N all Pa (hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> ((all N_2 (hBOOL(hAPP_nat_bool(Pa,N_2)) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))))) -> hBOOL(hAPP_nat_bool(Pa,N))))) # label(fact_1056_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1069 (all Com1_2 all Com2_2 com_size(semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1_2)),com_size(Com2_2))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1057_com_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1070 (all Com1_2 all Com2_2 size_size_com(semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com1_2)),size_size_com(Com2_2))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1058_com_Osize_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1071 (all Fun_1 all Com1 all Com2 com_size(cond(Fun_1,Com1,Com2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1)),com_size(Com2))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1061_com_Osize_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1072 (all Fun all Com1_1 all Com2_1 all Com1 all Com2 cond(Fun,Com1_1,Com2_1) != semi(Com1,Com2)) # label(fact_1062_com_Osimps_I45_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1073 (all Com1 all Com2 all Fun all Com1_1 all Com2_1 semi(Com1,Com2) != cond(Fun,Com1_1,Com2_1)) # label(fact_1063_com_Osimps_I44_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1074 (all Fun all Com1_1 all Com2_1 cond(Fun,Com1_1,Com2_1) != skip) # label(fact_1064_com_Osimps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1075 (all Fun all Com1_1 all Com2_1 skip != cond(Fun,Com1_1,Com2_1)) # label(fact_1065_com_Osimps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1076 (all Fun_1 all Com1 all Com2 all Fun all Com1_1 all Com2_1 (cond(Fun_1,Com1,Com2) = cond(Fun,Com1_1,Com2_1) <-> Fun_1 = Fun & Com1 = Com1_1 & Com2 = Com2_1)) # label(fact_1066_com_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1077 (all Fun_1 all Com1 all Com2 size_size_com(cond(Fun_1,Com1,Com2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com1)),size_size_com(Com2))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1067_com_Osize_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1078 (all Loc all Fun_1 all Com_1 size_size_com(local(Loc,Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1068_com_Osize_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1079 (all Loc all Fun_1 all Com_1 com_size(local(Loc,Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1069_com_Osize_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1080 (all Loc all Fun_1 all Com_1 all Fun all Com1_1 all Com2_1 local(Loc,Fun_1,Com_1) != cond(Fun,Com1_1,Com2_1)) # label(fact_1070_com_Osimps_I36_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1081 (all Fun all Com1_1 all Com2_1 all Loc all Fun_1 all Com_1 cond(Fun,Com1_1,Com2_1) != local(Loc,Fun_1,Com_1)) # label(fact_1071_com_Osimps_I37_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1082 (all Loc all Fun_1 all Com_1 all Loc_1 all Fun all Com (is_loc(Loc) & is_loc(Loc_1) -> (local(Loc,Fun_1,Com_1) = local(Loc_1,Fun,Com) <-> Loc = Loc_1 & Fun_1 = Fun & Com_1 = Com))) # label(fact_1072_com_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1083 (all Loc_1 all Fun all Com skip != local(Loc_1,Fun,Com)) # label(fact_1073_com_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1084 (all Loc_1 all Fun all Com local(Loc_1,Fun,Com) != skip) # label(fact_1074_com_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1085 (all Com1_1 all Com2_1 all Loc all Fun_1 all Com_1 semi(Com1_1,Com2_1) != local(Loc,Fun_1,Com_1)) # label(fact_1075_com_Osimps_I35_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1086 (all Loc all Fun_1 all Com_1 all Com1_1 all Com2_1 local(Loc,Fun_1,Com_1) != semi(Com1_1,Com2_1)) # label(fact_1076_com_Osimps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1087 (all Fun_1 all Com_1 com_size(while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1077_com_Osize_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1088 (all Fun_1 all Com_1 size_size_com(while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_com(Com_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1078_com_Osize_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1089 (all Fun all Com all Loc all Fun_1 all Com_1 while(Fun,Com) != local(Loc,Fun_1,Com_1)) # label(fact_1079_com_Osimps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1090 (all Loc all Fun_1 all Com_1 all Fun all Com local(Loc,Fun_1,Com_1) != while(Fun,Com)) # label(fact_1080_com_Osimps_I38_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1091 (all Fun all Com all Com1 all Com2 while(Fun,Com) != semi(Com1,Com2)) # label(fact_1081_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1092 (all Com1 all Com2 all Fun all Com semi(Com1,Com2) != while(Fun,Com)) # label(fact_1082_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1093 (all Fun all Com while(Fun,Com) != skip) # label(fact_1083_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1094 (all Fun all Com skip != while(Fun,Com)) # label(fact_1084_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1095 (all Fun_1 all Com_1 all Fun all Com (while(Fun_1,Com_1) = while(Fun,Com) <-> Fun_1 = Fun & Com_1 = Com)) # label(fact_1085_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1096 (all Fun all Com all Fun_1 all Com1 all Com2 while(Fun,Com) != cond(Fun_1,Com1,Com2)) # label(fact_1086_com_Osimps_I53_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1097 (all Fun_1 all Com1 all Com2 all Fun all Com cond(Fun_1,Com1,Com2) != while(Fun,Com)) # label(fact_1087_com_Osimps_I52_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1098 (all V (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,V))) -> hAPP_int_nat(number_number_of_nat,V) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(number_number_of_nat,V)),one_one_nat)))) # label(fact_1088_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1099 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_1),N_1))) # label(fact_1089_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1100 (all M_1 all I_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),I_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_1),N_1)),I_1)) # label(fact_1090_min__diff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1101 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,zero_zero_nat),N_1) = zero_zero_nat) # label(fact_1091_min__0L) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1102 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N_1),zero_zero_nat) = zero_zero_nat) # label(fact_1092_min__0R) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1103 (all V all W_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V)),hAPP_int_int(number_number_of_int,W_1)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),W_1))) # label(fact_1093_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1104 (all V all W_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V)),hAPP_int_int(number_number_of_int,W_1)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V),W_1))) # label(fact_1094_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1105 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,K)),hAPP_int_int(number_number_of_int,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)))) # label(fact_1095_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1106 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,K)),hAPP_int_int(number_number_of_int,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)))) # label(fact_1096_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1107 (all Z hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),Z) = Z) # label(fact_1097_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1108 (all Z hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),one_one_int) = Z) # label(fact_1098_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1109 (all W all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_1),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1)))) # label(fact_1099_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1110 (all Z all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z)) -> Z = W_1))) # label(fact_1100_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1111 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),K_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1))))) # label(fact_1101_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1112 (all Z all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z)))) # label(fact_1102_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1113 (all W_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),W_1))) # label(fact_1103_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1114 (all X all Y (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),Y)) | X = Y | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),X)))) # label(fact_1104_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1115 (all Z_1 all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W)) & Z_1 != W)) # label(fact_1105_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1116 (all Z1 all Z2 all Z3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),Z3))) # label(fact_1106_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1117 (all Z all W_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),W_1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z)) # label(fact_1107_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1118 (all W_1 all Z1 all Z2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z2))) # label(fact_1108_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1119 (all Z1 all Z2 all W_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)),W_1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W_1))) # label(fact_1109_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1120 (all Z1 all Z2 all Z3 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z2),Z3))) # label(fact_1110_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1121 (all X all Y all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Z))) # label(fact_1111_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1122 (all Z all W_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),W_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),Z)) # label(fact_1112_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1123 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),J))))) # label(fact_1113_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1124 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_1),K_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,J),K_1))))) # label(fact_1114_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1125 (all Z_3 all Z all W_2 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_2),W_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_3),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_2),Z_3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),Z)))))) # label(fact_1115_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1126 (all W all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z_1)))) # label(fact_1116_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1127 (all W all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),one_one_int)),Z_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1)))) # label(fact_1117_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1128 (all W_1 all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),one_one_int)),Z)))) # label(fact_1118_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1129 (all W all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1)) | W = Z_1)) # label(fact_1119_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.00 1130 (all Z1 all Z2 all W_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),W_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W_1))) # label(fact_1120_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1131 (all W_1 all Z1 all Z2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z2))) # label(fact_1121_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1132 (all N all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),N) = one_one_int <-> M = one_one_int & N = one_one_int))) # label(fact_1123_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1133 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1)))) # label(fact_1124_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1134 (all K all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),L)),zero_zero_int)))) # label(fact_1125_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1135 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),J)))))) # label(fact_1126_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1136 (all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),zero_zero_int) = Z) # label(fact_1127_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1137 (all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),Z) = Z) # label(fact_1128_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1138 (all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z))))) # label(fact_1129_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1139 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_1)),Z_1)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)))) # label(fact_1130_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1140 (all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z)),Z) != zero_zero_int) # label(fact_1131_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1141 (all B_1 all Q_2 all R_2 all B all Q_1 all R_1 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2))))))))) # label(fact_1132_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1142 (all B_1 all Q_1 all R_1 all Q_2 all R_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1))))))) # label(fact_1133_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1143 (all K_1 hAPP_int_int(number_number_of_int,K_1) = K_1) # label(fact_1134_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1144 (all R_2 all Q_2 all A (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) -> (A = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A),Q_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),one_one_int)))))) # label(fact_1136_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1145 (all R_2 all Q_2 all A (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) -> (A = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A),Q_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),A)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_2)))))) # label(fact_1137_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1146 (all B all Q_1 all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_1)))))) # label(fact_1138_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1147 (all B all Q_1 all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),zero_zero_int)))))) # label(fact_1139_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1148 (all B_1 all Q_1 all R_1 all Q_2 all R_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2))))))) # label(fact_1140_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1149 (all B_1 all Q_2 all R_2 all B all Q_1 all R_1 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B),Q_1)),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1))))))))) # label(fact_1141_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1150 (all Pa all I_2 all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K)) -> (hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),one_one_int))) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),K)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1142_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1151 (all Pa all I_2 all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K)) -> (hBOOL(hAPP_int_bool(Pa,K)) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1143_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1152 (all Pa all K all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I_2)) -> (hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K),one_one_int))) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1144_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1153 (all Pa all K all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I_2)) -> (hBOOL(hAPP_int_bool(Pa,K)) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1145_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1154 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)))))) # label(fact_1146_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1155 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_1149_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1156 (all K all Pa all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K)) -> (all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))))))))) # label(fact_1150_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1157 (all K all Pa all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K)) -> (all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))))))))) # label(fact_1151_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1158 (all P_1 all Pa all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(Pa) <-> hBOOL(P_1))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(Pa)) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P_1))))) # label(fact_1152_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1159 (all P_1 all Pa all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(Pa) <-> hBOOL(P_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(Pa) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P_1)))) # label(fact_1153_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1160 (all I_2 all Pa all K (hBOOL(hAPP_int_bool(Pa,K)) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))))) -> ((all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K)) -> (hBOOL(hAPP_int_bool(Pa,I)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_2)))))) # label(fact_1154_int__induct) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1161 (all Pa all P_1 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 all K_2 (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))))) -> ((exists Z_2 all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),X_2)) -> (hBOOL(hAPP_int_bool(Pa,X_2)) <-> hBOOL(hAPP_int_bool(P_1,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(Pa,X1)))))))) # label(fact_1155_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1162 (all Pa all P1 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((all X_2 all K_2 (hBOOL(hAPP_int_bool(P1,X_2)) <-> hBOOL(hAPP_int_bool(P1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))))) -> ((exists Z_2 all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z_2)) -> (hBOOL(hAPP_int_bool(Pa,X_2)) <-> hBOOL(hAPP_int_bool(P1,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(Pa,X1)))))))) # label(fact_1156_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1163 (all Y all X ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = zero_zero_int))) # label(fact_1157_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1164 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y)))))) # label(fact_1158_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1165 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y))) # label(fact_1159_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1166 (all Z all X all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D)))))) # label(fact_1160_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1167 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X),Y))) # label(fact_1161_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1168 (all Z hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z)))) # label(fact_1162_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1169 (all Pa ((exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) & hBOOL(hAPP_int_bool(Pa,X_2)))) <-> (exists X_2 hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_1163_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1170 (all Pa ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> hBOOL(hAPP_int_bool(Pa,X_2)))) <-> (all X_2 hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_1164_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1171 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)))) # label(fact_1167_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1172 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)))) # label(fact_1168_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1173 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y))) # label(fact_1169_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1174 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Y))) # label(fact_1170_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1175 (all M_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M_1))) # label(fact_1171_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1176 (all W all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1)) <-> (exists N_2 Z_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_2)))))) # label(fact_1173_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1177 (all M all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1174_zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1178 (all M all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1175_zless__int) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1179 (all M_1 all N_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) # label(fact_1176_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1180 (all M_1 all N_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1))) # label(fact_1177_int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1181 (all M_1 all N_1 all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,N_1)),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))),Z)) # label(fact_1178_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1182 (all M_1 all N_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) # label(fact_1179_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1183 (all W all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z_1)) <-> (exists N_2 Z_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),hAPP_nat_int(semiri1621563631at_int,N_2))))) # label(fact_1180_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1184 (all M_1 hAPP_int_int(abs_abs_int,hAPP_nat_int(semiri1621563631at_int,M_1)) = hAPP_nat_int(semiri1621563631at_int,M_1)) # label(fact_1181_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1185 (all N (hAPP_nat_int(semiri1621563631at_int,N) = zero_zero_int <-> N = zero_zero_nat)) # label(fact_1183_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1186 (all K_1 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K_1)),zero_zero_int))) # label(fact_1185_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1187 (all N_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_1186_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1188 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,N)),zero_zero_int)) <-> N = zero_zero_nat)) # label(fact_1187_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1189 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,Z_1)),one_one_int)) <-> Z_1 = zero_zero_int)) # label(fact_1188_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1190 (all M_1 all N_1 (hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1)) = one_one_int -> hAPP_int_int(abs_abs_int,M_1) = one_one_int)) # label(fact_1189_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1191 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)))) # label(fact_1190_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1192 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_1191_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1193 (all K_1 all I_1 all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),J)))))) # label(fact_1192_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1194 (all Pa all X_1 all Y_1 (hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_1)))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))))) & (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) -> hBOOL(hAPP_int_bool(Pa,zero_zero_int))))) # label(fact_1193_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1195 (all X all Z all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D))),Z)))) # label(fact_1194_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1196 (all K all F all N ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),N)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,N))) -> (exists I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) & hAPP_nat_int(F,I) = K)))))) # label(fact_1195_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1197 (all K all F all N ((all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),N)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,N))) -> (exists I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) & hAPP_nat_int(F,I) = K)))))) # label(fact_1196_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1198 (all X_1 all Y_1 (hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,Y_1) <-> X_1 = Y_1)) # label(fact_1197_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1199 (all X_1 all Y_1 all Pa ((hBOOL(Pa) -> hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1))) & (-hBOOL(Pa) -> hAPP_nat_int(semiri1621563631at_int,Y_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1))))) # label(fact_1198_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1200 (all M all N (hAPP_nat_int(semiri1621563631at_int,M) = hAPP_nat_int(semiri1621563631at_int,N) <-> M = N)) # label(fact_1199_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1201 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1202 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1203 (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].
% 1.58/2.01 1204 (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].
% 1.58/2.01 1205 (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].
% 1.58/2.01 1206 (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].
% 1.58/2.01 1207 (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].
% 1.58/2.01 1208 (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].
% 1.58/2.01 1209 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1210 (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].
% 1.58/2.01 1211 (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].
% 1.58/2.01 1212 (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].
% 1.58/2.01 1213 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1214 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1215 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1216 (all X all Y (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1217 (all X all Y (X != Y | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1218 (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].
% 1.58/2.01 1219 (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].
% 1.58/2.01 1220 (all P all Q (is_bool(P) -> hAPP_int_bool(cOMBK_bool_int(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1221 (all P all Q (is_bool(P) -> hAPP_nat_bool(cOMBK_bool_nat(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1222 (all P all Q all R hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(P),Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1223 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1224 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(cOMBB_bool_bool_int(P),Q),R) = hAPP_bool_bool(P,hAPP_int_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1225 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_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].
% 1.58/2.01 1226 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(cOMBS_int_bool_bool(P),Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1227 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_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].
% 1.58/2.01 1228 (all X all Y (-hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1229 (all X all Y (X != Y | hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1230 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1231 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1232 (all P all Q all R hAPP_i68813070l_bool(hAPP_f2144054103l_bool(cOMBB_1652995168ol_int(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1233 (all P all Q all R hAPP_n1006566506l_bool(hAPP_f1146629647l_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_001) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1234 (all P all Q (is_bool(P) -> hAPP_H242767318e_bool(cOMBK_988866959_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1235 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBB_325909978_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H242767318e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1236 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBS_865875691l_bool(P),Q),R) = hAPP_bool_bool(hAPP_H1270401638l_bool(P,R),hAPP_H242767318e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.58/2.01 1237 (all P all Q all R hAPP_H1270401638l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H242767318e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_002) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.87 1238 (all P all Q all R hAPP_H242767318e_bool(hAPP_H216526335e_bool(cOMBC_1967329268e_bool(P),Q),R) = hAPP_H242767318e_bool(hAPP_H216526335e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.87 1239 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBC_538205282l_bool(P),Q),R) = hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___003) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.87
% 2.63/2.87 ============================== end of process non-clausal formulas ===
% 2.63/2.87
% 2.63/2.87 ============================== PROCESS INITIAL CLAUSES ===============
% 2.63/2.87
% 2.63/2.87 ============================== PREDICATE ELIMINATION =================
% 2.63/2.87
% 2.63/2.87 ============================== end predicate elimination =============
% 2.63/2.87
% 2.63/2.87 Auto_denials: (non-Horn, no changes).
