TSTP Solution File: SWW470+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW470+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:05 EDT 2022
% Result : Unknown 278.31s 278.54s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW470+3 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 5 00:11:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.95/2.15 ============================== Prover9 ===============================
% 1.95/2.15 Prover9 (32) version 2009-11A, November 2009.
% 1.95/2.15 Process 28673 was started by sandbox2 on n028.cluster.edu,
% 1.95/2.15 Sun Jun 5 00:11:43 2022
% 1.95/2.15 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28519_n028.cluster.edu".
% 1.95/2.15 ============================== end of head ===========================
% 1.95/2.15
% 1.95/2.15 ============================== INPUT =================================
% 1.95/2.15
% 1.95/2.15 % Reading from file /tmp/Prover9_28519_n028.cluster.edu
% 1.95/2.15
% 1.95/2.15 set(prolog_style_variables).
% 1.95/2.15 set(auto2).
% 1.95/2.15 % set(auto2) -> set(auto).
% 1.95/2.15 % set(auto) -> set(auto_inference).
% 1.95/2.15 % set(auto) -> set(auto_setup).
% 1.95/2.15 % set(auto_setup) -> set(predicate_elim).
% 1.95/2.15 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.95/2.15 % set(auto) -> set(auto_limits).
% 1.95/2.15 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.95/2.15 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.95/2.15 % set(auto) -> set(auto_denials).
% 1.95/2.15 % set(auto) -> set(auto_process).
% 1.95/2.15 % set(auto2) -> assign(new_constants, 1).
% 1.95/2.15 % set(auto2) -> assign(fold_denial_max, 3).
% 1.95/2.15 % set(auto2) -> assign(max_weight, "200.000").
% 1.95/2.15 % set(auto2) -> assign(max_hours, 1).
% 1.95/2.15 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.95/2.15 % set(auto2) -> assign(max_seconds, 0).
% 1.95/2.15 % set(auto2) -> assign(max_minutes, 5).
% 1.95/2.15 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.95/2.15 % set(auto2) -> set(sort_initial_sos).
% 1.95/2.15 % set(auto2) -> assign(sos_limit, -1).
% 1.95/2.15 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.95/2.15 % set(auto2) -> assign(max_megs, 400).
% 1.95/2.15 % set(auto2) -> assign(stats, some).
% 1.95/2.15 % set(auto2) -> clear(echo_input).
% 1.95/2.15 % set(auto2) -> set(quiet).
% 1.95/2.15 % set(auto2) -> clear(print_initial_clauses).
% 1.95/2.15 % set(auto2) -> clear(print_given).
% 1.95/2.15 assign(lrs_ticks,-1).
% 1.95/2.15 assign(sos_limit,10000).
% 1.95/2.15 assign(order,kbo).
% 1.95/2.15 set(lex_order_vars).
% 1.95/2.15 clear(print_given).
% 1.95/2.15
% 1.95/2.15 % formulas(sos). % not echoed (1399 formulas)
% 1.95/2.15
% 1.95/2.15 ============================== end of input ==========================
% 1.95/2.15
% 1.95/2.15 % From the command line: assign(max_seconds, 300).
% 1.95/2.15
% 1.95/2.15 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.95/2.15
% 1.95/2.15 % Formulas that are not ordinary clauses:
% 1.95/2.15 1 (all B_1_1 all B_2_1 is_bool(big_se1603268663iple_a(B_1_1,B_2_1))) # label(gsy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 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].
% 1.95/2.15 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].
% 1.95/2.15 4 (all B_1_1 is_bool(finite1428139793iple_a(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 5 (all B_1_1 is_bool(finite2114894759a_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____uwgpyvfjxg__O_001) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 6 (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].
% 1.95/2.15 7 (all B_1_1 is_bool(finite1321096241t_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Int__Oint_000tc__fun_Itc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 8 (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].
% 1.95/2.15 9 (all B_1_1 is_bool(finite1071749497t_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 10 (all B_1_1 is_bool(finite648855052iple_a(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otri) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 11 (all B_1_1 is_bool(finite1803123436a_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otri_002) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 12 (all B_1_1 is_bool(finite1704255308nt_int(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Int__Oint_000tc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 13 (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].
% 1.95/2.15 14 (all B_1_1 is_bool(finite1860950092at_nat(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Nat__Onat_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 15 (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].
% 1.95/2.15 16 (all B_1_1 all B_2_1 is_bool(finite1753440478iple_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 17 (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].
% 1.95/2.15 18 (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].
% 1.95/2.15 19 (all B_1_1 all B_2_1 is_bool(finite1033474011iple_a(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].
% 1.95/2.15 20 (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].
% 1.95/2.15 21 (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].
% 1.95/2.15 22 (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].
% 1.95/2.15 23 (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].
% 1.95/2.15 24 (all B_1_1 all B_2_1 is_bool(hAPP_H1037229737a_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__HOL__) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 25 (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].
% 1.95/2.15 26 (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].
% 1.95/2.15 27 (all B_1_1 all B_2_1 is_bool(hAPP_f1695230391l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc) # label(hypothesis) # label(non_clause). [assumption].
% 1.95/2.15 28 (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].
% 1.95/2.15 29 (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].
% 1.95/2.15 30 (all B_1_1 all B_2_1 is_bool(hAPP_f2110825313l_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].
% 1.95/2.15 31 (all B_1_1 all B_2_1 is_bool(hAPP_f215623910l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 32 (all B_1_1 all B_2_1 is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 33 (all Ga hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),bot_bo797238721a_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 34 (all Fun1_2 all Com_2 all Fun2_2 all Fun1_1 all Com_1 all Fun2_1 (hoare_1916936827iple_a(Fun1_2,Com_2,Fun2_2) = hoare_1916936827iple_a(Fun1_1,Com_1,Fun2_1) <-> Fun1_2 = Fun1_1 & Com_2 = Com_1 & Fun2_2 = Fun2_1)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 35 (all Ga all G_1 all Ts (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(G_1),Ts)) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),G_1)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts))))) # label(fact_2_cut) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 36 (all Ts all Ga all T_2 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_2),bot_bo797238721a_bool))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_2),Ts)))))) # label(fact_3_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 37 (all Ga all Pa all Ca all Q_1 all C_5 ((hBOOL(C_5) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),Pa))),C_5),Ca,Q_1)),bot_bo797238721a_bool))))) # label(fact_4_constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 38 (all Ga all Ca all Q_1 all Pa ((all Z_11 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_2)),Ca,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(Q_1,Z_11)))),bot_bo797238721a_bool))))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))))) # label(fact_5_escape) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 39 (all Q_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_3)),bot_bo797238721a_bool))) -> ((all Z_11 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_11),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_2)))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 40 (all Pa all Ga all P_2 all Ca all Q_1 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_2,Ca,Q_1)),bot_bo797238721a_bool))) -> ((all Z_11 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_11),S_2)))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 41 (all Q_1 all Pa all Ga all P_2 all Ca all Q_3 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_2,Ca,Q_3)),bot_bo797238721a_bool))) -> ((all Z_11 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2)) -> (all S_3 ((all Z_12 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_12),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_12),S_3)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)))))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))))) # label(fact_8_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 42 (all A_13 all Ba all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),A))) -> (A_13 != Ba -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A))))) # label(fact_9_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 43 (all A_13 all Ba all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),A))) -> (A_13 != Ba -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A))))) # label(fact_10_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 44 (all A_13 all Ba all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),A))) -> (A_13 != Ba -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A))))) # label(fact_11_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 45 (all Ba all A_13 all B ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),B)) -> A_13 = Ba) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),B))))) # label(fact_12_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 46 (all Ba all A_13 all B ((-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),B)) -> A_13 = Ba) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),B))))) # label(fact_13_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 47 (all Ba all A_13 all B ((-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),B)) -> A_13 = Ba) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),B))))) # label(fact_14_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 48 (all A_13 -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),bot_bo797238721a_bool))) # label(fact_15_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 49 (all A_13 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),bot_bot_fun_nat_bool))) # label(fact_16_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 50 (all A_13 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),bot_bot_fun_int_bool))) # label(fact_17_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 51 (all A_13 hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(fequal_nat,A_13)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)) # label(fact_18_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 52 (all A_13 hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(fequal963300192iple_a,A_13)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool)) # label(fact_19_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 53 (all A_13 hAPP_f1805168059t_bool(collect_int,hAPP_i1948725293t_bool(fequal_int,A_13)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)) # label(fact_20_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 54 (all A_13 hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_13)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)) # label(fact_21_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 55 (all A_13 hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_13)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool)) # label(fact_22_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 56 (all A_13 hAPP_f1805168059t_bool(collect_int,hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),A_13)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)) # label(fact_23_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 57 (all Pa all A_13 ((hBOOL(hAPP_nat_bool(Pa,A_13)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(fequal_nat,A_13))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_13)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(fequal_nat,A_13))),Pa)) = bot_bot_fun_nat_bool))) # label(fact_24_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 58 (all Pa all A_13 ((hBOOL(hAPP_H1037229737a_bool(Pa,A_13)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_H426895267a_bool(fequal963300192iple_a,A_13))),Pa)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool)) & (-hBOOL(hAPP_H1037229737a_bool(Pa,A_13)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_H426895267a_bool(fequal963300192iple_a,A_13))),Pa)) = bot_bo797238721a_bool))) # label(fact_25_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 59 (all Pa all A_13 ((hBOOL(hAPP_int_bool(Pa,A_13)) -> hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(fequal_int,A_13))),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)) & (-hBOOL(hAPP_int_bool(Pa,A_13)) -> hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(fequal_int,A_13))),Pa)) = bot_bot_fun_int_bool))) # label(fact_26_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 60 (all Pa all A_13 ((hBOOL(hAPP_nat_bool(Pa,A_13)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_13))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_13)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_13))),Pa)) = bot_bot_fun_nat_bool))) # label(fact_27_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 61 (all Pa all A_13 ((hBOOL(hAPP_H1037229737a_bool(Pa,A_13)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_13))),Pa)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool)) & (-hBOOL(hAPP_H1037229737a_bool(Pa,A_13)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_13))),Pa)) = bot_bo797238721a_bool))) # label(fact_28_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 62 (all Pa all A_13 ((hBOOL(hAPP_int_bool(Pa,A_13)) -> hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),A_13))),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)) & (-hBOOL(hAPP_int_bool(Pa,A_13)) -> hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),A_13))),Pa)) = bot_bot_fun_int_bool))) # label(fact_29_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 63 (all A_13 all A (A = bot_bo797238721a_bool -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)))) # label(fact_30_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 64 (all A_13 all A (A = bot_bot_fun_nat_bool -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)))) # label(fact_31_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 65 (all A_13 all A (A = bot_bot_fun_int_bool -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)))) # label(fact_32_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 66 (all Pa (hAPP_f20753329a_bool(collec351493750iple_a,Pa) = bot_bo797238721a_bool <-> (all X_2 -hBOOL(hAPP_H1037229737a_bool(Pa,X_2))))) # label(fact_33_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 67 (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_34_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 68 (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_35_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 69 (all Ca -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),bot_bo797238721a_bool))) # label(fact_36_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 70 (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].
% 1.95/2.15 71 (all Ca -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),bot_bot_fun_int_bool))) # label(fact_38_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 72 (all Pa (bot_bo797238721a_bool = hAPP_f20753329a_bool(collec351493750iple_a,Pa) <-> (all X_2 -hBOOL(hAPP_H1037229737a_bool(Pa,X_2))))) # label(fact_39_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 73 (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_40_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.15 74 (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_41_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 75 (all A ((exists X_2 hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A))) <-> A != bot_bo797238721a_bool)) # label(fact_42_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 76 (all A ((exists X_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))) <-> A != bot_bot_fun_nat_bool)) # label(fact_43_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 77 (all A ((exists X_2 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))) <-> A != bot_bot_fun_int_bool)) # label(fact_44_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 78 (all A ((all X_2 -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A))) <-> A = bot_bo797238721a_bool)) # label(fact_45_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 79 (all A ((all X_2 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))) <-> A = bot_bot_fun_nat_bool)) # label(fact_46_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 80 (all A ((all X_2 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))) <-> A = bot_bot_fun_int_bool)) # label(fact_47_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 81 (all A_13 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A) = A)) # label(fact_51_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 82 (all A_13 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A) = A)) # label(fact_52_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 83 (all A_13 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A) = A)) # label(fact_53_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 84 (all Ba all A_13 all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),B))))) # label(fact_54_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 85 (all Ba all A_13 all B (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),B)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),B))))) # label(fact_55_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 86 (all Ba all A_13 all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),B))))) # label(fact_56_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 87 (all B all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B) <-> A = B)))) # label(fact_57_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 88 (all B all X_1 all A (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B)) -> (hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),B) <-> A = B)))) # label(fact_58_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 89 (all B all X_1 all A (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B) <-> A = B)))) # label(fact_59_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 90 (all Y_1 all A all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_nat_bool(A,X_1)))) # label(fact_60_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 91 (all Y_1 all A all X_1 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),A),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_H1037229737a_bool(A,X_1)))) # label(fact_61_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 92 (all Y_1 all A all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),A),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_int_bool(A,X_1)))) # label(fact_62_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 93 (all A_13 all Ba all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),A))) <-> A_13 = Ba | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)))) # label(fact_63_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 94 (all A_13 all Ba all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),A))) <-> A_13 = Ba | hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)))) # label(fact_64_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 95 (all A_13 all Ba all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),A))) <-> A_13 = Ba | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)))) # label(fact_65_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 96 (all X_1 all Y_1 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A))) # label(fact_66_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 97 (all X_1 all Y_1 all A hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),A)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A))) # label(fact_67_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 98 (all X_1 all Y_1 all A hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),A)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A))) # label(fact_68_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 99 (all X_1 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) # label(fact_69_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 100 (all X_1 all A hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) # label(fact_70_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 101 (all X_1 all A hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) # label(fact_71_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 102 (all A_13 all Pa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),hAPP_f800510211t_bool(collect_nat,Pa)) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fimplies),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_13)))),Pa))) # label(fact_72_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 103 (all A_13 all Pa hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),hAPP_f20753329a_bool(collec351493750iple_a,Pa)) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fimplies),hAPP_f20753329a_bool(hAPP_f604201481a_bool(cOMBB_1882975613iple_a,fNot),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_13)))),Pa))) # label(fact_73_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 104 (all A_13 all Pa hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),hAPP_f1805168059t_bool(collect_int,Pa)) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fimplies),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,fNot),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),A_13)))),Pa))) # label(fact_74_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 105 (all A_13 all B hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_13))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B)))) # label(fact_75_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 106 (all A_13 all B hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fdisj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_13))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B)))) # label(fact_76_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 107 (all A_13 all B hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fdisj),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),A_13))),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),B)))) # label(fact_77_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 108 (all A_13 all B hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)))) # label(fact_78_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 109 (all A_13 all B hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B)))) # label(fact_79_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 110 (all A_13 all B hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B)))) # label(fact_80_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 111 (all X_2 all Xa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),Xa) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_2))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),Xa)))) # label(fact_81_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 112 (all X_2 all Xa hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),Xa) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fdisj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),X_2))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),Xa)))) # label(fact_82_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 113 (all X_2 all Xa hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),Xa) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fdisj),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),X_2))),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),Xa)))) # label(fact_83_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 114 (all A_13 all Ba (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool) -> A_13 = Ba)) # label(fact_84_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 115 (all A_13 all Ba (hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),bot_bo797238721a_bool) -> A_13 = Ba)) # label(fact_85_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 116 (all A_13 all Ba (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),bot_bot_fun_int_bool) -> A_13 = Ba)) # label(fact_86_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 117 (all Ba all A_13 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) -> Ba = A_13)) # label(fact_87_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 118 (all Ba all A_13 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) -> Ba = A_13)) # label(fact_88_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 119 (all Ba all A_13 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) -> Ba = A_13)) # label(fact_89_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 120 (all A_13 all Ba all Ca all D_1 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_1),bot_bot_fun_nat_bool)) <-> A_13 = Ca & Ba = D_1 | A_13 = D_1 & Ba = Ca)) # label(fact_90_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 121 (all A_13 all Ba all Ca all D_1 (hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),bot_bo797238721a_bool)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ca),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,D_1),bot_bo797238721a_bool)) <-> A_13 = Ca & Ba = D_1 | A_13 = D_1 & Ba = Ca)) # label(fact_91_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 122 (all A_13 all Ba all Ca all D_1 (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),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_13 = Ca & Ba = D_1 | A_13 = D_1 & Ba = Ca)) # label(fact_92_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 123 (all Ba all A_13 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) <-> Ba = A_13)) # label(fact_93_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 124 (all Ba all A_13 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) <-> Ba = A_13)) # label(fact_94_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 125 (all Ba all A_13 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) <-> Ba = A_13)) # label(fact_95_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 126 (all A_13 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A) != bot_bot_fun_nat_bool) # label(fact_96_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 127 (all A_13 all A hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A) != bot_bo797238721a_bool) # label(fact_97_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 128 (all A_13 all A hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A) != bot_bot_fun_int_bool) # label(fact_98_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 129 (all A_13 all A bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A)) # label(fact_99_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 130 (all A_13 all A bot_bo797238721a_bool != hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A)) # label(fact_100_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 131 (all A_13 all A bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A)) # label(fact_101_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 132 (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_102_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 133 (all X_1 hAPP_f1693662087iple_a(the_el1519802624iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)) = X_1) # label(fact_103_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 134 (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_104_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 135 (all X_1 (hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_105_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 136 (all X_1 (hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_106_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 137 (all X_1 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_107_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 138 (all X_2 (hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_108_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 139 (all X_2 (hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_109_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 140 (all X_2 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_110_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 141 (all Ga all Pa hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,skip,Pa)),bot_bo797238721a_bool)))) # label(fact_111_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 142 (all D_1 all R_1 all Ga all Pa all Ca all Q_1 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Q_1,D_1,R_1)),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,semi(Ca,D_1),R_1)),bot_bo797238721a_bool)))))) # label(fact_112_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 143 (all Y_1 -(all Fun1 all Com all Fun2 Y_1 != hoare_1916936827iple_a(Fun1,Com,Fun2))) # label(fact_113_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 144 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> -(all B_35 (A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B_35) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_35)))))) # label(fact_114_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 145 (all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> -(all B_35 (A = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),B_35) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B_35)))))) # label(fact_115_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 146 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> -(all B_35 (A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B_35) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B_35)))))) # label(fact_116_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 147 (all A_13 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> (exists B_35 (A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B_35) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),B_35)))))) # label(fact_117_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 148 (all A_13 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> (exists B_35 (A = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B_35) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),B_35)))))) # label(fact_118_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 149 (all A_13 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> (exists B_35 (A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B_35) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),B_35)))))) # label(fact_119_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 150 (all A ((all Y_21 -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Y_21),A))) -> A = bot_bo797238721a_bool)) # label(fact_120_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 151 (all A ((all Y_21 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_21),A))) -> A = bot_bot_fun_nat_bool)) # label(fact_121_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 152 (all A ((all Y_21 -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_21),A))) -> A = bot_bot_fun_int_bool)) # label(fact_122_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 153 (all Q_1 all Ga all Ca all Pa ((all Z_11 all S_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2)) -> (exists P_1 exists Q_2 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool))) & (all S_3 ((all Z_12 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)))))))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))))) # label(fact_123_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 154 (all A (A != bot_bot_fun_nat_bool <-> (exists X_2 exists B_35 (A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_35) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_35)))))) # label(fact_124_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 155 (all A (A != bot_bo797238721a_bool <-> (exists X_2 exists B_35 (A = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),B_35) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B_35)))))) # label(fact_125_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 156 (all A (A != bot_bot_fun_int_bool <-> (exists X_2 exists B_35 (A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),B_35) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_35)))))) # label(fact_126_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 157 (all Com1_2 all Com2_2 semi(Com1_2,Com2_2) != skip) # label(fact_127_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 158 (all Com1_2 all Com2_2 skip != semi(Com1_2,Com2_2)) # label(fact_128_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 159 (all X_28 hAPP_f22106695ol_nat(the_elem_nat,X_28) = hAPP_f22106695ol_nat(the_nat,hAPP_f158894502t_bool(hAPP_f1777703707t_bool(cOMBB_955900739ol_nat,hAPP_f103356543l_bool(fequal_fun_nat_bool,X_28)),hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,insert_nat),bot_bot_fun_nat_bool)))) # label(fact_129_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 160 (all X_28 hAPP_f1693662087iple_a(the_el1519802624iple_a,X_28) = hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_f1194757675a_bool(hAPP_f1697223433a_bool(cOMBB_1610959875iple_a,hAPP_f1767618879l_bool(fequal874423448a_bool,X_28)),hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,insert956547291iple_a),bot_bo797238721a_bool)))) # label(fact_130_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 161 (all X_28 hAPP_f1594865479ol_int(the_elem_int,X_28) = hAPP_f1594865479ol_int(the_int,hAPP_f2119767738t_bool(hAPP_f423804115t_bool(cOMBB_1418110531ol_int,hAPP_f284875647l_bool(fequal_fun_int_bool,X_28)),hAPP_f1048215610t_bool(hAPP_f472159229t_bool(cOMBC_1683390479t_bool,insert_int),bot_bot_fun_int_bool)))) # label(fact_131_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 162 (all Com1_1 all Com2_1 all Com1 all Com2 (semi(Com1_1,Com2_1) = semi(Com1,Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_132_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 163 (all F all A_13 all Ba (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)),Ba)) <-> A_13 = Ba)) # label(fact_133_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 164 (all F all A_13 all Ba (hBOOL(hAPP_H1037229737a_bool(finite1621280049iple_a(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool)),Ba)) <-> A_13 = Ba)) # label(fact_134_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 165 (all F all A_13 all Ba (hBOOL(hAPP_int_bool(finite_fold1Set_int(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)),Ba)) <-> A_13 = Ba)) # label(fact_135_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 166 (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_136_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 167 (all X_1 all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)) = X_1)) # label(fact_137_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 168 (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_138_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 169 (all X_2 (hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X_2)) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),bot_bo797238721a_bool)))) # label(fact_139_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 170 (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_140_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 171 (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_141_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 172 (all Ga all Pa all X_28 all A_13 hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f100967412e_bool(hAPP_f1460451647e_bool(cOMBC_524597097e_bool,hAPP_f1406200875e_bool(hAPP_f635443597e_bool(cOMBB_2139825703bool_a,cOMBB_844853809_state),Pa)),hAPP_f871651461_state(hAPP_f851239890_state(cOMBS_777315357_state,hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,update),X_28)),A_13)),ass(X_28,A_13),Pa)),bot_bo797238721a_bool)))) # label(fact_142_Ass) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 173 (all F all A_13 hAPP_f22106695ol_nat(finite_fold1_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)) = A_13) # label(fact_143_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 174 (all F all A_13 hAPP_f1693662087iple_a(finite1465856449iple_a(F),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool)) = A_13) # label(fact_144_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 175 (all F all A_13 hAPP_f1594865479ol_int(finite_fold1_int(F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)) = A_13) # label(fact_145_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 176 (all A_13 all G all F (G = finite_fold1_nat(F) -> hAPP_f22106695ol_nat(G,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)) = A_13)) # label(fact_146_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 177 (all A_13 all G all F (G = finite1465856449iple_a(F) -> hAPP_f1693662087iple_a(G,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool)) = A_13)) # label(fact_147_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 178 (all A_13 all G all F (G = finite_fold1_int(F) -> hAPP_f1594865479ol_int(G,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)) = A_13)) # label(fact_148_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 179 (all Ca all A ((A = bot_bo797238721a_bool -> image_48635758_a_nat(hAPP_n1653940209_a_nat(cOMBK_1028443109iple_a,Ca),A) = bot_bot_fun_nat_bool) & (A != bot_bo797238721a_bool -> image_48635758_a_nat(hAPP_n1653940209_a_nat(cOMBK_1028443109iple_a,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool)))) # label(fact_149_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 180 (all Ca all A ((A = bot_bot_fun_int_bool -> image_int_nat(hAPP_nat_fun_int_nat(cOMBK_nat_int,Ca),A) = bot_bot_fun_nat_bool) & (A != bot_bot_fun_int_bool -> image_int_nat(hAPP_nat_fun_int_nat(cOMBK_nat_int,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool)))) # label(fact_150_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 181 (all Ca all A ((A = bot_bo797238721a_bool -> image_533441733iple_a(hAPP_H2085992369iple_a(cOMBK_2052406350iple_a,Ca),A) = bot_bo797238721a_bool) & (A != bot_bo797238721a_bool -> image_533441733iple_a(hAPP_H2085992369iple_a(cOMBK_2052406350iple_a,Ca),A) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ca),bot_bo797238721a_bool)))) # label(fact_151_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 182 (all Ca all A ((A = bot_bot_fun_int_bool -> image_int_int(hAPP_int_fun_int_int(cOMBK_int_int,Ca),A) = bot_bot_fun_int_bool) & (A != bot_bot_fun_int_bool -> image_int_int(hAPP_int_fun_int_int(cOMBK_int_int,Ca),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ca),bot_bot_fun_int_bool)))) # label(fact_152_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 183 (all Ca all A ((A = bot_bot_fun_nat_bool -> image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,Ca),A) = bot_bot_fun_nat_bool) & (A != bot_bot_fun_nat_bool -> image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool)))) # label(fact_153_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 184 (all Ca all A ((A = bot_bot_fun_nat_bool -> image_nat_int(hAPP_int_fun_nat_int(cOMBK_int_nat,Ca),A) = bot_bot_fun_int_bool) & (A != bot_bot_fun_nat_bool -> image_nat_int(hAPP_int_fun_nat_int(cOMBK_int_nat,Ca),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ca),bot_bot_fun_int_bool)))) # label(fact_154_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 185 (all A all Ba all F all X_1 (Ba = hAPP_H905846293iple_a(F,X_1) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_533441733iple_a(F,A)))))) # label(fact_155_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 186 (all A all Ba all F all X_1 (Ba = hAPP_n261501868iple_a(F,X_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_1865589340iple_a(F,A)))))) # label(fact_156_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 187 (all A all Ba all F all X_1 (Ba = hAPP_i240634960iple_a(F,X_1) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_1844722432iple_a(F,A)))))) # label(fact_157_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 188 (all A all Ba all F all X_1 (Ba = hAPP_H592031934_a_nat(F,X_1) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_48635758_a_nat(F,A)))))) # label(fact_158_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 189 (all A all Ba all F all X_1 (Ba = hAPP_int_int(F,X_1) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_int_int(F,A)))))) # label(fact_159_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 190 (all A all Ba all F all X_1 (Ba = hAPP_H1229305626_a_int(F,X_1) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_685909450_a_int(F,A)))))) # label(fact_160_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 191 (all A all Ba all F all X_1 (Ba = hAPP_nat_nat(F,X_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_nat_nat(F,A)))))) # label(fact_161_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 192 (all A all Ba all F all X_1 (Ba = hAPP_nat_int(F,X_1) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_nat_int(F,A)))))) # label(fact_162_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 193 (all F all A hAPP_f1594865479ol_int(finite_fold1_int(F),A) = hAPP_f1594865479ol_int(the_int,finite_fold1Set_int(F,A))) # label(fact_163_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 194 (all F all A hAPP_f1693662087iple_a(finite1465856449iple_a(F),A) = hAPP_f1693662087iple_a(the_Ho830102290iple_a,finite1621280049iple_a(F,A))) # label(fact_164_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 195 (all F all A hAPP_f22106695ol_nat(finite_fold1_nat(F),A) = hAPP_f22106695ol_nat(the_nat,finite_fold1Set_nat(F,A))) # label(fact_165_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 196 (all Vname_1 all Fun_1 all Vname all Fun (is_vname(Vname_1) & is_vname(Vname) -> (ass(Vname_1,Fun_1) = ass(Vname,Fun) <-> Vname_1 = Vname & Fun_1 = Fun))) # label(fact_166_com_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 197 (all Ba all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (Ba = hAPP_H905846293iple_a(F,X_1) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_533441733iple_a(F,A)))))) # label(fact_167_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 198 (all Ba all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (Ba = hAPP_n261501868iple_a(F,X_1) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_1865589340iple_a(F,A)))))) # label(fact_168_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 199 (all Ba all F all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (Ba = hAPP_i240634960iple_a(F,X_1) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_1844722432iple_a(F,A)))))) # label(fact_169_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 200 (all Ba all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (Ba = hAPP_H592031934_a_nat(F,X_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_48635758_a_nat(F,A)))))) # label(fact_170_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 201 (all Ba all F all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (Ba = hAPP_int_int(F,X_1) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_int_int(F,A)))))) # label(fact_171_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 202 (all Ba all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (Ba = hAPP_H1229305626_a_int(F,X_1) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_685909450_a_int(F,A)))))) # label(fact_172_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 203 (all Ba all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (Ba = hAPP_nat_nat(F,X_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_nat_nat(F,A)))))) # label(fact_173_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 204 (all Ba all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (Ba = hAPP_nat_int(F,X_1) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_nat_int(F,A)))))) # label(fact_174_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 205 (all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_H905846293iple_a(F,X_1)),image_533441733iple_a(F,A))))) # label(fact_175_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 206 (all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_n261501868iple_a(F,X_1)),image_1865589340iple_a(F,A))))) # label(fact_176_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 207 (all F all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_i240634960iple_a(F,X_1)),image_1844722432iple_a(F,A))))) # label(fact_177_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 208 (all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_H592031934_a_nat(F,X_1)),image_48635758_a_nat(F,A))))) # label(fact_178_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 209 (all F all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(F,X_1)),image_int_int(F,A))))) # label(fact_179_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 210 (all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_H1229305626_a_int(F,X_1)),image_685909450_a_int(F,A))))) # label(fact_180_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 211 (all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(F,X_1)),image_nat_nat(F,A))))) # label(fact_181_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 212 (all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A))))) # label(fact_182_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 213 (all Z_1 all F all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Z_1),image_533441733iple_a(F,A))) <-> (exists X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) & Z_1 = hAPP_H905846293iple_a(F,X_2))))) # label(fact_183_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 214 (all Z_1 all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Z_1),image_int_int(F,A))) <-> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & Z_1 = hAPP_int_int(F,X_2))))) # label(fact_184_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 215 (all Z_1 all F all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_1),image_nat_nat(F,A))) <-> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & Z_1 = hAPP_nat_nat(F,X_2))))) # label(fact_185_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 216 (all Z_1 all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Z_1),image_nat_int(F,A))) <-> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & Z_1 = hAPP_nat_int(F,X_2))))) # label(fact_186_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 217 (all F all G all A image_nat_int(F,image_int_nat(G,A)) = image_int_int(hAPP_f147134065nt_int(hAPP_f1673907925nt_int(cOMBB_nat_int_int,F),G),A)) # label(fact_187_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 218 (all F all G all A image_int_int(F,image_nat_int(G,A)) = image_nat_int(hAPP_f1139079189at_int(hAPP_f1431025877at_int(cOMBB_int_int_nat,F),G),A)) # label(fact_188_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 219 (all Y_23 image_int_int(cOMBI_int,Y_23) = Y_23) # label(fact_189_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 220 (all Y_23 image_533441733iple_a(cOMBI_1301683934iple_a,Y_23) = Y_23) # label(fact_190_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 221 (all Y_23 image_nat_nat(cOMBI_nat,Y_23) = Y_23) # label(fact_191_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 222 (all Vname_1 all Fun_1 all Com1 all Com2 ass(Vname_1,Fun_1) != semi(Com1,Com2)) # label(fact_192_com_Osimps_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 223 (all Com1 all Com2 all Vname_1 all Fun_1 semi(Com1,Com2) != ass(Vname_1,Fun_1)) # label(fact_193_com_Osimps_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 224 (all Vname all Fun skip != ass(Vname,Fun)) # label(fact_194_com_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 225 (all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) <-> hBOOL(hAPP_H1037229737a_bool(A,X_1)))) # label(fact_195_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 226 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_nat_bool(A,X_1)))) # label(fact_196_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 227 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) <-> hBOOL(hAPP_int_bool(A,X_1)))) # label(fact_197_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 228 (all Pa hAPP_f1805168059t_bool(collect_int,Pa) = Pa) # label(fact_198_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 229 (all Pa hAPP_f20753329a_bool(collec351493750iple_a,Pa) = Pa) # label(fact_199_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 230 (all Pa hAPP_f800510211t_bool(collect_nat,Pa) = Pa) # label(fact_200_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 231 (all Vname all Fun ass(Vname,Fun) != skip) # label(fact_201_com_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 232 (all F all A (image_533441733iple_a(F,A) = bot_bo797238721a_bool <-> A = bot_bo797238721a_bool)) # label(fact_202_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 233 (all F all A (image_int_int(F,A) = bot_bot_fun_int_bool <-> A = bot_bot_fun_int_bool)) # label(fact_203_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 234 (all F all A (image_nat_nat(F,A) = bot_bot_fun_nat_bool <-> A = bot_bot_fun_nat_bool)) # label(fact_204_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 235 (all F all A (image_nat_int(F,A) = bot_bot_fun_int_bool <-> A = bot_bot_fun_nat_bool)) # label(fact_205_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 236 (all F image_533441733iple_a(F,bot_bo797238721a_bool) = bot_bo797238721a_bool) # label(fact_206_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 237 (all F image_int_int(F,bot_bot_fun_int_bool) = bot_bot_fun_int_bool) # label(fact_207_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 238 (all F image_nat_nat(F,bot_bot_fun_nat_bool) = bot_bot_fun_nat_bool) # label(fact_208_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 239 (all F image_nat_int(F,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool) # label(fact_209_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 240 (all F all A (bot_bo797238721a_bool = image_533441733iple_a(F,A) <-> A = bot_bo797238721a_bool)) # label(fact_210_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 241 (all F all A (bot_bot_fun_int_bool = image_int_int(F,A) <-> A = bot_bot_fun_int_bool)) # label(fact_211_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 242 (all F all A (bot_bot_fun_nat_bool = image_nat_nat(F,A) <-> A = bot_bot_fun_nat_bool)) # label(fact_212_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 243 (all F all A (bot_bot_fun_int_bool = image_nat_int(F,A) <-> A = bot_bot_fun_nat_bool)) # label(fact_213_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 244 (all F all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_int_nat(F,X_1)),image_int_nat(F,A)) = image_int_nat(F,A))) # label(fact_214_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 245 (all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_H905846293iple_a(F,X_1)),image_533441733iple_a(F,A)) = image_533441733iple_a(F,A))) # label(fact_215_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 246 (all F all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_int_int(F,X_1)),image_int_int(F,A)) = image_int_int(F,A))) # label(fact_216_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 247 (all F all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_H1229305626_a_int(F,X_1)),image_685909450_a_int(F,A)) = image_685909450_a_int(F,A))) # label(fact_217_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 248 (all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_nat_nat(F,X_1)),image_nat_nat(F,A)) = image_nat_nat(F,A))) # label(fact_218_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 249 (all F all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A)) = image_nat_int(F,A))) # label(fact_219_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 250 (all F all A_13 all B image_48635758_a_nat(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_H592031934_a_nat(F,A_13)),image_48635758_a_nat(F,B))) # label(fact_220_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 251 (all F all A_13 all B image_int_nat(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_int_nat(F,A_13)),image_int_nat(F,B))) # label(fact_221_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 252 (all F all A_13 all B image_533441733iple_a(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_H905846293iple_a(F,A_13)),image_533441733iple_a(F,B))) # label(fact_222_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 253 (all F all A_13 all B image_1865589340iple_a(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_n261501868iple_a(F,A_13)),image_1865589340iple_a(F,B))) # label(fact_223_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 254 (all F all A_13 all B image_int_int(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_int_int(F,A_13)),image_int_int(F,B))) # label(fact_224_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 255 (all F all A_13 all B image_nat_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_nat_nat(F,A_13)),image_nat_nat(F,B))) # label(fact_225_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 256 (all F all A_13 all B image_nat_int(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,A_13)),image_nat_int(F,B))) # label(fact_226_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 257 (all F all A all X_1 (hBOOL(hAPP_H1037229737a_bool(finite1621280049iple_a(F,A),X_1)) -> A != bot_bo797238721a_bool)) # label(fact_227_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 258 (all F all A all X_1 (hBOOL(hAPP_int_bool(finite_fold1Set_int(F,A),X_1)) -> A != bot_bot_fun_int_bool)) # label(fact_228_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 259 (all F all A all X_1 (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F,A),X_1)) -> A != bot_bot_fun_nat_bool)) # label(fact_229_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 260 (all F all X_1 -hBOOL(hAPP_H1037229737a_bool(finite1621280049iple_a(F,bot_bo797238721a_bool),X_1))) # label(fact_230_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 261 (all F all X_1 -hBOOL(hAPP_int_bool(finite_fold1Set_int(F,bot_bot_fun_int_bool),X_1))) # label(fact_231_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 262 (all F all X_1 -hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F,bot_bot_fun_nat_bool),X_1))) # label(fact_232_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 263 (all Ca all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> image_48635758_a_nat(hAPP_n1653940209_a_nat(cOMBK_1028443109iple_a,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_233_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 264 (all Ca all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> image_int_nat(hAPP_nat_fun_int_nat(cOMBK_nat_int,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_234_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 265 (all Ca all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> image_533441733iple_a(hAPP_H2085992369iple_a(cOMBK_2052406350iple_a,Ca),A) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ca),bot_bo797238721a_bool))) # label(fact_235_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 266 (all Ca all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> image_int_int(hAPP_int_fun_int_int(cOMBK_int_int,Ca),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ca),bot_bot_fun_int_bool))) # label(fact_236_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 267 (all Ca all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> image_685909450_a_int(hAPP_i1475897073_a_int(cOMBK_1007576201iple_a,Ca),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ca),bot_bot_fun_int_bool))) # label(fact_237_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 268 (all Ca all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,Ca),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ca),bot_bot_fun_nat_bool))) # label(fact_238_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 269 (all Ca all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> image_nat_int(hAPP_int_fun_nat_int(cOMBK_int_nat,Ca),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ca),bot_bot_fun_int_bool))) # label(fact_239_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 270 (all Ba all F all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_533441733iple_a(F,A))) -> -(all X_2 (Ba = hAPP_H905846293iple_a(F,X_2) -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)))))) # label(fact_240_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 271 (all Ba all F all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_48635758_a_nat(F,A))) -> -(all X_2 (Ba = hAPP_H592031934_a_nat(F,X_2) -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)))))) # label(fact_241_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 272 (all Ba all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_685909450_a_int(F,A))) -> -(all X_2 (Ba = hAPP_H1229305626_a_int(F,X_2) -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)))))) # label(fact_242_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 273 (all Ba all F all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_1865589340iple_a(F,A))) -> -(all X_2 (Ba = hAPP_n261501868iple_a(F,X_2) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)))))) # label(fact_243_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 274 (all Ba all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_int_int(F,A))) -> -(all X_2 (Ba = hAPP_int_int(F,X_2) -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)))))) # label(fact_244_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 275 (all Ba all F all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ba),image_1844722432iple_a(F,A))) -> -(all X_2 (Ba = hAPP_i240634960iple_a(F,X_2) -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)))))) # label(fact_245_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 276 (all Ba all F all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),image_nat_nat(F,A))) -> -(all X_2 (Ba = hAPP_nat_nat(F,X_2) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)))))) # label(fact_246_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 277 (all Ba all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),image_nat_int(F,A))) -> -(all X_2 (Ba = hAPP_nat_int(F,X_2) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)))))) # label(fact_247_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 278 (all X_1 hAPP_f1594865479ol_int(the_int,hAPP_i1948725293t_bool(fequal_int,X_1)) = X_1) # label(fact_248_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 279 (all X_1 hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_H426895267a_bool(fequal963300192iple_a,X_1)) = X_1) # label(fact_249_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 280 (all X_1 hAPP_f22106695ol_nat(the_nat,hAPP_n1699378549t_bool(fequal_nat,X_1)) = X_1) # label(fact_250_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 281 (all A_13 hAPP_f1594865479ol_int(the_int,hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),A_13)) = A_13) # label(fact_251_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 282 (all A_13 hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_13)) = A_13) # label(fact_252_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 283 (all A_13 hAPP_f22106695ol_nat(the_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_13)) = A_13) # label(fact_253_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 284 (all X_1 all Y_1 all Pa ((hBOOL(Pa) -> X_1 = hAPP_f1594865479ol_int(the_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),X_1)))),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),Y_1))))) & (-hBOOL(Pa) -> Y_1 = hAPP_f1594865479ol_int(the_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),X_1)))),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),Y_1))))))) # label(fact_254_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 285 (all X_1 all Y_1 all Pa ((hBOOL(Pa) -> X_1 = hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f604201481a_bool(cOMBB_1882975613iple_a,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),X_1)))),hAPP_f20753329a_bool(hAPP_f604201481a_bool(cOMBB_1882975613iple_a,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),Y_1))))) & (-hBOOL(Pa) -> Y_1 = hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f604201481a_bool(cOMBB_1882975613iple_a,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),X_1)))),hAPP_f20753329a_bool(hAPP_f604201481a_bool(cOMBB_1882975613iple_a,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),Y_1))))))) # label(fact_255_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 286 (all X_1 all Y_1 all Pa ((hBOOL(Pa) -> X_1 = hAPP_f22106695ol_nat(the_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_1)))),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),Y_1))))) & (-hBOOL(Pa) -> Y_1 = hAPP_f22106695ol_nat(the_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,hAPP_b589554111l_bool(fimplies,Pa)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X_1)))),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),Y_1))))))) # label(fact_256_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 287 (all F all G all M_3 all N_3 (M_3 = N_3 -> ((all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),N_3)) -> hAPP_H905846293iple_a(F,X_2) = hAPP_H905846293iple_a(G,X_2))) -> image_533441733iple_a(F,M_3) = image_533441733iple_a(G,N_3)))) # label(fact_257_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 288 (all F all G all M_3 all N_3 (M_3 = N_3 -> ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),N_3)) -> hAPP_int_int(F,X_2) = hAPP_int_int(G,X_2))) -> image_int_int(F,M_3) = image_int_int(G,N_3)))) # label(fact_258_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 289 (all F all G all M_3 all N_3 (M_3 = N_3 -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_3)) -> hAPP_nat_nat(F,X_2) = hAPP_nat_nat(G,X_2))) -> image_nat_nat(F,M_3) = image_nat_nat(G,N_3)))) # label(fact_259_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 290 (all F all G all M_3 all N_3 (M_3 = N_3 -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_3)) -> hAPP_nat_int(F,X_2) = hAPP_nat_int(G,X_2))) -> image_nat_int(F,M_3) = image_nat_int(G,N_3)))) # label(fact_260_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 291 (all F all A_13 all A all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),A_13),A),X_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A)),X_1))))) # label(fact_261_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 292 (all F all A_13 all A all X_1 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),A_13),A),X_1)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hBOOL(hAPP_H1037229737a_bool(finite1621280049iple_a(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A)),X_1))))) # label(fact_262_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 293 (all F all A_13 all A all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),A_13),A),X_1)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hBOOL(hAPP_int_bool(finite_fold1Set_int(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A)),X_1))))) # label(fact_263_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 294 (all Pa all A_13 (hBOOL(hAPP_int_bool(Pa,A_13)) -> ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> X_2 = A_13)) -> hAPP_f1594865479ol_int(the_int,Pa) = A_13))) # label(fact_264_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 295 (all Pa all A_13 (hBOOL(hAPP_H1037229737a_bool(Pa,A_13)) -> ((all X_2 (hBOOL(hAPP_H1037229737a_bool(Pa,X_2)) -> X_2 = A_13)) -> hAPP_f1693662087iple_a(the_Ho830102290iple_a,Pa) = A_13))) # label(fact_265_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 296 (all Pa all A_13 (hBOOL(hAPP_nat_bool(Pa,A_13)) -> ((all X_2 (hBOOL(hAPP_nat_bool(Pa,X_2)) -> X_2 = A_13)) -> hAPP_f22106695ol_nat(the_nat,Pa) = A_13))) # label(fact_266_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 297 (all X_1 all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A))))))) # label(fact_267_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 298 (all X_1 all A all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (A != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(F_1,A))))))) # label(fact_268_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.16 299 (all X_1 all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (A != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A))))))) # label(fact_269_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 300 (all A all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f1693662087iple_a(F_1,A) = hAPP_f1693662087iple_a(finite1465856449iple_a(F),A)))) # label(fact_270_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 301 (all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(F_1,A) = hAPP_f22106695ol_nat(finite_fold1_nat(F),A)))) # label(fact_271_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 302 (all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(F_1,A) = hAPP_f1594865479ol_int(finite_fold1_int(F),A)))) # label(fact_272_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 303 (all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> ((all X_2 all Y_21 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_21)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_21),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A)),A))))))) # label(fact_273_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 304 (all A all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (A != bot_bo797238721a_bool -> ((all X_2 all Y_21 hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),Y_21)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_21),bot_bo797238721a_bool))))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_f1693662087iple_a(F_1,A)),A))))))) # label(fact_274_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 305 (all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (A != bot_bot_fun_int_bool -> ((all X_2 all Y_21 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_21)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_21),bot_bot_fun_int_bool))))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(F_1,A)),A))))))) # label(fact_275_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 306 (all Q_1 all Pa (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Pa))) | hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Q_1))) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),Pa)),Q_1)))))) # label(fact_276_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 307 (all Q_1 all Pa (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,Pa))) | hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,Q_1))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),Pa)),Q_1)))))) # label(fact_277_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 308 (all Q_1 all Pa (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Pa))) | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Q_1))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),Pa)),Q_1)))))) # label(fact_278_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 309 (all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A))))) # label(fact_282_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 310 (all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A))))) # label(fact_283_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 311 (all A_13 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A))))) # label(fact_284_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 312 (all H all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,image_533441733iple_a(H,F_1))))) # label(fact_285_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 313 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,image_1865589340iple_a(H,F_1))))) # label(fact_286_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 314 (all H all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,image_1844722432iple_a(H,F_1))))) # label(fact_287_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 315 (all H all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_48635758_a_nat(H,F_1))))) # label(fact_288_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 316 (all H all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_int_int(H,F_1))))) # label(fact_289_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 317 (all H all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_685909450_a_int(H,F_1))))) # label(fact_290_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 318 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(H,F_1))))) # label(fact_291_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 319 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(H,F_1))))) # label(fact_292_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 320 (all Pa all Q_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Pa))) & hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Q_1))))) # label(fact_293_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 321 (all Pa all Q_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,Pa))) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,Q_1))))) # label(fact_294_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 322 (all Pa all Q_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Pa))) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Q_1))))) # label(fact_295_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 323 (all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)))) # label(fact_296_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 324 (all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A))) <-> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)))) # label(fact_297_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 325 (all A_13 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)))) # label(fact_298_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 326 (all F all Z_1 hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),bot_bo797238721a_bool),Z_1))) # label(fact_299_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 327 (all F all Z_1 hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),bot_bot_fun_int_bool),Z_1))) # label(fact_300_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 328 (all F all Z_1 hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),bot_bot_fun_nat_bool),Z_1))) # label(fact_301_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 329 (all F all Z_1 all X_1 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),bot_bo797238721a_bool),X_1)) -> X_1 = Z_1)) # label(fact_302_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 330 (all F all Z_1 all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),bot_bot_fun_int_bool),X_1)) -> X_1 = Z_1)) # label(fact_303_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 331 (all F all Z_1 all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),bot_bot_fun_nat_bool),X_1)) -> X_1 = Z_1)) # label(fact_304_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 332 (all F all Z_1 all Y_1 all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),Y_1)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Y_1)))))) # label(fact_305_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 333 (all F all Z_1 all Y_1 all X_1 all A (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),Y_1)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)),hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),Y_1)))))) # label(fact_306_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 334 (all F all Z_1 all Y_1 all X_1 all A (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),Y_1)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Y_1)))))) # label(fact_307_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 335 (all F all A_13 all X_28 all X_1 (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),X_28)),X_1)) -> -(all A_12 all A_43 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),X_28) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_12),A_43) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),A_12),A_43),X_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_12),A_43))))))) # label(fact_308_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 336 (all F all A_13 all X_28 all X_1 (hBOOL(hAPP_H1037229737a_bool(finite1621280049iple_a(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),X_28)),X_1)) -> -(all A_12 all A_43 (hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),X_28) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_12),A_43) -> (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),A_12),A_43),X_1)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_12),A_43))))))) # label(fact_309_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 337 (all F all A_13 all X_28 all X_1 (hBOOL(hAPP_int_bool(finite_fold1Set_int(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),X_28)),X_1)) -> -(all A_12 all A_43 (hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),X_28) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_12),A_43) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),A_12),A_43),X_1)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_12),A_43))))))) # label(fact_310_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 338 (all F all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (A != bot_bo797238721a_bool -> (exists X1 hBOOL(hAPP_H1037229737a_bool(finite1621280049iple_a(F,A),X1)))))) # label(fact_311_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 339 (all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> (exists X1 hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F,A),X1)))))) # label(fact_312_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 340 (all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (A != bot_bot_fun_int_bool -> (exists X1 hBOOL(hAPP_int_bool(finite_fold1Set_int(F,A),X1)))))) # label(fact_313_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 341 (all A_13 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_13)) <-> A_13 = bot_bot_fun_nat_bool | (exists A_43 exists A_12 (A_13 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_12),A_43) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_43)))))) # label(fact_314_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 342 (all A_13 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_13)) <-> A_13 = bot_bo797238721a_bool | (exists A_43 exists A_12 (A_13 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_12),A_43) & hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_43)))))) # label(fact_315_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 343 (all A_13 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_13)) <-> A_13 = bot_bot_fun_int_bool | (exists A_43 exists A_12 (A_13 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_12),A_43) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_43)))))) # label(fact_316_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 344 (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_317_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 345 (all Pa all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,bot_bo797238721a_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_2)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),F_2)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,F_2)) -> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),F_2))))))) -> hBOOL(hAPP_f1695230391l_bool(Pa,F_1)))))) # label(fact_318_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 346 (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_319_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 347 (all F all A (-hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,image_533441733iple_a(F,A))) -> (exists X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) & -hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A))),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,hAPP_f960023481a_bool(hAPP_f1786170683a_bool(cOMBB_683172471iple_a,fequal963300192iple_a),F)),hAPP_H905846293iple_a(F,X_2))))))))))) # label(fact_320_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 348 (all F all A (-hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_48635758_a_nat(F,A))) -> (exists X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) & -hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A))),hAPP_n1919155532a_bool(hAPP_f228417655a_bool(cOMBC_364739t_bool,hAPP_f1872860171t_bool(hAPP_f1981448543t_bool(cOMBB_1391527205iple_a,fequal_nat),F)),hAPP_H592031934_a_nat(F,X_2))))))))))) # label(fact_321_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 349 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_int_nat(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),A))),hAPP_n1082236369t_bool(hAPP_f175561985t_bool(cOMBC_int_nat_bool,hAPP_f876579787t_bool(hAPP_f2026117279t_bool(cOMBB_1437810218ol_int,fequal_nat),F)),hAPP_int_nat(F,X_2))))))))))) # label(fact_322_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 350 (all F all A (-hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_685909450_a_int(F,A))) -> (exists X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) & -hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A))),hAPP_i611776424a_bool(hAPP_f920351535a_bool(cOMBC_1530706207t_bool,hAPP_f2142913731t_bool(hAPP_f1329415375t_bool(cOMBB_1505691757iple_a,fequal_int),F)),hAPP_H1229305626_a_int(F,X_2))))))))))) # label(fact_323_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 351 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,image_1865589340iple_a(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A))),hAPP_H144868812t_bool(hAPP_f1886543991t_bool(cOMBC_533513393a_bool,hAPP_f260875897a_bool(hAPP_f1930382715a_bool(cOMBB_1063143712ol_nat,fequal963300192iple_a),F)),hAPP_n261501868iple_a(F,X_2))))))))))) # label(fact_324_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 352 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_int_int(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),A))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,hAPP_f1791153283t_bool(hAPP_f1399575567t_bool(cOMBB_118231410ol_int,fequal_int),F)),hAPP_int_int(F,X_2))))))))))) # label(fact_325_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 353 (all F all A (-hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,image_1844722432iple_a(F,A))) -> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) & -hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),A))),hAPP_H1675210280t_bool(hAPP_f936407855t_bool(cOMBC_1719122773a_bool,hAPP_f298605433a_bool(hAPP_f1421841531a_bool(cOMBB_1700417404ol_int,fequal963300192iple_a),F)),hAPP_i240634960iple_a(F,X_2))))))))))) # label(fact_326_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 354 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,fequal_nat),F)),hAPP_nat_nat(F,X_2))))))))))) # label(fact_327_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 355 (all F all A (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(F,A))) -> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A))),hAPP_i418383825t_bool(hAPP_f482008321t_bool(cOMBC_nat_int_bool,hAPP_f1533130627t_bool(hAPP_f879109391t_bool(cOMBB_1628441366ol_nat,fequal_int),F)),hAPP_nat_int(F,X_2))))))))))) # label(fact_328_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 356 (all F all Z_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (exists X1 hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),X1))))) # label(fact_329_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 357 (all F all Z_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (exists X1 hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),X1))))) # label(fact_330_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 358 (all F all Z_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (exists X1 hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),X1))))) # label(fact_331_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 359 (all F all A1 all A2 (hBOOL(hAPP_nat_bool(finite_fold1Set_nat(F,A1),A2)) <-> (exists A_12 exists A_43 exists X_2 (A1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_12),A_43) & A2 = X_2 & hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),A_12),A_43),X_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_12),A_43)))))) # label(fact_332_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 360 (all F all A1 all A2 (hBOOL(hAPP_H1037229737a_bool(finite1621280049iple_a(F,A1),A2)) <-> (exists A_12 exists A_43 exists X_2 (A1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_12),A_43) & A2 = X_2 & hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),A_12),A_43),X_2)) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_12),A_43)))))) # label(fact_333_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 361 (all F all A1 all A2 (hBOOL(hAPP_int_bool(finite_fold1Set_int(F,A1),A2)) <-> (exists A_12 exists A_43 exists X_2 (A1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_12),A_43) & A2 = X_2 & hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),A_12),A_43),X_2)) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_12),A_43)))))) # label(fact_334_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 362 (all Pa all A_13 (hBOOL(hAPP_int_bool(Pa,A_13)) -> ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> X_2 = A_13)) -> hBOOL(hAPP_int_bool(Pa,hAPP_f1594865479ol_int(the_int,Pa)))))) # label(fact_335_theI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 363 (all Pa all A_13 (hBOOL(hAPP_H1037229737a_bool(Pa,A_13)) -> ((all X_2 (hBOOL(hAPP_H1037229737a_bool(Pa,X_2)) -> X_2 = A_13)) -> hBOOL(hAPP_H1037229737a_bool(Pa,hAPP_f1693662087iple_a(the_Ho830102290iple_a,Pa)))))) # label(fact_336_theI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 364 (all Pa all A_13 (hBOOL(hAPP_nat_bool(Pa,A_13)) -> ((all X_2 (hBOOL(hAPP_nat_bool(Pa,X_2)) -> X_2 = A_13)) -> hBOOL(hAPP_nat_bool(Pa,hAPP_f22106695ol_nat(the_nat,Pa)))))) # label(fact_337_theI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 365 (all A_13 all Pa ((exists X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) & (all Y_21 (hBOOL(hAPP_int_bool(Pa,Y_21)) -> Y_21 = X_2)))) -> (hBOOL(hAPP_int_bool(Pa,A_13)) -> hAPP_f1594865479ol_int(the_int,Pa) = A_13))) # label(fact_338_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 366 (all A_13 all Pa ((exists X_2 (hBOOL(hAPP_H1037229737a_bool(Pa,X_2)) & (all Y_21 (hBOOL(hAPP_H1037229737a_bool(Pa,Y_21)) -> Y_21 = X_2)))) -> (hBOOL(hAPP_H1037229737a_bool(Pa,A_13)) -> hAPP_f1693662087iple_a(the_Ho830102290iple_a,Pa) = A_13))) # label(fact_339_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 367 (all A_13 all Pa ((exists X_2 (hBOOL(hAPP_nat_bool(Pa,X_2)) & (all Y_21 (hBOOL(hAPP_nat_bool(Pa,Y_21)) -> Y_21 = X_2)))) -> (hBOOL(hAPP_nat_bool(Pa,A_13)) -> hAPP_f22106695ol_nat(the_nat,Pa) = A_13))) # label(fact_340_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 368 (all Pa ((exists X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) & (all Y_21 (hBOOL(hAPP_int_bool(Pa,Y_21)) -> Y_21 = X_2)))) -> hBOOL(hAPP_int_bool(Pa,hAPP_f1594865479ol_int(the_int,Pa))))) # label(fact_341_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 369 (all Pa ((exists X_2 (hBOOL(hAPP_H1037229737a_bool(Pa,X_2)) & (all Y_21 (hBOOL(hAPP_H1037229737a_bool(Pa,Y_21)) -> Y_21 = X_2)))) -> hBOOL(hAPP_H1037229737a_bool(Pa,hAPP_f1693662087iple_a(the_Ho830102290iple_a,Pa))))) # label(fact_342_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 370 (all Pa ((exists X_2 (hBOOL(hAPP_nat_bool(Pa,X_2)) & (all Y_21 (hBOOL(hAPP_nat_bool(Pa,Y_21)) -> Y_21 = X_2)))) -> hBOOL(hAPP_nat_bool(Pa,hAPP_f22106695ol_nat(the_nat,Pa))))) # label(fact_343_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 371 (all F all Z_1 all A1 all A2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A1),A2)) <-> A1 = bot_bot_fun_nat_bool & A2 = Z_1 | (exists X_2 exists A_43 exists Y_21 (A1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_43) & A2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_21) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_43)) & hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A_43),Y_21)))))) # label(fact_344_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 372 (all F all Z_1 all A1 all A2 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A1),A2)) <-> A1 = bot_bo797238721a_bool & A2 = Z_1 | (exists X_2 exists A_43 exists Y_21 (A1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_43) & A2 = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),Y_21) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_43)) & hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A_43),Y_21)))))) # label(fact_345_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 373 (all F all Z_1 all A1 all A2 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A1),A2)) <-> A1 = bot_bot_fun_int_bool & A2 = Z_1 | (exists X_2 exists A_43 exists Y_21 (A1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),A_43) & A2 = hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_21) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A_43)) & hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A_43),Y_21)))))) # label(fact_346_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 374 (all X_1 all A all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A)))))) # label(fact_347_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 375 (all X_1 all A all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (A != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(F_1,A)))))) # label(fact_348_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 376 (all X_1 all A all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (A != bot_bot_fun_int_bool -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A)))))) # label(fact_349_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 377 (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_350_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 378 (all Pa all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (F_1 != bot_bo797238721a_bool -> ((all X_2 hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_2)) -> (F_2 != bot_bo797238721a_bool -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),F_2)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,F_2)) -> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),F_2)))))))) -> hBOOL(hAPP_f1695230391l_bool(Pa,F_1))))))) # label(fact_351_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 379 (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_352_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 380 (all A all F all F_1 (hBOOL(big_se1603268663iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f1693662087iple_a(F_1,A) = hAPP_f1693662087iple_a(finite1465856449iple_a(F),A)))) # label(fact_353_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 381 (all A all F all F_1 (hBOOL(big_se275732192ig_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(F_1,A) = hAPP_f22106695ol_nat(finite_fold1_nat(F),A)))) # label(fact_354_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 382 (all A all F all F_1 (hBOOL(big_se913005884ig_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(F_1,A) = hAPP_f1594865479ol_int(finite_fold1_int(F),A)))) # label(fact_355_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 383 (all X_1 all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,A) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,A) = 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),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))))) # label(fact_356_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 384 (all X_1 all A all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)) = bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,A) = X_1) & (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)) != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,A) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))))))))) # label(fact_357_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 385 (all X_1 all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),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) = X_1) & (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),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) = 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),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))))) # label(fact_358_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 386 (all X_1 all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = X_1) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = 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),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_359_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 387 (all X_1 all A all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)) = bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = X_1) & (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)) != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)))))))) # label(fact_360_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 388 (all X_1 all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),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)) = X_1) & (hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),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)) = 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),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))))) # label(fact_361_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 389 (all X_1 all A (A != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A)))))) # label(fact_362_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 390 (all X_1 all A (A != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),A)))))) # label(fact_363_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 391 (all B all Ca all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),B)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)))))) # label(fact_364_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 392 (all B all Ca all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))))) # label(fact_365_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 393 (all B all Ca all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))))) # label(fact_366_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 394 (all Ca all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))) -> -(hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),B))))) # label(fact_367_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 395 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_368_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 396 (all Ca all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) -> -(hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B))))) # label(fact_369_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 397 (all B all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))))) # label(fact_370_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 398 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_371_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 399 (all B all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))) # label(fact_372_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 400 (all X_1 all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),X_1) = X_1)) # label(fact_373_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 401 (all X_1 all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),X_1) = X_1)) # label(fact_374_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 402 (all X_1 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),X_1) = X_1)) # label(fact_375_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 403 (all A all B hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A))),hAPP_f20753329a_bool(hAPP_f604201481a_bool(cOMBB_1882975613iple_a,fNot),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B))))) # label(fact_376_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 404 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A))),hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B))))) # label(fact_377_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 405 (all A all B hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B) = hAPP_f1805168059t_bool(collect_int,hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),A))),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,fNot),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),B))))) # label(fact_378_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 406 (all Ca all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),A)) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),B)))) # label(fact_379_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 407 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)))) # label(fact_380_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 408 (all Ca all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A)) & -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B)))) # label(fact_381_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 409 (all A all B hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) # label(fact_382_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 410 (all A all B hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)),B) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)) # label(fact_383_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 411 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) # label(fact_384_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 412 (all Ca all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),A)))) # label(fact_385_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 413 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)))) # label(fact_386_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 414 (all Ca all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A)))) # label(fact_387_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 415 (all Ca all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))) -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),B)))) # label(fact_388_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 416 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)))) # label(fact_389_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 417 (all Ca all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B)))) # label(fact_390_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 418 (all A hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,bot_bo797238721a_bool),A) = bot_bo797238721a_bool) # label(fact_391_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 419 (all A hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),A) = bot_bot_fun_int_bool) # label(fact_392_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 420 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A) = bot_bot_fun_nat_bool) # label(fact_393_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 421 (all A hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),bot_bo797238721a_bool) = A) # label(fact_394_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 422 (all A hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),bot_bot_fun_int_bool) = A) # label(fact_395_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 423 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),bot_bot_fun_nat_bool) = A) # label(fact_396_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 424 (all A hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),A) = bot_bo797238721a_bool) # label(fact_397_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 425 (all A hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),A) = bot_bot_fun_int_bool) # label(fact_398_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 426 (all A hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),A) = bot_bot_fun_nat_bool) # label(fact_399_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 427 (all A all B (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))) <-> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A))))) # label(fact_400_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 428 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_401_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 429 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))))) # label(fact_402_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 430 (all A all X_1 all B ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_403_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 431 (all A all X_1 all B ((hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)),B) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)) & (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)),B) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))))) # label(fact_404_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 432 (all A all X_1 all B ((hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))) # label(fact_405_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 433 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) # label(fact_406_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 434 (all A all X_1 all B (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)),B) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))) # label(fact_407_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 435 (all A all X_1 all B (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) # label(fact_408_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 436 (all A_13 all Ba all A all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(times_times_nat),Ba),A),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),A)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(times_times_nat),A_13),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool)))),X_1)))))) # label(fact_409_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 437 (all A_13 all Ba all A all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(times_times_int),Ba),A),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),A)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(times_times_int),A_13),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool)))),X_1)))))) # label(fact_410_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 438 (all A all A_13 all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) # label(fact_411_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 439 (all A all A_13 all B hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) # label(fact_412_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 440 (all A all A_13 all B hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) # label(fact_413_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 441 (all A all A_13 all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))),B)) # label(fact_414_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 442 (all A all A_13 all B hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))),B)) # label(fact_415_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 443 (all A all A_13 all B hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))),B)) # label(fact_416_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 444 (all A_13 all A hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A)) # label(fact_417_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 445 (all A_13 all A hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A)) # label(fact_418_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 446 (all A_13 all A hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A)) # label(fact_419_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 447 (all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = A)) # label(fact_420_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 448 (all X_1 all A (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)) = A)) # label(fact_421_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 449 (all X_1 all A (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = A)) # label(fact_422_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 450 (all A_13 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) = A)) # label(fact_423_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 451 (all A_13 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) = A)) # label(fact_424_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 452 (all A_13 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) = A)) # label(fact_425_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 453 (all A all A_13 all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_426_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 454 (all A all A_13 all B (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B)))) <-> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))))) # label(fact_427_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 455 (all A all A_13 all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B)))) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))) # label(fact_428_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 456 (all Z_1 all Ba all A all Y_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(times_times_nat),Ba),A),Y_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ba),A)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(times_times_nat),Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),A)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Z_1),Y_1)))))) # label(fact_429_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 457 (all Z_1 all Ba all A all Y_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(times_times_int),Ba),A),Y_1)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),A)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(times_times_int),Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),A)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),Y_1)))))) # label(fact_430_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 458 (all X_1 all A all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(F_1,A)) = hAPP_f1693662087iple_a(F_1,A))))) # label(fact_431_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 459 (all X_1 all A all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A)) = hAPP_f22106695ol_nat(F_1,A))))) # label(fact_432_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 460 (all X_1 all A all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A)) = hAPP_f1594865479ol_int(F_1,A))))) # label(fact_433_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 461 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (A != bot_bot_fun_nat_bool -> ((all X_2 all Y_21 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_2),Y_21)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_21),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),A)),A)))))) # label(fact_434_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 462 (all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (A != bot_bot_fun_int_bool -> ((all X_2 all Y_21 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_2),Y_21)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_21),bot_bot_fun_int_bool))))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),A)),A)))))) # label(fact_435_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.17 463 (all N_3 all H all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> ((all X_2 all Y_21 hAPP_H905846293iple_a(H,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),Y_21)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_H905846293iple_a(H,X_2)),hAPP_H905846293iple_a(H,Y_21))) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,N_3)) -> (N_3 != bot_bo797238721a_bool -> hAPP_H905846293iple_a(H,hAPP_f1693662087iple_a(F_1,N_3)) = hAPP_f1693662087iple_a(F_1,image_533441733iple_a(H,N_3))))))) # label(fact_436_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 464 (all N_3 all H all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> ((all X_2 all Y_21 hAPP_int_int(H,hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_21)) = hAPP_int_int(hAPP_int_fun_int_int(F,hAPP_int_int(H,X_2)),hAPP_int_int(H,Y_21))) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,N_3)) -> (N_3 != bot_bot_fun_int_bool -> hAPP_int_int(H,hAPP_f1594865479ol_int(F_1,N_3)) = hAPP_f1594865479ol_int(F_1,image_int_int(H,N_3))))))) # label(fact_437_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 465 (all N_3 all H all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> ((all X_2 all Y_21 hAPP_nat_nat(H,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_21)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_nat_nat(H,X_2)),hAPP_nat_nat(H,Y_21))) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) -> (N_3 != bot_bot_fun_nat_bool -> hAPP_nat_nat(H,hAPP_f22106695ol_nat(F_1,N_3)) = hAPP_f22106695ol_nat(F_1,image_nat_nat(H,N_3))))))) # label(fact_438_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 466 (all Pa all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A)) -> ((all A_12 all A_43 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_43)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_12),A_43)) -> (hBOOL(hAPP_f54304608l_bool(Pa,A_43)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_43),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_12),bot_bot_fun_nat_bool)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)))))) # label(fact_439_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 467 (all Pa all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,A)) -> ((all A_12 all A_43 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_43)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_12),A_43)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,A_43)) -> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_43),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_12),bot_bo797238721a_bool)))))))) -> hBOOL(hAPP_f1695230391l_bool(Pa,bot_bo797238721a_bool)))))) # label(fact_440_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 468 (all Pa all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(Pa,A)) -> ((all A_12 all A_43 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_43)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_12),A_43)) -> (hBOOL(hAPP_f448129468l_bool(Pa,A_43)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_43),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_12),bot_bot_fun_int_bool)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)))))) # label(fact_441_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 469 (all A all B all X_1 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_int_bool(A,X_1)),hAPP_int_bool(B,X_1))))) # label(fact_442_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 470 (all A all B all X_1 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H1037229737a_bool(A,X_1)),hAPP_H1037229737a_bool(B,X_1))))) # label(fact_443_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 471 (all A all B all X_1 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A,X_1)),hAPP_nat_bool(B,X_1))))) # label(fact_444_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 472 (all A all B all X_2 (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_int_bool(A,X_2)),hAPP_int_bool(B,X_2))))) # label(fact_445_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 473 (all A all B all X_2 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H1037229737a_bool(A,X_2)),hAPP_H1037229737a_bool(B,X_2))))) # label(fact_446_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 474 (all A all B all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A,X_2)),hAPP_nat_bool(B,X_2))))) # label(fact_447_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 475 (all X_1 all Z_1 all F (hBOOL(finite58652534t_bool(F)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),Z_1)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),Z_1))) # label(fact_451_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 476 (all X_1 all Z_1 all F (hBOOL(finite1803123436a_bool(F)) -> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),Z_1)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),Z_1))) # label(fact_452_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 477 (all X_1 all Z_1 all F (hBOOL(finite1956789438t_bool(F)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),Z_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),Z_1))) # label(fact_453_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 478 (all A_13 all Z_1 all A all Y_1 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),Y_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> (exists Y_22 (Y_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,A_13),Y_22) & hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))),Y_22)))))))) # label(fact_457_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 479 (all A_13 all Z_1 all A all Y_1 all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),Y_1)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> (exists Y_22 (Y_1 = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,A_13),Y_22) & hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))),Y_22)))))))) # label(fact_458_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 480 (all A_13 all Z_1 all A all Y_1 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),Y_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> (exists Y_22 (Y_1 = hAPP_int_int(hAPP_int_fun_int_int(F,A_13),Y_22) & hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))),Y_22)))))))) # label(fact_459_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 481 (all F all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),A)),hAPP_nat_int(F,A_13))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) = hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),A)))) # label(fact_460_setsum__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 482 (all F all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),A)),hAPP_H1229305626_a_int(F,A_13))) & (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) = hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),A)))) # label(fact_461_setsum__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 483 (all F all A_13 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),A)),hAPP_int_int(F,A_13))) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) = hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),A)))) # label(fact_462_setsum__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 484 (all F all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),A)),hAPP_nat_int(F,A_13))))) # label(fact_463_setsum__diff1__ring) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 485 (all F all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),A)),hAPP_H1229305626_a_int(F,A_13))))) # label(fact_464_setsum__diff1__ring) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 486 (all F all A_13 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),A)),hAPP_int_int(F,A_13))))) # label(fact_465_setsum__diff1__ring) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 487 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(big_co1705425894at_nat(G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(G,X_1)),hAPP_f22106695ol_nat(big_co1705425894at_nat(G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))) # label(fact_466_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 488 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f2097660464ol_nat(big_co1815942735_a_nat(G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_H592031934_a_nat(G,X_1)),hAPP_f2097660464ol_nat(big_co1815942735_a_nat(G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)))))) # label(fact_467_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 489 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f957591787ol_nat(big_co911457418nt_nat(G),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(G,X_1)),hAPP_f957591787ol_nat(big_co911457418nt_nat(G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))) # label(fact_468_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 490 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f659380387ol_int(big_co195215938at_int(G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(G,X_1)),hAPP_f659380387ol_int(big_co195215938at_int(G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))) # label(fact_469_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 491 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f587450508ol_int(big_co305732779_a_int(G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_H1229305626_a_int(G,X_1)),hAPP_f587450508ol_int(big_co305732779_a_int(G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)))))) # label(fact_470_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 492 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(big_co1548731110nt_int(G),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(G,X_1)),hAPP_f1594865479ol_int(big_co1548731110nt_int(G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))) # label(fact_471_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 493 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(big_co1705425894at_nat(G),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(G,X_1)),hAPP_f22106695ol_nat(big_co1705425894at_nat(G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_472_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 494 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f2097660464ol_nat(big_co1815942735_a_nat(G),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_H592031934_a_nat(G,X_1)),hAPP_f2097660464ol_nat(big_co1815942735_a_nat(G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))))))) # label(fact_473_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 495 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(big_co911457418nt_nat(G),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(G,X_1)),hAPP_f957591787ol_nat(big_co911457418nt_nat(G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_474_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 496 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f659380387ol_int(big_co195215938at_int(G),A) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(G,X_1)),hAPP_f659380387ol_int(big_co195215938at_int(G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_475_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 497 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f587450508ol_int(big_co305732779_a_int(G),A) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_H1229305626_a_int(G,X_1)),hAPP_f587450508ol_int(big_co305732779_a_int(G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))))))) # label(fact_476_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 498 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1594865479ol_int(big_co1548731110nt_int(G),A) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(G,X_1)),hAPP_f1594865479ol_int(big_co1548731110nt_int(G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_477_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 499 (all B all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),A) = hAPP_f800510211t_bool(finite1578363458t_bool(hAPP_f10625010t_bool(hAPP_f1115950719t_bool(cOMBB_1654519265ol_nat,hAPP_f1311642927t_bool(cOMBC_646315179t_bool,minus_2067140911t_bool)),hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,insert_nat),bot_bot_fun_nat_bool)),B),A))) # label(fact_478_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 500 (all B all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,B),A) = hAPP_f20753329a_bool(finite1215486064a_bool(hAPP_f550111323a_bool(hAPP_f615286271a_bool(cOMBB_1176122337iple_a,hAPP_f957014749a_bool(cOMBC_288844080a_bool,minus_85316870a_bool)),hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,insert956547291iple_a),bot_bo797238721a_bool)),B),A))) # label(fact_479_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 501 (all B all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B),A) = hAPP_f1805168059t_bool(finite1827710202t_bool(hAPP_f1468280982t_bool(hAPP_f1596157055t_bool(cOMBB_765314529ol_int,hAPP_f194616807t_bool(cOMBC_922884543t_bool,minus_1449998731t_bool)),hAPP_f1048215610t_bool(hAPP_f472159229t_bool(cOMBC_1683390479t_bool,insert_int),bot_bot_fun_int_bool)),B),A))) # label(fact_480_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 502 (all X_1 all Z_1 all A all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),A)) = hAPP_f1693662087iple_a(finite1205970312iple_a(F,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),Z_1)),A)))) # label(fact_481_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 503 (all X_1 all Z_1 all A all F (hBOOL(finite2114894759a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),A)) = hAPP_f20753329a_bool(finite1215486064a_bool(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),Z_1)),A)))) # label(fact_482_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 504 (all X_1 all Z_1 all A all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)),A)))) # label(fact_483_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 505 (all X_1 all Z_1 all A all F (hBOOL(finite1071749497t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),A)) = hAPP_f800510211t_bool(finite1578363458t_bool(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),Z_1)),A)))) # label(fact_484_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 506 (all X_1 all Z_1 all A all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)),A)))) # label(fact_485_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 507 (all X_1 all Z_1 