% 2.63/2.87
% 2.63/2.87 Term ordering decisions:
% 2.63/2.87 Function symbol KB weights: ord_less_eq_nat=1. ord_less_nat=1. plus_plus_nat=1. times_times_nat=1. ord_less_eq_int=1. ord_le1449778818e_bool=1. plus_plus_int=1. zero_zero_nat=1. times_times_int=1. ord_less_int=1. insert1744391420_state=1. suc=1. insert_int=1. insert_nat=1. bot_bo784226126e_bool=1. minus_minus_nat=1. bot_bot_fun_int_bool=1. bot_bot_fun_nat_bool=1. member_int=1. member_nat=1. member1667945571_state=1. finite_finite_int=1. finite_finite_nat=1. semiri1621563631at_int=1. zero_zero_int=1. finite694102371_state=1. minus_1449998731t_bool=1. minus_2067140911t_bool=1. minus_1805465033e_bool=1. ord_le2137177998e_bool=1. one_one_int=1. minus_minus_int=1. one_one_nat=1. ord_le1568362934t_bool=1. ord_le951220754t_bool=1. finite1401757860_state=1. finite_card_int=1. finite_card_nat=1. bot_bot_bool=1. ord_le1912455174t_bool=1. ord_le382113706t_bool=1. number_number_of_int=1. collec637225377_state=1. minus_minus_bool=1. ord_less_eq_bool=1. abs_abs_int=1. bot_bot_nat=1. collect_int=1. collect_nat=1. fFalse=1. fNot=1. fconj=1. fdisj=1. fimplies=1. ord_min_nat=1. nat_tsub=1. fTrue=1. fequal1440809015_state=1. fequal_int=1. fequal_nat=1. number_number_of_nat=1. ord_less_bool=1. skip=1. c=1. ord_le694194916l_bool=1. p=1. q=1. the_el2080696983_state=1. the_elem_int=1. the_elem_nat=1. hAPP_nat_nat=1. hAPP_nat_bool=1. hAPP_nat_fun_nat_nat=1. hAPP_int_bool=1. hAPP_n1699378549t_bool=1. hAPP_f1378282496l_bool=1. hAPP_int_int=1. hAPP_int_fun_int_int=1. hAPP_i1948725293t_bool=1. hAPP_f448129468l_bool=1. hAPP_f54304608l_bool=1. hAPP_f806699093e_bool=1. hAPP_f1805168059t_bool=1. hAPP_f800510211t_bool=1. hAPP_f849457489l_bool=1. hAPP_H1902130436e_bool=1. hAPP_i1529485324t_bool=1. hAPP_n1512601776t_bool=1. hAPP_i2112223885l_bool=1. hAPP_n215258509l_bool=1. hAPP_nat_int=1. hAPP_H2039996199l_bool=1. hAPP_H242767318e_bool=1. hAPP_f103356543l_bool=1. hAPP_f284875647l_bool=1. hAPP_f22106695ol_nat=1. hAPP_f1223193598t_bool=1. hAPP_f1730770594t_bool=1. hAPP_f1794460506e_bool=1. hAPP_f1676271015ol_nat=1. hAPP_f1594865479ol_int=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. hAPP_f957591787ol_nat=1. finite772772422nt_int=1. finite929467206at_nat=1. hAPP_f166061059ol_int=1. hAPP_i468480167e_bool=1. hAPP_n1497837059e_bool=1. finite1946095968_state=1. hAPP_f718417177_state=1. finite_fold_int_int=1. finite_fold_nat_nat=1. hAPP_H280516760_state=1. hAPP_H574424047_state=1. hAPP_state_bool=1. hAPP_s1806633685e_bool=1. finite1626084323ne_int=1. finite683959609_state=1. finite988810631ne_nat=1. semi=1. while=1. finite416071164_state=1. hAPP_H216526335e_bool=1. finite1432773856em_int=1. finite795500164em_nat=1. finite212984546_state=1. hAPP_f1146629647l_bool=1. hAPP_f2144054103l_bool=1. hAPP_f832587837l_bool=1. hAPP_int_nat=1. big_se1212619424_state=1. big_se275732192ig_nat=1. big_se913005884ig_int=1. hAPP_H1270401638l_bool=1. hAPP_f1410040974l_bool=1. hAPP_i68813070l_bool=1. hAPP_n1006566506l_bool=1. hAPP_f1516997247l_bool=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f114=1. f115=1. f116=1. f117=1. f118=1. f119=1. f132=1. f133=1. f134=1. f135=1. f136=1. f137=1. f138=1. f139=1. f140=1. f168=1. f169=1. f170=1. f171=1. f172=1. f173=1. f174=1. f175=1. f176=1. f187=1. f188=1. f189=1. f190=1. f191=1. f192=1. f193=1. f194=1. f195=1. f196=1. f197=1. f200=1. f204=1. f205=1. f208=1. f210=1. f211=1. f212=1. f215=1. f216=1. f217=1. f220=1. f221=1. f242=1. f243=1. hoare_512830354_state=1. finite1973466193nt_int=1. finite2130160977at_nat=1. com_size=1. size_size_com=1. finite2066257190_state=1. finite_fold1Set_int=1. finite_fold1Set_nat=1. finite1720675051_state=1. finite_fold1_int=1. finite_fold1_nat=1. cOMBB_1015721476ol_nat=1. cOMBB_1291456124_state=1. cOMBB_1652995168ol_int=1. cOMBC_226598744l_bool=1. cOMBC_538205282l_bool=1. cOMBC_94739984l_bool=1. cOMBS_865875691l_bool=1. cOMBS_int_bool_bool=1. cOMBS_nat_bool_bool=1. finite1255650454_state=1. if_nat=1. cOMBB_325909978_state=1. cOMBB_bool_bool_int=1. cOMBB_bool_bool_nat=1. cOMBC_1967329268e_bool=1. cOMBC_int_int_bool=1. cOMBC_nat_nat_bool=1. cOMBK_988866959_state=1. cOMBK_bool_int=1. cOMBK_bool_nat=1. finite1956789438t_bool=1. finite2036162504e_bool=1. finite58652534t_bool=1. hoare_919241616_state=1. powp_H1405539888_state=1. hoare_Mirabelle_MGT=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f29=1. f30=1. f31=1. f35=1. f36=1. f37=1. f38=1. f39=1. f40=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f180=1. f181=1. f182=1. f183=1. f203=1. f213=1. f218=1. f219=1. f238=1. f239=1. f240=1. f241=1. hoare_1191504582_state=1. cond=1. local=1. f108=1. f109=1. f110=1. f111=1. f112=1. f113=1. f120=1. f121=1. f122=1. f123=1. f124=1. f125=1. f147=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f156=1. f157=1. f158=1. f198=1. f199=1. f201=1. f202=1. f206=1. f207=1. f209=1. f214=1. f222=1. f223=1. f224=1. f225=1. f226=1. f227=1. f228=1. f229=1. f230=1. f231=1. f233=1. f234=1. f235=1. f237=1. f244=1. f245=1. f246=1. f247=1. f32=1. f33=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f126=1. f127=1. f128=1. f129=1. f130=1. f131=1. f159=1. f160=1. f161=1. f162=1. f163=1. f164=1. f165=1. f166=1. f167=1. f232=1. f236=1. f1=1. f2=1. f3=1. f4=1. f177=1. f178=1. f179=1. f184=1. f185=1. f186=1. f5=1. f6=1. f7=1. f34=1.
% 7.62/7.87
% 7.62/7.87 ============================== end of process initial clauses ========
% 7.62/7.87
% 7.62/7.87 ============================== CLAUSES FOR SEARCH ====================
% 7.62/7.87
% 7.62/7.87 ============================== end of clauses for search =============
% 7.62/7.87
% 7.62/7.87 ============================== SEARCH ================================
% 7.62/7.87
% 7.62/7.87 % Starting search at 1.10 seconds.
% 7.62/7.87
% 7.62/7.87 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 1.81 sec).
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=43.000, iters=3415
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=39.000, iters=3433
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=36.000, iters=3359
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=35.000, iters=3442
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=34.000, iters=3389
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=32.000, iters=3453
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=31.000, iters=3381
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=30.000, iters=3356
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=29.000, iters=3389
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=28.000, iters=3481
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=27.000, iters=3368
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=26.000, iters=3382
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=25.000, iters=3339
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=24.000, iters=3587
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=23.000, iters=3351
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=22.000, iters=3382
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=21.000, iters=3423
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=20.000, iters=3349
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=19.000, iters=3426
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=18.000, iters=3347
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=17.000, iters=3334
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=16.000, iters=3360
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=15.000, iters=3344
% 7.62/7.87
% 7.62/7.87 Low Water (keep): wt=14.000, Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------