all A all F (hBOOL(finite1321096241t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),A)) = hAPP_f1805168059t_bool(finite1827710202t_bool(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),Z_1)),A)))) # label(fact_486_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 508 (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_487_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 509 (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_488_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 510 (all F all B all A hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1473602334at_nat(hAPP_f630508183at_nat(cOMBC_1505178355ol_nat,hAPP_f299305025ol_nat(hAPP_f1632710027ol_nat(cOMBB_1453893592at_nat,big_co1740723097nt_nat),F)),B)),A) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f787214110nt_nat(hAPP_f261731407nt_nat(cOMBC_462113011ol_nat,hAPP_f1501159417ol_nat(hAPP_f1029311995ol_nat(cOMBB_1562322300at_int,big_co387207925at_nat),hAPP_f446977493at_nat(cOMBC_nat_int_nat,F))),A)),B)) # label(fact_489_setsum__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 511 (all F all B all A hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f2122367971at_nat(hAPP_f870149665at_nat(cOMBC_2036134968ol_nat,hAPP_f883871819ol_nat(hAPP_f424754463ol_nat(cOMBB_1716606670at_nat,big_co1340561246_a_nat),F)),B)),A) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f1464798435_a_nat(hAPP_f1012303887_a_nat(cOMBC_1159891896ol_nat,hAPP_f1669765561ol_nat(hAPP_f1073041467ol_nat(cOMBB_10565751iple_a,big_co387207925at_nat),hAPP_f2146713109at_nat(cOMBC_441305270_a_nat,F))),A)),B)) # label(fact_490_setsum__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 512 (all F all B all A hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f787214110nt_nat(hAPP_f261731407nt_nat(cOMBC_462113011ol_nat,hAPP_f1501159417ol_nat(hAPP_f1029311995ol_nat(cOMBB_1562322300at_int,big_co387207925at_nat),F)),B)),A) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1473602334at_nat(hAPP_f630508183at_nat(cOMBC_1505178355ol_nat,hAPP_f299305025ol_nat(hAPP_f1632710027ol_nat(cOMBB_1453893592at_nat,big_co1740723097nt_nat),hAPP_f879494613nt_nat(cOMBC_int_nat_nat,F))),A)),B)) # label(fact_491_setsum__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 513 (all F all B all A hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f1464798435_a_nat(hAPP_f1012303887_a_nat(cOMBC_1159891896ol_nat,hAPP_f1669765561ol_nat(hAPP_f1073041467ol_nat(cOMBB_10565751iple_a,big_co387207925at_nat),F)),B)),A) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f2122367971at_nat(hAPP_f870149665at_nat(cOMBC_2036134968ol_nat,hAPP_f883871819ol_nat(hAPP_f424754463ol_nat(cOMBB_1716606670at_nat,big_co1340561246_a_nat),hAPP_f1903462933_a_nat(cOMBC_667342884at_nat,F))),A)),B)) # label(fact_492_setsum__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 514 (all Z_1 all A all Y_1 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),Y_1)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A) = Y_1))) # label(fact_493_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 515 (all Z_1 all A all Y_1 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),Y_1)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A) = Y_1))) # label(fact_494_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 516 (all Z_1 all A all Y_1 all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),Y_1)) -> hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),A) = Y_1))) # label(fact_495_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 517 (all Z_1 all A all Y_1 all F (hBOOL(finite1321096241t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(hAPP_f1634429330l_bool(finite1008073724t_bool(F),Z_1),A),Y_1)) -> hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),A) = Y_1))) # label(fact_496_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 518 (all Z_1 all A all Y_1 all F (hBOOL(finite2114894759a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(hAPP_f1577095245l_bool(finite1152845682a_bool(F),Z_1),A),Y_1)) -> hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),A) = Y_1))) # label(fact_497_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 519 (all Z_1 all A all Y_1 all F (hBOOL(finite1071749497t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(hAPP_f1266913334l_bool(finite758726980t_bool(F),Z_1),A),Y_1)) -> hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),A) = Y_1))) # label(fact_498_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 520 (all F all Z_1 hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),bot_bo797238721a_bool) = Z_1) # label(fact_499_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 521 (all F all Z_1 hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),bot_bo797238721a_bool) = Z_1) # label(fact_500_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 522 (all F all Z_1 hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),bot_bot_fun_int_bool) = Z_1) # label(fact_501_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 523 (all F all Z_1 hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),bot_bot_fun_int_bool) = Z_1) # label(fact_502_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 524 (all F all Z_1 hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),bot_bot_fun_nat_bool) = Z_1) # label(fact_503_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 525 (all F all Z_1 hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),bot_bot_fun_nat_bool) = Z_1) # label(fact_504_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 526 (all Z_1 all X_1 all A all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)),A))))) # label(fact_505_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 527 (all Z_1 all X_1 all A all F (hBOOL(finite1071749497t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f800510211t_bool(finite1578363458t_bool(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),Z_1)),A))))) # label(fact_506_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 528 (all Z_1 all X_1 all A all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f1693662087iple_a(finite1205970312iple_a(F,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),Z_1)),A))))) # label(fact_507_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 529 (all Z_1 all X_1 all A all F (hBOOL(finite2114894759a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f20753329a_bool(finite1215486064a_bool(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),Z_1)),A))))) # label(fact_508_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 530 (all Z_1 all X_1 all A all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)),A))))) # label(fact_509_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 531 (all Z_1 all X_1 all A all F (hBOOL(finite1321096241t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1805168059t_bool(finite1827710202t_bool(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),Z_1)),A))))) # label(fact_510_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 532 (all Z_1 all X_1 all A all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A)))))) # label(fact_511_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 533 (all Z_1 all X_1 all A all F (hBOOL(finite1071749497t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),A)))))) # label(fact_512_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 534 (all Z_1 all X_1 all A all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),A)))))) # label(fact_513_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 535 (all Z_1 all X_1 all A all F (hBOOL(finite2114894759a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),A)))))) # label(fact_514_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 536 (all Z_1 all X_1 all A all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A)))))) # label(fact_515_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 537 (all Z_1 all X_1 all A all F (hBOOL(finite1321096241t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),A)))))) # label(fact_516_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 538 (all Z_1 all A all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),A)))))) # label(fact_517_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 539 (all Z_1 all A all F (hBOOL(finite2114894759a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(hAPP_f1577095245l_bool(finite1152845682a_bool(F),Z_1),A),hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),A)))))) # label(fact_518_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 540 (all Z_1 all A all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A)))))) # label(fact_519_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 541 (all Z_1 all A all F (hBOOL(finite1071749497t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(hAPP_f1266913334l_bool(finite758726980t_bool(F),Z_1),A),hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),A)))))) # label(fact_520_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 542 (all Z_1 all A all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A)))))) # label(fact_521_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 543 (all Z_1 all A all F (hBOOL(finite1321096241t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(hAPP_f1634429330l_bool(finite1008073724t_bool(F),Z_1),A),hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),A)))))) # label(fact_522_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 544 (all F all A all G all B hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),B)) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1473602334at_nat(hAPP_f630508183at_nat(cOMBC_1505178355ol_nat,hAPP_f299305025ol_nat(hAPP_f1632710027ol_nat(cOMBB_1453893592at_nat,big_co1740723097nt_nat),hAPP_f237327688nt_nat(hAPP_f1633513941nt_nat(cOMBC_1218031117nt_nat,hAPP_f2080483477nt_nat(hAPP_f1701814485nt_nat(cOMBB_737513486at_nat,cOMBB_nat_nat_int),hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,times_times_nat),F))),G))),B)),A)) # label(fact_523_setsum__product) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 545 (all F all A all G all B hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),B)) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f2122367971at_nat(hAPP_f870149665at_nat(cOMBC_2036134968ol_nat,hAPP_f883871819ol_nat(hAPP_f424754463ol_nat(cOMBB_1716606670at_nat,big_co1340561246_a_nat),hAPP_f1393576712_a_nat(hAPP_f145529813_a_nat(cOMBC_309106125_a_nat,hAPP_f1485673429_a_nat(hAPP_f2006236373_a_nat(cOMBB_2005430478at_nat,cOMBB_1250632933iple_a),hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,times_times_nat),F))),G))),B)),A)) # label(fact_524_setsum__product) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 546 (all F all A all G all B hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),B)) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f787214110nt_nat(hAPP_f261731407nt_nat(cOMBC_462113011ol_nat,hAPP_f1501159417ol_nat(hAPP_f1029311995ol_nat(cOMBB_1562322300at_int,big_co387207925at_nat),hAPP_f1169617132at_nat(hAPP_f701299925at_nat(cOMBC_1294079849at_nat,hAPP_f1033905301at_nat(hAPP_f1315855317at_nat(cOMBB_891709290at_int,cOMBB_nat_nat_nat),hAPP_f1463450952at_nat(hAPP_f1087393429at_nat(cOMBB_1601129847at_int,times_times_nat),F))),G))),B)),A)) # label(fact_525_setsum__product) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 547 (all F all A all G all B hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),B)) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f1464798435_a_nat(hAPP_f1012303887_a_nat(cOMBC_1159891896ol_nat,hAPP_f1669765561ol_nat(hAPP_f1073041467ol_nat(cOMBB_10565751iple_a,big_co387207925at_nat),hAPP_f221335601at_nat(hAPP_f388255893at_nat(cOMBC_1038836708at_nat,hAPP_f1879857877at_nat(hAPP_f481016213at_nat(cOMBB_1672982117iple_a,cOMBB_nat_nat_nat),hAPP_f429024520at_nat(hAPP_f703420885at_nat(cOMBB_789959282iple_a,times_times_nat),F))),G))),B)),A)) # label(fact_526_setsum__product) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 548 (all F all A all R_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)),R_2) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,times_times_nat),F)),R_2)),A)) # label(fact_527_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 549 (all F all A all R_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A)),R_2) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_nat_fun_int_nat(hAPP_f879494613nt_nat(cOMBC_int_nat_nat,hAPP_f1463450952at_nat(hAPP_f1087393429at_nat(cOMBB_1601129847at_int,times_times_nat),F)),R_2)),A)) # label(fact_528_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 550 (all F all A all R_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A)),R_2) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_n1653940209_a_nat(hAPP_f1903462933_a_nat(cOMBC_667342884at_nat,hAPP_f429024520at_nat(hAPP_f703420885at_nat(cOMBB_789959282iple_a,times_times_nat),F)),R_2)),A)) # label(fact_529_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 551 (all R_2 all F all A hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,R_2),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,hAPP_nat_fun_nat_nat(times_times_nat,R_2)),F)),A)) # label(fact_530_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 552 (all R_2 all F all A hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,R_2),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A)) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f2132704789nt_nat(hAPP_f901215189nt_nat(cOMBB_nat_nat_int,hAPP_nat_fun_nat_nat(times_times_nat,R_2)),F)),A)) # label(fact_531_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 553 (all R_2 all F all A hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,R_2),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A)) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f106743253_a_nat(hAPP_f500900629_a_nat(cOMBB_1250632933iple_a,hAPP_nat_fun_nat_nat(times_times_nat,R_2)),F)),A)) # label(fact_532_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 554 (all Y_1 all Z_1 all A all X_1 all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),X_1)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),Y_1)) -> Y_1 = X_1)))) # label(fact_535_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 555 (all Y_1 all Z_1 all A all X_1 all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),Y_1)) -> Y_1 = X_1)))) # label(fact_536_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 556 (all Y_1 all Z_1 all A all X_1 all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),X_1)) -> (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),Y_1)) -> Y_1 = X_1)))) # label(fact_537_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 557 (all G all H all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f2097660464ol_nat(big_co1815942735_a_nat(hAPP_f106743253_a_nat(hAPP_f1418102009_a_nat(cOMBS_1756972052at_nat,hAPP_f429024520at_nat(hAPP_f703420885at_nat(cOMBB_789959282iple_a,times_times_nat),G)),H)),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_f2097660464ol_nat(big_co1815942735_a_nat(G),A)),hAPP_f2097660464ol_nat(big_co1815942735_a_nat(H),A)))) # label(fact_538_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 558 (all G all H all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f587450508ol_int(big_co305732779_a_int(hAPP_f1561000661_a_int(hAPP_f789902073_a_int(cOMBS_1600277268nt_int,hAPP_f231878828nt_int(hAPP_f1621780181nt_int(cOMBB_1885471694iple_a,times_times_int),G)),H)),A) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_f587450508ol_int(big_co305732779_a_int(G),A)),hAPP_f587450508ol_int(big_co305732779_a_int(H),A)))) # label(fact_539_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 559 (all Z_1 all X_1 all A all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A) = 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),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_540_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 560 (all Z_1 all X_1 all A all F (hBOOL(finite1071749497t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))))) # label(fact_541_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 561 (all Z_1 all X_1 all A all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),A) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)))))))) # label(fact_542_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 562 (all Z_1 all X_1 all A all F (hBOOL(finite2114894759a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),A) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)))))))) # label(fact_543_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 563 (all Z_1 all X_1 all A all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A) = 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),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))))) # label(fact_544_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 564 (all Z_1 all X_1 all A all F (hBOOL(finite1321096241t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))))) # label(fact_545_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 565 (all Z_1 all X_1 all A all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = 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),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_546_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 566 (all Z_1 all X_1 all A all F (hBOOL(finite1071749497t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_547_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 567 (all Z_1 all X_1 all A all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))))))) # label(fact_548_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 568 (all Z_1 all X_1 all A all F (hBOOL(finite2114894759a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))))))) # label(fact_549_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 569 (all Z_1 all X_1 all A all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = 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),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_550_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 570 (all Z_1 all X_1 all A all F (hBOOL(finite1321096241t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_551_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 571 (all F all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f22106695ol_nat(big_co1705425894at_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(F,A_13)),hAPP_f22106695ol_nat(big_co1705425894at_nat(F),A))))) # label(fact_552_setprod__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 572 (all F all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f2097660464ol_nat(big_co1815942735_a_nat(F),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_H592031934_a_nat(F,A_13)),hAPP_f2097660464ol_nat(big_co1815942735_a_nat(F),A))))) # label(fact_553_setprod__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 573 (all F all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f659380387ol_int(big_co195215938at_int(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(F,A_13)),hAPP_f659380387ol_int(big_co195215938at_int(F),A))))) # label(fact_554_setprod__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 574 (all F all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f587450508ol_int(big_co305732779_a_int(F),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_H1229305626_a_int(F,A_13)),hAPP_f587450508ol_int(big_co305732779_a_int(F),A))))) # label(fact_555_setprod__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 575 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(big_co1705425894at_nat(G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(G,X_1)),hAPP_f22106695ol_nat(big_co1705425894at_nat(G),A))))) # label(fact_556_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 576 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f2097660464ol_nat(big_co1815942735_a_nat(G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_H592031934_a_nat(G,X_1)),hAPP_f2097660464ol_nat(big_co1815942735_a_nat(G),A))))) # label(fact_557_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 577 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f659380387ol_int(big_co195215938at_int(G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(G,X_1)),hAPP_f659380387ol_int(big_co195215938at_int(G),A))))) # label(fact_558_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 578 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f587450508ol_int(big_co305732779_a_int(G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_H1229305626_a_int(G,X_1)),hAPP_f587450508ol_int(big_co305732779_a_int(G),A))))) # label(fact_559_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 579 (all F all A_13 all A ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)),hAPP_nat_nat(F,A_13))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)))) # label(fact_560_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 580 (all F all A_13 all A ((hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A)),hAPP_H592031934_a_nat(F,A_13))) & (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A)))) # label(fact_561_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 581 (all F all A_13 all A ((hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A)),hAPP_int_nat(F,A_13))) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A)))) # label(fact_562_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 582 (all F all Z_1 all A hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A) = hAPP_f1594865479ol_int(the_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A))) # label(fact_563_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 583 (all F all Z_1 all A hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A) = hAPP_f22106695ol_nat(the_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A))) # label(fact_564_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 584 (all F all Z_1 all A hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),A) = hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A))) # label(fact_565_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 585 (all F all Z_1 all A hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),A) = hAPP_f631471077t_bool(the_fun_int_bool,hAPP_f284875647l_bool(hAPP_f1634429330l_bool(finite1008073724t_bool(F),Z_1),A))) # label(fact_566_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 586 (all F all Z_1 all A hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),A) = hAPP_f258822235a_bool(the_fu1555441254a_bool,hAPP_f1767618879l_bool(hAPP_f1577095245l_bool(finite1152845682a_bool(F),Z_1),A))) # label(fact_567_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 587 (all F all Z_1 all A hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),A) = hAPP_f582319405t_bool(the_fun_nat_bool,hAPP_f103356543l_bool(hAPP_f1266913334l_bool(finite758726980t_bool(F),Z_1),A))) # label(fact_568_fold__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 588 (all Z_1 all X_1 all A all F (hBOOL(finite1860950092at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Z_1)),A)))) # label(fact_569_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 589 (all Z_1 all X_1 all A all F (hBOOL(finite1956789438t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f800510211t_bool(finite1578363458t_bool(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),Z_1)),A)))) # label(fact_570_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 590 (all Z_1 all X_1 all A all F (hBOOL(finite648855052iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f1693662087iple_a(finite1205970312iple_a(F,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),Z_1)),A)))) # label(fact_571_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 591 (all Z_1 all X_1 all A all F (hBOOL(finite1803123436a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f20753329a_bool(finite1215486064a_bool(F,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),Z_1)),A)))) # label(fact_572_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 592 (all Z_1 all X_1 all A all F (hBOOL(finite1704255308nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Z_1)),A)))) # label(fact_573_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 593 (all Z_1 all X_1 all A all F (hBOOL(finite58652534t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1805168059t_bool(finite1827710202t_bool(F,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),Z_1)),A)))) # label(fact_574_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 594 (all Z_1 all X_1 all A all F (hBOOL(finite1860950092at_nat(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(finite_fold_nat_nat(F,Z_1),A))))) # label(fact_575_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 595 (all Z_1 all X_1 all A all F (hBOOL(finite1956789438t_bool(F)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(F,X_1),hAPP_f800510211t_bool(finite1578363458t_bool(F,Z_1),A))))) # label(fact_576_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 596 (all Z_1 all X_1 all A all F (hBOOL(finite648855052iple_a(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),hAPP_f1693662087iple_a(finite1205970312iple_a(F,Z_1),A))))) # label(fact_577_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 597 (all Z_1 all X_1 all A all F (hBOOL(finite1803123436a_bool(F)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(F,X_1),hAPP_f20753329a_bool(finite1215486064a_bool(F,Z_1),A))))) # label(fact_578_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 598 (all Z_1 all X_1 all A all F (hBOOL(finite1704255308nt_int(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(finite_fold_int_int(F,Z_1),A))))) # label(fact_579_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 599 (all Z_1 all X_1 all A all F (hBOOL(finite58652534t_bool(F)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(F,X_1),hAPP_f1805168059t_bool(finite1827710202t_bool(F,Z_1),A))))) # label(fact_580_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 600 (all X_1 all A all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,X_1),A))))) # label(fact_581_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 601 (all X_1 all A all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_f1693662087iple_a(finite1205970312iple_a(F,X_1),A))))) # label(fact_582_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 602 (all X_1 all A all F all F_1 (hBOOL(finite1626084323ne_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,X_1),A))))) # label(fact_583_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 603 (all A_13 all A all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(F,A_13),A)))) # label(fact_584_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 604 (all A_13 all A all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),A)) = hAPP_f1693662087iple_a(finite1205970312iple_a(F,A_13),A)))) # label(fact_585_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 605 (all A_13 all A all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A)) = hAPP_f1594865479ol_int(finite_fold_int_int(F,A_13),A)))) # label(fact_586_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 606 (all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f22106695ol_nat(finite_fold1_nat(times_times_nat),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),A)) = hAPP_f22106695ol_nat(finite_fold_nat_nat(times_times_nat,A_13),A)))) # label(fact_587_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 607 (all A_13 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f1594865479ol_int(finite_fold1_int(times_times_int),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),A)) = hAPP_f1594865479ol_int(finite_fold_int_int(times_times_int,A_13),A)))) # label(fact_588_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 608 (all Z_1 all X_1 all A all V all F (hBOOL(finite2130160977at_nat(F)) -> (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),V)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> -(all Y_21 (V = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),Y_21) -> -hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(finite929467206at_nat(F),Z_1),A),Y_21)))))))) # label(fact_589_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 609 (all Z_1 all X_1 all A all V all F (hBOOL(finite1428139793iple_a(F)) -> (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)),V)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> -(all Y_21 (V = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_1),Y_21) -> -hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(finite90892550iple_a(F),Z_1),A),Y_21)))))))) # label(fact_590_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 610 (all Z_1 all X_1 all A all V all F (hBOOL(finite1973466193nt_int(F)) -> (hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),V)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> -(all Y_21 (V = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),Y_21) -> -hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(finite772772422nt_int(F),Z_1),A),Y_21)))))))) # label(fact_591_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 611 (all G all F all S_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,S_1)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),S_1) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f966999552at_nat(hAPP_f724467227at_nat(cOMBB_161916371at_nat,hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G)),hAPP_f2087582327a_bool(hAPP_f1396758363a_bool(cOMBB_391046962ol_nat,collec351493750iple_a),hAPP_f2087582327a_bool(hAPP_f1396758363a_bool(cOMBB_391046962ol_nat,hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_1)))),hAPP_f228417655a_bool(cOMBC_364739t_bool,hAPP_f1872860171t_bool(hAPP_f1981448543t_bool(cOMBB_1391527205iple_a,fequal_nat),F)))))),image_48635758_a_nat(F,S_1)))) # label(fact_592_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 612 (all G all F all S_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,S_1)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),S_1) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f389300155at_nat(hAPP_f109563153at_nat(cOMBB_1381347800at_nat,hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G)),hAPP_f2022049025t_bool(hAPP_f1986088027t_bool(cOMBB_2101530536ol_nat,collect_int),hAPP_f2022049025t_bool(hAPP_f1986088027t_bool(cOMBB_2101530536ol_nat,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),S_1)))),hAPP_f175561985t_bool(cOMBC_int_nat_bool,hAPP_f876579787t_bool(hAPP_f2026117279t_bool(cOMBB_1437810218ol_int,fequal_nat),F)))))),image_int_nat(F,S_1)))) # label(fact_593_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 613 (all G all F all S_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S_1)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),S_1) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f2085403241_a_nat(hAPP_f734830747_a_nat(cOMBB_1107515603iple_a,hAPP_f782000547ol_nat(big_co387207925at_nat,G)),hAPP_f27379319t_bool(hAPP_f196067081t_bool(cOMBB_437532599iple_a,collect_nat),hAPP_f27379319t_bool(hAPP_f196067081t_bool(cOMBB_437532599iple_a,hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))),hAPP_f1886543991t_bool(cOMBC_533513393a_bool,hAPP_f260875897a_bool(hAPP_f1930382715a_bool(cOMBB_1063143712ol_nat,fequal963300192iple_a),F)))))),image_1865589340iple_a(F,S_1)))) # label(fact_594_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 614 (all G all F all S_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,S_1)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),S_1) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f1134349059nt_nat(hAPP_f2100446809nt_nat(cOMBB_2018621492at_int,hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G)),hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,collect_int),hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),S_1)))),hAPP_f428220345t_bool(cOMBC_int_int_bool,hAPP_f1791153283t_bool(hAPP_f1399575567t_bool(cOMBB_118231410ol_int,fequal_int),F)))))),image_int_int(F,S_1)))) # label(fact_595_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 615 (all G all F all S_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,S_1)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),S_1) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f342603021_a_nat(hAPP_f575660003_a_nat(cOMBB_1357028143iple_a,hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G)),hAPP_f138254639t_bool(hAPP_f1998609161t_bool(cOMBB_1870764287iple_a,collect_int),hAPP_f138254639t_bool(hAPP_f1998609161t_bool(cOMBB_1870764287iple_a,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),S_1)))),hAPP_f936407855t_bool(cOMBC_1719122773a_bool,hAPP_f298605433a_bool(hAPP_f1421841531a_bool(cOMBB_1700417404ol_int,fequal963300192iple_a),F)))))),image_1844722432iple_a(F,S_1)))) # label(fact_596_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 616 (all G all F all S_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S_1)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),S_1) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f1161717855nt_nat(hAPP_f1964560145nt_nat(cOMBB_1125113304at_int,hAPP_f782000547ol_nat(big_co387207925at_nat,G)),hAPP_f783004929t_bool(hAPP_f1410409747t_bool(cOMBB_1746576572ol_int,collect_nat),hAPP_f783004929t_bool(hAPP_f1410409747t_bool(cOMBB_1746576572ol_int,hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))),hAPP_f482008321t_bool(cOMBC_nat_int_bool,hAPP_f1533130627t_bool(hAPP_f879109391t_bool(cOMBB_1628441366ol_nat,fequal_int),F)))))),image_nat_int(F,S_1)))) # label(fact_597_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 617 (all G all H all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> ((all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) -> hAPP_H592031934_a_nat(G,X_2) = hAPP_H592031934_a_nat(H,X_2))) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),A) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,H),A)))) # label(fact_598_setsum_Ocong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 618 (all G all H all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hAPP_nat_nat(G,X_2) = hAPP_nat_nat(H,X_2))) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),A) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,H),A)))) # label(fact_599_setsum_Ocong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 619 (all G all H all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) -> hAPP_int_nat(G,X_2) = hAPP_int_nat(H,X_2))) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),A) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,H),A)))) # label(fact_600_setsum_Ocong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 620 (all F all R_1 all T_1 all S_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,S_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,T_1)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f1161717855nt_nat(hAPP_f369809936nt_nat(cOMBS_1063588099ol_nat,hAPP_f1501159417ol_nat(hAPP_f1029311995ol_nat(cOMBB_1562322300at_int,big_co387207925at_nat),F)),hAPP_f783004929t_bool(hAPP_f1410409747t_bool(cOMBB_1746576572ol_int,collect_nat),hAPP_f783004929t_bool(hAPP_f1410409747t_bool(cOMBB_1746576572ol_int,hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),T_1)))),R_1)))),S_1) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f389300155at_nat(hAPP_f1750007732at_nat(cOMBS_2106653443ol_nat,hAPP_f299305025ol_nat(hAPP_f1632710027ol_nat(cOMBB_1453893592at_nat,big_co1740723097nt_nat),hAPP_f879494613nt_nat(cOMBC_int_nat_nat,F))),hAPP_f2022049025t_bool(hAPP_f1986088027t_bool(cOMBB_2101530536ol_nat,collect_int),hAPP_f2022049025t_bool(hAPP_f1986088027t_bool(cOMBB_2101530536ol_nat,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),S_1)))),hAPP_f175561985t_bool(cOMBC_int_nat_bool,R_1))))),T_1)))) # label(fact_601_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 621 (all F all R_1 all T_1 all S_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,S_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,T_1)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f2085403241_a_nat(hAPP_f1052116629_a_nat(cOMBS_397915080ol_nat,hAPP_f1669765561ol_nat(hAPP_f1073041467ol_nat(cOMBB_10565751iple_a,big_co387207925at_nat),F)),hAPP_f27379319t_bool(hAPP_f196067081t_bool(cOMBB_437532599iple_a,collect_nat),hAPP_f27379319t_bool(hAPP_f196067081t_bool(cOMBB_437532599iple_a,hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),T_1)))),R_1)))),S_1) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f966999552at_nat(hAPP_f264818750at_nat(cOMBS_1274158152ol_nat,hAPP_f883871819ol_nat(hAPP_f424754463ol_nat(cOMBB_1716606670at_nat,big_co1340561246_a_nat),hAPP_f1903462933_a_nat(cOMBC_667342884at_nat,F))),hAPP_f2087582327a_bool(hAPP_f1396758363a_bool(cOMBB_391046962ol_nat,collec351493750iple_a),hAPP_f2087582327a_bool(hAPP_f1396758363a_bool(cOMBB_391046962ol_nat,hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_1)))),hAPP_f228417655a_bool(cOMBC_364739t_bool,R_1))))),T_1)))) # label(fact_602_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.18 622 (all F all R_1 all T_1 all S_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,S_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,T_1)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f342603021_a_nat(hAPP_f270087133_a_nat(cOMBS_1333400172ol_nat,hAPP_f224922881ol_nat(hAPP_f543861963ol_nat(cOMBB_1075417391iple_a,big_co1740723097nt_nat),F)),hAPP_f138254639t_bool(hAPP_f1998609161t_bool(cOMBB_1870764287iple_a,collect_int),hAPP_f138254639t_bool(hAPP_f1998609161t_bool(cOMBB_1870764287iple_a,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),T_1)))),R_1)))),S_1) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f2050777416nt_nat(hAPP_f1895921634nt_nat(cOMBS_202713324ol_nat,hAPP_f1442126667ol_nat(hAPP_f1072896543ol_nat(cOMBB_206396714at_int,big_co1340561246_a_nat),hAPP_f183615253_a_nat(cOMBC_2020858056nt_nat,F))),hAPP_f1718504751a_bool(hAPP_f481410067a_bool(cOMBB_1028320654ol_int,collec351493750iple_a),hAPP_f1718504751a_bool(hAPP_f481410067a_bool(cOMBB_1028320654ol_int,hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_1)))),hAPP_f920351535a_bool(cOMBC_1530706207t_bool,R_1))))),T_1)))) # label(fact_603_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 623 (all F all R_1 all T_1 all S_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,T_1)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f389300155at_nat(hAPP_f1750007732at_nat(cOMBS_2106653443ol_nat,hAPP_f299305025ol_nat(hAPP_f1632710027ol_nat(cOMBB_1453893592at_nat,big_co1740723097nt_nat),F)),hAPP_f2022049025t_bool(hAPP_f1986088027t_bool(cOMBB_2101530536ol_nat,collect_int),hAPP_f2022049025t_bool(hAPP_f1986088027t_bool(cOMBB_2101530536ol_nat,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),T_1)))),R_1)))),S_1) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f1161717855nt_nat(hAPP_f369809936nt_nat(cOMBS_1063588099ol_nat,hAPP_f1501159417ol_nat(hAPP_f1029311995ol_nat(cOMBB_1562322300at_int,big_co387207925at_nat),hAPP_f446977493at_nat(cOMBC_nat_int_nat,F))),hAPP_f783004929t_bool(hAPP_f1410409747t_bool(cOMBB_1746576572ol_int,collect_nat),hAPP_f783004929t_bool(hAPP_f1410409747t_bool(cOMBB_1746576572ol_int,hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))),hAPP_f482008321t_bool(cOMBC_nat_int_bool,R_1))))),T_1)))) # label(fact_604_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 624 (all F all R_1 all T_1 all S_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,T_1)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f966999552at_nat(hAPP_f264818750at_nat(cOMBS_1274158152ol_nat,hAPP_f883871819ol_nat(hAPP_f424754463ol_nat(cOMBB_1716606670at_nat,big_co1340561246_a_nat),F)),hAPP_f2087582327a_bool(hAPP_f1396758363a_bool(cOMBB_391046962ol_nat,collec351493750iple_a),hAPP_f2087582327a_bool(hAPP_f1396758363a_bool(cOMBB_391046962ol_nat,hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),T_1)))),R_1)))),S_1) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f2085403241_a_nat(hAPP_f1052116629_a_nat(cOMBS_397915080ol_nat,hAPP_f1669765561ol_nat(hAPP_f1073041467ol_nat(cOMBB_10565751iple_a,big_co387207925at_nat),hAPP_f2146713109at_nat(cOMBC_441305270_a_nat,F))),hAPP_f27379319t_bool(hAPP_f196067081t_bool(cOMBB_437532599iple_a,collect_nat),hAPP_f27379319t_bool(hAPP_f196067081t_bool(cOMBB_437532599iple_a,hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))),hAPP_f1886543991t_bool(cOMBC_533513393a_bool,R_1))))),T_1)))) # label(fact_605_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 625 (all F all R_1 all T_1 all S_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,S_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,T_1)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f1134349059nt_nat(hAPP_f446447448nt_nat(cOMBS_1999073191ol_nat,hAPP_f1548925761ol_nat(hAPP_f1331458699ol_nat(cOMBB_2091167284at_int,big_co1740723097nt_nat),F)),hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,collect_int),hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),T_1)))),R_1)))),S_1) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f1134349059nt_nat(hAPP_f446447448nt_nat(cOMBS_1999073191ol_nat,hAPP_f1548925761ol_nat(hAPP_f1331458699ol_nat(cOMBB_2091167284at_int,big_co1740723097nt_nat),hAPP_f909851349nt_nat(cOMBC_int_int_nat,F))),hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,collect_int),hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),S_1)))),hAPP_f428220345t_bool(cOMBC_int_int_bool,R_1))))),T_1)))) # label(fact_606_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 626 (all F all R_1 all T_1 all S_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,S_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,T_1)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f2050777416nt_nat(hAPP_f1895921634nt_nat(cOMBS_202713324ol_nat,hAPP_f1442126667ol_nat(hAPP_f1072896543ol_nat(cOMBB_206396714at_int,big_co1340561246_a_nat),F)),hAPP_f1718504751a_bool(hAPP_f481410067a_bool(cOMBB_1028320654ol_int,collec351493750iple_a),hAPP_f1718504751a_bool(hAPP_f481410067a_bool(cOMBB_1028320654ol_int,hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),T_1)))),R_1)))),S_1) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f342603021_a_nat(hAPP_f270087133_a_nat(cOMBS_1333400172ol_nat,hAPP_f224922881ol_nat(hAPP_f543861963ol_nat(cOMBB_1075417391iple_a,big_co1740723097nt_nat),hAPP_f1451619093nt_nat(cOMBC_1917249810_a_nat,F))),hAPP_f138254639t_bool(hAPP_f1998609161t_bool(cOMBB_1870764287iple_a,collect_int),hAPP_f138254639t_bool(hAPP_f1998609161t_bool(cOMBB_1870764287iple_a,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),S_1)))),hAPP_f936407855t_bool(cOMBC_1719122773a_bool,R_1))))),T_1)))) # label(fact_607_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 627 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(G,X_1)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_608_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 628 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,G),A) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(G,X_1)),hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))))) # label(fact_609_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 629 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,G),A) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_H1229305626_a_int(G,X_1)),hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))))))) # label(fact_610_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 630 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,G),A) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(G,X_1)),hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_611_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 631 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_H592031934_a_nat(G,X_1)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))))))) # label(fact_612_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 632 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(G,X_1)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))))) # label(fact_613_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 633 (all F all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,A_13)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))))))) # label(fact_614_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 634 (all F all A_13 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),A)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),A) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(F,A_13)),hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),bot_bot_fun_nat_bool))))))) # label(fact_615_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 635 (all F all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),A) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_H1229305626_a_int(F,A_13)),hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))))))) # label(fact_616_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 636 (all F all A_13 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),A) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(F,A_13)),hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))))))) # label(fact_617_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 637 (all F all A_13 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_H592031934_a_nat(F,A_13)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),bot_bo797238721a_bool))))))) # label(fact_618_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 638 (all F all A_13 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(F,A_13)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),bot_bot_fun_int_bool))))))) # label(fact_619_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 639 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(G,X_1)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))) # label(fact_620_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 640 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(G,X_1)),hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,G),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))))) # label(fact_621_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 641 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_H1229305626_a_int(G,X_1)),hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)))))) # label(fact_622_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 642 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,G),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(G,X_1)),hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))) # label(fact_623_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 643 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_H592031934_a_nat(G,X_1)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool)))))) # label(fact_624_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 644 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(G,X_1)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))))) # label(fact_625_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 645 (all F all G all A hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1914919701at_nat(hAPP_f1408247010at_nat(cOMBS_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),F)),G)),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),A))) # label(fact_626_setsum__addf) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 646 (all F all G all A hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f2132704789nt_nat(hAPP_f1399363134nt_nat(cOMBS_int_nat_nat,hAPP_f1463450952at_nat(hAPP_f1087393429at_nat(cOMBB_1601129847at_int,plus_plus_nat),F)),G)),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),A))) # label(fact_627_setsum__addf) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 647 (all F all G all A hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f106743253_a_nat(hAPP_f1418102009_a_nat(cOMBS_1756972052at_nat,hAPP_f429024520at_nat(hAPP_f703420885at_nat(cOMBB_789959282iple_a,plus_plus_nat),F)),G)),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),A))) # label(fact_628_setsum__addf) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 648 (all G all H all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1914919701at_nat(hAPP_f1408247010at_nat(cOMBS_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),G)),H)),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),A)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,H),A)))) # label(fact_629_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 649 (all G all H all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,hAPP_f106743253_a_nat(hAPP_f1418102009_a_nat(cOMBS_1756972052at_nat,hAPP_f429024520at_nat(hAPP_f703420885at_nat(cOMBB_789959282iple_a,plus_plus_nat),G)),H)),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),A)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,H),A)))) # label(fact_630_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 650 (all G all H all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,hAPP_f1561000661_a_int(hAPP_f789902073_a_int(cOMBS_1600277268nt_int,hAPP_f231878828nt_int(hAPP_f1621780181nt_int(cOMBB_1885471694iple_a,plus_plus_int),G)),H)),A) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,G),A)),hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,H),A)))) # label(fact_631_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 651 (all G all H all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,hAPP_f2132704789nt_nat(hAPP_f1399363134nt_nat(cOMBS_int_nat_nat,hAPP_f1463450952at_nat(hAPP_f1087393429at_nat(cOMBB_1601129847at_int,plus_plus_nat),G)),H)),A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),A)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,H),A)))) # label(fact_632_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 652 (all F all A_13 all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),F_1)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),F_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,A_13)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),F_1))))) # label(fact_633_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 653 (all F all A_13 all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_13),F_1)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),F_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(F,A_13)),hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,F),F_1))))) # label(fact_634_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 654 (all F all A_13 all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),F_1)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),F_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_H1229305626_a_int(F,A_13)),hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,F),F_1))))) # label(fact_635_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 655 (all F all A_13 all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_13),F_1)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),F_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_H592031934_a_nat(F,A_13)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),F_1))))) # label(fact_636_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 656 (all F all A_13 all F_1 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_13),F_1)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),F_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(F,A_13)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),F_1))))) # label(fact_637_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 657 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(G,X_1)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),A))))) # label(fact_638_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 658 (all G all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,G),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(G,X_1)),hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,G),A))))) # label(fact_639_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 659 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_H1229305626_a_int(G,X_1)),hAPP_f587450508ol_int(hAPP_f1544320301ol_int(big_co1977834938_a_int,G),A))))) # label(fact_640_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 660 (all G all X_1 all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_H592031934_a_nat(G,X_1)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),A))))) # label(fact_641_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 661 (all G all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(G,X_1)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),A))))) # label(fact_642_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 662 (all A_13 all E all Ca all Ba 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_13),E)),Ca) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),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,Ba),A_13)),E)),D_1))) # label(fact_643_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 663 (all A_13 all E all Ca all Ba 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_13),E)),Ca) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),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_13),Ba)),E)),Ca) = D_1)) # label(fact_644_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 664 (all A_42 all B_34 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_42),B_34)),B_34) = A_42) # label(fact_645_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 665 (all A_41 all B_33 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_41),B_33)),B_33) = A_41) # label(fact_646_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 666 (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_647_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 667 (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_648_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 668 (all A_40 all E_1 all B_32 all C_28 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_40),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_32),E_1)),C_28)) = 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_40),B_32)),E_1)),C_28)) # label(fact_649_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 669 (all A_40 all E_1 all B_32 all C_28 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_40),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_32),E_1)),C_28)) = 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_40),B_32)),E_1)),C_28)) # label(fact_650_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 670 (all A_39 all M_4 all B_31 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_39),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_31),M_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_39),B_31)),M_4)) # label(fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 671 (all A_39 all M_4 all B_31 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_39),M_4)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_31),M_4)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_39),B_31)),M_4)) # label(fact_652_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 672 (all B_30 all A_38 all C_27 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_30),A_38) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_27),A_38) -> B_30 = C_27)) # label(fact_653_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 673 (all B_30 all A_38 all C_27 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_30),A_38) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_27),A_38) -> B_30 = C_27)) # label(fact_654_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 674 (all A_37 all B_29 all C_26 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_37),B_29) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_37),C_26) -> B_29 = C_26)) # label(fact_655_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 675 (all A_37 all B_29 all C_26 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_37),B_29) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_37),C_26) -> B_29 = C_26)) # label(fact_656_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 676 (all A_36 all B_28 all C_25 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_36),B_28) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_36),C_25) -> B_28 = C_25)) # label(fact_657_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 677 (all A_36 all B_28 all C_25 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_36),B_28) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_36),C_25) -> B_28 = C_25)) # label(fact_658_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 678 (all A_35 all B_27 all C_24 all D_6 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_35),B_27)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_24),D_6)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_35),C_24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_27),D_6))) # label(fact_659_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 679 (all A_35 all B_27 all C_24 all D_6 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_35),B_27)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_24),D_6)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_35),C_24)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_27),D_6))) # label(fact_660_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 680 (all Ba all A_13 all Ca (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),A_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_13) <-> Ba = Ca)) # label(fact_661_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 681 (all Ba all A_13 all Ca (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),A_13) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_13) <-> Ba = Ca)) # label(fact_662_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 682 (all A_13 all Ba all Ca (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),Ca) <-> Ba = Ca)) # label(fact_663_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 683 (all A_13 all Ba all Ca (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),Ba) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),Ca) <-> Ba = Ca)) # label(fact_664_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 684 (all A_34 all B_26 all C_23 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_34),B_26)),C_23) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_34),C_23)),B_26)) # label(fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 685 (all A_34 all B_26 all C_23 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_34),B_26)),C_23) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_34),C_23)),B_26)) # label(fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 686 (all A_33 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(plus_plus_nat,A_33),B_25)),C_22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_33),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_25),C_22))) # label(fact_667_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 687 (all A_33 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(plus_plus_int,A_33),B_25)),C_22) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_33),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_25),C_22))) # label(fact_668_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 688 (all A_32 all B_24 all C_21 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_32),B_24)),C_21) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_32),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_24),C_21))) # label(fact_669_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 689 (all A_32 all B_24 all C_21 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_32),B_24)),C_21) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_32),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_24),C_21))) # label(fact_670_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 690 (all A_31 all C_20 all D_5 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_31),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_20),D_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_31),C_20)),D_5)) # label(fact_671_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 691 (all A_31 all C_20 all D_5 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_31),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_20),D_5)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_31),C_20)),D_5)) # label(fact_672_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 692 (all A_30 all C_19 all D_4 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_19),D_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_30),D_4))) # label(fact_673_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 693 (all A_30 all C_19 all D_4 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_19),D_4)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_19),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_30),D_4))) # label(fact_674_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 694 (all A_29 all C_18 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_29),C_18) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_18),A_29)) # label(fact_675_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 695 (all A_29 all C_18 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_29),C_18) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_18),A_29)) # label(fact_676_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 696 (all Lx_6 all Ly_4 all Rx_6 all Ry_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),Ly_4)),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,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),Rx_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly_4),Ry_4))) # label(fact_677_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 697 (all Lx_6 all Ly_4 all Rx_6 all Ry_4 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),Ly_4)),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,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),Rx_6)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly_4),Ry_4))) # label(fact_678_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 698 (all Lx_5 all Ly_3 all Rx_5 all 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),Ly_3)),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,Rx_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_5),Ly_3)),Ry_3))) # label(fact_679_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 699 (all Lx_5 all Ly_3 all Rx_5 all 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),Ly_3)),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,Rx_5),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_5),Ly_3)),Ry_3))) # label(fact_680_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 700 (all Lx_4 all Ly_2 all Rx_4 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_4),Ly_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_4),Ry_2)) = 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_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_4),Ry_2)))) # label(fact_681_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 701 (all Lx_4 all Ly_2 all Rx_4 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_4),Ly_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_4),Ry_2)) = 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_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_4),Ry_2)))) # label(fact_682_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 702 (all Lx_3 all Ly_1 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_1)),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_1)) # label(fact_683_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 703 (all Lx_3 all Ly_1 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_1)),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_1)) # label(fact_684_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 704 (all Lx_2 all Ly all Rx_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)),Rx_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),Rx_2))) # label(fact_685_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 705 (all Lx_2 all Ly all Rx_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)),Rx_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),Rx_2))) # label(fact_686_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 706 (all A_28 all B_23 all C_17 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_28),B_23)),C_17) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_28),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_23),C_17))) # label(fact_687_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 707 (all A_28 all B_23 all C_17 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_28),B_23)),C_17) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_28),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_23),C_17))) # label(fact_688_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 708 (all Lx_1 all Rx_1 all Ry_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_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,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_1),Rx_1)),Ry_1)) # label(fact_689_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 709 (all Lx_1 all Rx_1 all Ry_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_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,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_1),Rx_1)),Ry_1)) # label(fact_690_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 710 (all Lx all Rx all Ry hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx),Ry)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),Ry))) # label(fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 711 (all Lx all Rx all Ry hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx),Ry)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),Ry))) # label(fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 712 (all A_27 all B_22 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_27),B_22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_22),A_27)) # label(fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 713 (all A_27 all B_22 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_27),B_22) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_22),A_27)) # label(fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 714 (all A_13 all Ba all Ca all D_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_13),Ba) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ca),D_1) -> (A_13 = Ba <-> Ca = D_1))) # label(fact_695_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 715 (all X_27 all Y_20 all Z_10 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_27),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_20),Z_10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_27),Y_20)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_27),Z_10))) # label(fact_696_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 716 (all X_27 all Y_20 all Z_10 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_27),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y_20),Z_10)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_27),Y_20)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_27),Z_10))) # label(fact_697_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 717 (all Ca all D_1 all A_13 all Ba (A_13 != Ba & 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_13),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ba),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_13),D_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ba),Ca)))) # label(fact_698_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 718 (all Ca all D_1 all A_13 all Ba (A_13 != Ba & 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_13),Ca)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),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_13),D_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),Ca)))) # label(fact_699_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 719 (all A_26 all B_21 all C_16 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_26),B_21)),C_16) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_26),C_16)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_21),C_16))) # label(fact_700_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 720 (all A_26 all B_21 all C_16 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_26),B_21)),C_16) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_26),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_21),C_16))) # label(fact_701_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 721 (all A_25 all B_20 all C_15 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_25),B_20)),C_15) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_25),C_15)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_20),C_15))) # label(fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 722 (all A_25 all B_20 all C_15 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_25),B_20)),C_15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_25),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_20),C_15))) # label(fact_703_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 723 (all F all G all A ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) -> hAPP_int_nat(F,X_2) = hAPP_int_nat(G,X_2))) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),A))) # label(fact_704_setsum__cong2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 724 (all F all G all A ((all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) -> hAPP_H592031934_a_nat(F,X_2) = hAPP_H592031934_a_nat(G,X_2))) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),A))) # label(fact_705_setsum__cong2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 725 (all F all G all A ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hAPP_nat_nat(F,X_2) = hAPP_nat_nat(G,X_2))) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),A))) # label(fact_706_setsum__cong2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 726 (all F all G all A all B (A = B -> ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B)) -> hAPP_int_nat(F,X_2) = hAPP_int_nat(G,X_2))) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),B)))) # label(fact_707_setsum__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 727 (all F all G all A all B (A = B -> ((all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B)) -> hAPP_H592031934_a_nat(F,X_2) = hAPP_H592031934_a_nat(G,X_2))) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),B)))) # label(fact_708_setsum__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 728 (all F all G all A all B (A = B -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) -> hAPP_nat_nat(F,X_2) = hAPP_nat_nat(G,X_2))) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),B)))) # label(fact_709_setsum__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 729 (all H all G all A all B (A = B -> ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B)) -> hAPP_int_nat(H,X_2) = hAPP_int_nat(G,X_2))) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,H),A) = hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),B)))) # label(fact_710_setsum_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 730 (all H all G all A all B (A = B -> ((all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B)) -> hAPP_H592031934_a_nat(H,X_2) = hAPP_H592031934_a_nat(G,X_2))) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,H),A) = hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),B)))) # label(fact_711_setsum_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 731 (all H all G all A all B (A = B -> ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) -> hAPP_nat_nat(H,X_2) = hAPP_nat_nat(G,X_2))) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,H),A) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),B)))) # label(fact_712_setsum_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 732 (all K_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,K_1),bot_bot_fun_nat_bool)),hAPP_n1699378549t_bool(ord_lessThan_nat,K_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,K_1),bot_bot_fun_nat_bool)) # label(fact_713_single__Diff__lessThan) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 733 (all K_1 hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,K_1),bot_bot_fun_int_bool)),hAPP_i1948725293t_bool(ord_lessThan_int,K_1)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,K_1),bot_bot_fun_int_bool)) # label(fact_714_single__Diff__lessThan) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 734 (all F all A all B (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,B),A)) -> hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),A)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),B))))) # label(fact_715_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 735 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) -> hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),A)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),B))))) # label(fact_716_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 736 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),A)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),B))))) # label(fact_717_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 737 (all X_1 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),X_1))) # label(fact_718_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 738 (all X_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),X_1))) # label(fact_719_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 739 (all X_26 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_26),X_26))) # label(fact_720_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 740 (all X_26 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_26),X_26))) # label(fact_721_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 741 (all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) -> A = B))) # label(fact_722_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 742 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> A = B))) # label(fact_723_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 743 (all Ca all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Ca),B))))) # label(fact_724_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 744 (all Ca all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ca),B))))) # label(fact_725_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 745 (all Ca all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B))))) # label(fact_726_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 746 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A))) # label(fact_727_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 747 (all A hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A))) # label(fact_728_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 748 (all A hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,bot_bo797238721a_bool),A))) # label(fact_729_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 749 (all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,ord_le1523781517a_bool),A)))))) # label(fact_730_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 750 (all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(collect_fun_int_bool,hAPP_f284875647l_bool(hAPP_f1399552105l_bool(cOMBC_605892544l_bool,ord_le951220754t_bool),A)))))) # label(fact_731_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 751 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(collect_fun_nat_bool,hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,ord_le1568362934t_bool),A)))))) # label(fact_732_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 752 (all R_1 all S_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),R_1)),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_1))) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,R_1),S_1)))) # label(fact_733_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 753 (all R_1 all S_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),R_1)),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),S_1))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,R_1),S_1)))) # label(fact_734_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 754 (all R_1 all S_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)))) # label(fact_735_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 755 (all X_25 all Y_19 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_25),Y_19)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_19),X_25)))) # label(fact_736_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 756 (all X_25 all Y_19 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_25),Y_19)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_19),X_25)))) # label(fact_737_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 757 (all X_1 all F all G (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G,X_1))))) # label(fact_738_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 758 (all X_1 all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))))) # label(fact_739_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 759 (all Z_1 all Y_1 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_1),Y_1)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_1),X_1))))) # label(fact_740_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 760 (all Z_1 all Y_1 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_1))))) # label(fact_741_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 761 (all Z_9 all Y_18 all X_24 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_18),X_24)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_9),Y_18)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_9),X_24))))) # label(fact_742_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 762 (all Z_9 all Y_18 all X_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_24)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_9),Y_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_9),X_24))))) # label(fact_743_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 763 (all Y_1 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) -> X_1 = Y_1))) # label(fact_744_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 764 (all Y_1 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) -> X_1 = Y_1))) # label(fact_745_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 765 (all Y_17 all X_23 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_17),X_23)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_23),Y_17)) -> X_23 = Y_17))) # label(fact_746_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 766 (all Y_17 all X_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_23)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_23),Y_17)) -> X_23 = Y_17))) # label(fact_747_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 767 (all Z_1 all X_1 all Y_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),Z_1)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Z_1))))) # label(fact_748_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 768 (all Z_1 all X_1 all Y_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),Z_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Z_1))))) # label(fact_749_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 769 (all Z_8 all X_22 all Y_16 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_22),Y_16)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_16),Z_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_22),Z_8))))) # label(fact_750_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 770 (all Z_8 all X_22 all Y_16 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_22),Y_16)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),Z_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_22),Z_8))))) # label(fact_751_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 771 (all X_1 all Y_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> X_1 = Y_1))) # label(fact_752_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 772 (all X_1 all Y_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> X_1 = Y_1))) # label(fact_753_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 773 (all X_21 all Y_15 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_21),Y_15)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_15),X_21)) -> X_21 = Y_15))) # label(fact_754_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 774 (all X_21 all Y_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_21),Y_15)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_21)) -> X_21 = Y_15))) # label(fact_755_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 775 (all Ca all Ba all A_13 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ba),A_13)) -> (Ba = Ca -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ca),A_13))))) # label(fact_756_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 776 (all Ca all Ba all A_13 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),A_13)) -> (Ba = Ca -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),A_13))))) # label(fact_757_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 777 (all C_14 all B_19 all A_24 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_19),A_24)) -> (B_19 = C_14 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),A_24))))) # label(fact_758_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 778 (all C_14 all B_19 all A_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_24)) -> (B_19 = C_14 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),A_24))))) # label(fact_759_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 779 (all Ca all A_13 all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_13),Ba)) -> (Ba = Ca -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_13),Ca))))) # label(fact_760_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 780 (all Ca all A_13 all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_13),Ba)) -> (Ba = Ca -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_13),Ca))))) # label(fact_761_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 781 (all C_13 all A_23 all B_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_23),B_18)) -> (B_18 = C_13 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_23),C_13))))) # label(fact_762_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 782 (all C_13 all A_23 all B_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),B_18)) -> (B_18 = C_13 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),C_13))))) # label(fact_763_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 783 (all Ca all A_13 all Ba (A_13 = Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ca),Ba)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ca),A_13))))) # label(fact_764_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 784 (all Ca all A_13 all Ba (A_13 = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),A_13))))) # label(fact_765_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 785 (all C_12 all A_22 all B_17 (A_22 = B_17 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),B_17)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),A_22))))) # label(fact_766_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 786 (all C_12 all A_22 all B_17 (A_22 = B_17 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_12),B_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_12),A_22))))) # label(fact_767_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 787 (all Ca all A_13 all Ba (A_13 = Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ba),Ca)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_13),Ca))))) # label(fact_768_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 788 (all Ca all A_13 all Ba (A_13 = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_13),Ca))))) # label(fact_769_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 789 (all C_11 all A_21 all B_16 (A_21 = B_16 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_16),C_11)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_21),C_11))))) # label(fact_770_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 790 (all C_11 all A_21 all B_16 (A_21 = B_16 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_16),C_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),C_11))))) # label(fact_771_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 791 (all Y_1 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_772_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 792 (all Y_1 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_773_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 793 (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_774_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 794 (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_775_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 795 (all X_1 all F all G (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G,X_1))))) # label(fact_776_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 796 (all X_1 all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))))) # label(fact_777_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 797 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)))) # label(fact_778_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 798 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)))) # label(fact_779_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 799 (all X_20 all Y_14 (X_20 = Y_14 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_14)))) # label(fact_780_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 800 (all X_20 all Y_14 (X_20 = Y_14 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),Y_14)))) # label(fact_781_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 801 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)))) # label(fact_782_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 802 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)))) # label(fact_783_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 803 (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_784_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 804 (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_785_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 805 (all X_19 all Y_13 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_19),Y_13)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_13),X_19)))) # label(fact_786_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 806 (all X_19 all Y_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_13)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_19)))) # label(fact_787_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 807 (all F all G (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G,X_2)))))) # label(fact_788_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 808 (all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2)))))) # label(fact_789_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 809 (all A all B (A = B -> -(hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))))) # label(fact_790_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.19 810 (all A all B (A = B -> -(hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))))) # label(fact_791_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 811 (all C_5 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_5)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_5))))) # label(fact_792_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 812 (all C_5 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C_5)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_5))))) # label(fact_793_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 813 (all X_1 all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B))))) # label(fact_794_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 814 (all X_1 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))))) # label(fact_795_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 815 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_796_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 816 (all B all X_1 all A (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B))))) # label(fact_797_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 817 (all B all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))))) # label(fact_798_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 818 (all B all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_799_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 819 (all X_1 all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B))))) # label(fact_800_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 820 (all X_1 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))))) # label(fact_801_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 821 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_802_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 822 (all A all B (A = B -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)))) # label(fact_803_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 823 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)))) # label(fact_804_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 824 (all A all B (A = B -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)))) # label(fact_805_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 825 (all A all B (A = B -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_806_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 826 (all A all B (A = B <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)))) # label(fact_807_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 827 (all A all B (A = B <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)))) # label(fact_808_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 828 (all A hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),A))) # label(fact_809_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 829 (all A hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A))) # label(fact_810_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 830 (all X_1 all Pa all Q_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Pa),Q_1)) -> (hBOOL(hAPP_int_bool(Pa,X_1)) -> hBOOL(hAPP_int_bool(Q_1,X_1))))) # label(fact_811_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 831 (all X_1 all Pa all Q_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1)) -> (hBOOL(hAPP_nat_bool(Pa,X_1)) -> hBOOL(hAPP_nat_bool(Q_1,X_1))))) # label(fact_812_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 832 (all Q_1 all Pa all X_1 (hBOOL(hAPP_int_bool(Pa,X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Pa),Q_1)) -> hBOOL(hAPP_int_bool(Q_1,X_1))))) # label(fact_813_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 833 (all Q_1 all Pa all X_1 (hBOOL(hAPP_nat_bool(Pa,X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1)) -> hBOOL(hAPP_nat_bool(Q_1,X_1))))) # label(fact_814_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 834 (all X_1 all Y_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_i1948725293t_bool(ord_lessThan_int,X_1)),hAPP_i1948725293t_bool(ord_lessThan_int,Y_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)))) # label(fact_815_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 835 (all X_1 all Y_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(ord_lessThan_nat,X_1)),hAPP_n1699378549t_bool(ord_lessThan_nat,Y_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)))) # label(fact_816_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 836 (all X_1 all Y_1 (hAPP_n1699378549t_bool(ord_lessThan_nat,X_1) = hAPP_n1699378549t_bool(ord_lessThan_nat,Y_1) <-> X_1 = Y_1)) # label(fact_817_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 837 (all C_10 all A_20 all B_15 (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_15))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_20),B_15)))) # label(fact_818_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 838 (all C_10 all A_20 all B_15 (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_15))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_15)))) # label(fact_819_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 839 (all A_19 all C_9 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_19),C_9)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_14),C_9))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),B_14)))) # label(fact_820_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 840 (all A_19 all C_9 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_19),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),C_9))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),B_14)))) # label(fact_821_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 841 (all C_8 all D_3 all A_18 all B_13 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_18),B_13)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_8),D_3)) -> 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_13),D_3)))))) # label(fact_822_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 842 (all C_8 all D_3 all A_18 all B_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_18),B_13)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_8),D_3)) -> 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_13),D_3)))))) # label(fact_823_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 843 (all C_7 all A_17 all B_12 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_17),B_12)) -> 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_12))))) # label(fact_824_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 844 (all C_7 all A_17 all B_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),B_12)) -> 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_12))))) # label(fact_825_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 845 (all C_6 all A_16 all B_11 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_16),B_11)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_16),C_6)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_11),C_6))))) # label(fact_826_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 846 (all C_6 all A_16 all B_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_16),B_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_16),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_6))))) # label(fact_827_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 847 (all Ca all A_13 all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),A_13)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ca),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_13),Ba)))) # label(fact_828_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 848 (all Ca all A_13 all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),A_13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_13),Ba)))) # label(fact_829_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 849 (all A_13 all Ca all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),Ca))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_13),Ba)))) # label(fact_830_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 850 (all A_13 all Ca all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_13),Ba)))) # label(fact_831_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 851 (all A_13 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_13),bot_bot_bool)) -> (hBOOL(A_13) <-> hBOOL(bot_bot_bool)))) # label(fact_832_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 852 (all A_13 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_13),bot_bot_fun_nat_bool)) -> A_13 = bot_bot_fun_nat_bool)) # label(fact_833_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 853 (all A_13 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_13),bot_bot_fun_int_bool)) -> A_13 = bot_bot_fun_int_bool)) # label(fact_834_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 854 (all A_13 (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A_13),bot_bo797238721a_bool)) -> A_13 = bot_bo797238721a_bool)) # label(fact_835_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 855 (all A_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_15),bot_bot_nat)) -> A_15 = bot_bot_nat)) # label(fact_836_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 856 (all A_13 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_13),bot_bot_bool)) <-> (hBOOL(A_13) <-> hBOOL(bot_bot_bool)))) # label(fact_837_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 857 (all A_13 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_13),bot_bot_fun_nat_bool)) <-> A_13 = bot_bot_fun_nat_bool)) # label(fact_838_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 858 (all A_13 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_13),bot_bot_fun_int_bool)) <-> A_13 = bot_bot_fun_int_bool)) # label(fact_839_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 859 (all A_13 (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A_13),bot_bo797238721a_bool)) <-> A_13 = bot_bo797238721a_bool)) # label(fact_840_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 860 (all A_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_13),bot_bot_nat)) <-> A_13 = bot_bot_nat)) # label(fact_841_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 861 (all A_13 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_13))) # label(fact_842_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 862 (all A_13 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_13))) # label(fact_843_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 863 (all A_13 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_13))) # label(fact_844_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 864 (all A_13 hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,bot_bo797238721a_bool),A_13))) # label(fact_845_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 865 (all A_14 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_14))) # label(fact_846_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 866 (all A_13 all Ba all Ca all D_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_13),Ba) = 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_13),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ca),D_1))))) # label(fact_847_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 867 (all A (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),bot_bot_fun_nat_bool)) <-> A = bot_bot_fun_nat_bool)) # label(fact_848_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 868 (all A (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),bot_bot_fun_int_bool)) <-> A = bot_bot_fun_int_bool)) # label(fact_849_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 869 (all A (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),bot_bo797238721a_bool)) <-> A = bot_bo797238721a_bool)) # label(fact_850_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 870 (all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A))))) # label(fact_851_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 871 (all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))))) # label(fact_852_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 872 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_853_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 873 (all A all B (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A))))) # label(fact_854_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 874 (all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))))) # label(fact_855_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 875 (all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))))) # label(fact_856_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 876 (all A_13 all C_5 all D_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_5),D_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),C_5)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),D_2))))) # label(fact_857_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 877 (all A_13 all C_5 all D_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_5),D_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),C_5)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),D_2))))) # label(fact_858_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 878 (all A_13 all C_5 all D_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,C_5),D_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),C_5)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),D_2))))) # label(fact_859_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 879 (all Ba all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),B))))) # label(fact_860_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 880 (all Ba all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),B))))) # label(fact_861_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 881 (all Ba all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),B))))) # label(fact_862_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 882 (all B all X_1 all A (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))))) # label(fact_863_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 883 (all B all X_1 all A (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))))) # label(fact_864_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 884 (all B all X_1 all A (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),B))) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B))))) # label(fact_865_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 885 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_866_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 886 (all X_1 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)))) # label(fact_867_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 887 (all X_1 all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),A)),B)) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),B)) & hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)))) # label(fact_868_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 888 (all B all A_13 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_13),B)))) # label(fact_869_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 889 (all B all A_13 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_13),B)))) # label(fact_870_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 890 (all B all A_13 hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,B),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_13),B)))) # label(fact_871_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 891 (all F all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_int_int(F,A)),image_int_int(F,B))))) # label(fact_872_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 892 (all F all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,image_533441733iple_a(F,A)),image_533441733iple_a(F,B))))) # label(fact_873_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 893 (all F all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),image_nat_int(F,B))))) # label(fact_874_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 894 (all F all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_nat_nat(F,A)),image_nat_nat(F,B))))) # label(fact_875_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 895 (all B all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_int_int(F,A))) <-> (exists AA (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,AA),A)) & B = image_int_int(F,AA))))) # label(fact_876_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 896 (all B all F all A (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,B),image_533441733iple_a(F,A))) <-> (exists AA (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,AA),A)) & B = image_533441733iple_a(F,AA))))) # label(fact_877_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 897 (all B all F all A (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A))) <-> (exists AA (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A)) & B = image_nat_int(F,AA))))) # label(fact_878_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 898 (all B all F all A (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_nat_nat(F,A))) <-> (exists AA (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A)) & B = image_nat_nat(F,AA))))) # label(fact_879_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 899 (all C_5 all A all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_5)) -> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_5),A)) = A))) # label(fact_880_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 900 (all C_5 all A all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,B),C_5)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,B),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,C_5),A)) = A))) # label(fact_881_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 901 (all C_5 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C_5)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_5),A)) = A))) # label(fact_882_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 902 (all D_2 all B all A all C_5 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_5)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,D_2),B)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_5),D_2)))))) # label(fact_883_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 903 (all D_2 all B all A all C_5 (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),C_5)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,D_2),B)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,C_5),D_2)))))) # label(fact_884_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 904 (all D_2 all B all A all C_5 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_5)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,D_2),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_5),D_2)))))) # label(fact_885_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 905 (all A all B hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),A))) # label(fact_886_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 906 (all A all B hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B)),A))) # label(fact_887_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 907 (all A all B hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),A))) # label(fact_888_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 908 (all Ts all Ga all Ts_1 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts_1)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,Ts),Ts_1)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts))))) # label(fact_889_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 909 (all Ts all Ga (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,Ts),Ga)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts)))) # label(fact_890_asm) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 910 (all A all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) -> A = bot_bot_fun_nat_bool | A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) # label(fact_891_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 911 (all A all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) -> A = bot_bot_fun_int_bool | A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) # label(fact_892_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 912 (all A all X_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))) -> A = bot_bo797238721a_bool | A = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))) # label(fact_893_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 913 (all B all F all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_int_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_894_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 914 (all B all F all A (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,B),image_533441733iple_a(F,A))) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B))))) # label(fact_895_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 915 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))))) # label(fact_896_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 916 (all B all F all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_nat_nat(F,A))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))))) # label(fact_897_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 917 (all F all A all B hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_int_int(F,A)),image_int_int(F,B))),image_int_int(F,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))) # label(fact_898_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 918 (all F all A all B hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,image_533441733iple_a(F,A)),image_533441733iple_a(F,B))),image_533441733iple_a(F,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),B))))) # label(fact_899_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 919 (all F all A all B hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(F,A)),image_nat_int(F,B))),image_nat_int(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_900_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 920 (all F all A all B hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,image_nat_nat(F,A)),image_nat_nat(F,B))),image_nat_nat(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))) # label(fact_901_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 921 (all A_13 all E all Ca all Ba 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_13),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),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_13),Ba)),E)),Ca)),D_1)))) # label(fact_902_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 922 (all A_13 all E all Ca all Ba 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_13),E)),Ca)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),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,Ba),A_13)),E)),D_1))))) # label(fact_903_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 923 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)))))) # label(fact_904_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 924 (all A all X_1 all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)))))) # label(fact_905_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 925 (all A all X_1 all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))),B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),B)))))) # label(fact_906_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 926 (all A all X_1 all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) <-> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B))) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))))) # label(fact_907_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 927 (all A all X_1 all B (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B))) <-> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B))) & (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))))) # label(fact_908_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 928 (all A all X_1 all B (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),B))) <-> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_1),bot_bo797238721a_bool))),B))) & (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_1),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B))))) # label(fact_909_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 929 (all B all A all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A)) -> (B != bot_bo797238721a_bool -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,B),A)) -> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,B)),hAPP_f1693662087iple_a(F_1,A)) = hAPP_f1693662087iple_a(F_1,A)))))) # label(fact_910_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 930 (all B all A all F all F_1 (hBOOL(finite1432773856em_int(F,F_1)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (B != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) -> hAPP_int_int(hAPP_int_fun_int_int(F,hAPP_f1594865479ol_int(F_1,B)),hAPP_f1594865479ol_int(F_1,A)) = hAPP_f1594865479ol_int(F_1,A)))))) # label(fact_911_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 931 (all B all A all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (B != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,B)),hAPP_f22106695ol_nat(F_1,A)) = hAPP_f22106695ol_nat(F_1,A)))))) # label(fact_912_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 932 (all Pa all A 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)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all A_12 all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_12),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_12),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_12),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1))))))) # label(fact_913_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 933 (all Pa all A 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)) -> (hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) -> ((all A_12 all F_2 (hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_12),A)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_12),F_2)) -> (hBOOL(hAPP_f448129468l_bool(Pa,F_2)) -> hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_12),F_2)))))))) -> hBOOL(hAPP_f448129468l_bool(Pa,F_1))))))) # label(fact_914_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 934 (all Pa all A all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,F_1),A)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,bot_bo797238721a_bool)) -> ((all A_12 all F_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_2)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_12),A)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_12),F_2)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,F_2)) -> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_12),F_2)))))))) -> hBOOL(hAPP_f1695230391l_bool(Pa,F_1))))))) # label(fact_915_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 935 (all B all A ((all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B)))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),B)))) # label(fact_916_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 936 (all B all A ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)))) # label(fact_917_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 937 (all B all A ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_918_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 938 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_int_int(F,A))) -> (exists C_4 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_4),A)) & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_4)) & B = image_int_int(F,C_4)))))) # label(fact_919_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 939 (all F all A all B (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,B),image_533441733iple_a(F,A))) -> (exists C_4 (hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,C_4),A)) & hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,C_4)) & B = image_533441733iple_a(F,C_4)))))) # label(fact_920_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 940 (all F all A all B (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A))) -> (exists C_4 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_4),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_4)) & B = image_nat_int(F,C_4)))))) # label(fact_921_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 941 (all F all A all B (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_nat_nat(F,A))) -> (exists C_4 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_4),A)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_4)) & B = image_nat_nat(F,C_4)))))) # label(fact_922_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 942 (all F all G all K_3 ((all I_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,I_2),K_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(F,I_2)),hAPP_int_nat(G,I_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,F),K_3)),hAPP_f957591787ol_nat(hAPP_f1109019371ol_nat(big_co1740723097nt_nat,G),K_3))))) # label(fact_923_setsum__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 943 (all F all G all K_3 ((all I_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,I_2),K_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_H592031934_a_nat(F,I_2)),hAPP_H592031934_a_nat(G,I_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,F),K_3)),hAPP_f2097660464ol_nat(hAPP_f1371399797ol_nat(big_co1340561246_a_nat,G),K_3))))) # label(fact_924_setsum__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 944 (all F all G all K_3 ((all I_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,I_2),K_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(G,I_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),K_3)),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,G),K_3))))) # label(fact_925_setsum__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 945 (all F all B all A ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(F,X_2)),B)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_int_int(F,A)),B)))) # label(fact_926_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 946 (all F all B all A ((all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_H905846293iple_a(F,X_2)),B)))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,image_533441733iple_a(F,A)),B)))) # label(fact_927_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 947 (all F all B all A ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_2)),B)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),B)))) # label(fact_928_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 948 (all F all B all A ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(F,X_2)),B)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_nat_nat(F,A)),B)))) # label(fact_929_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 949 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G,X_2)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)))) # label(fact_930_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 950 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)))) # label(fact_931_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 951 (all A all Ba ((hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),bot_bot_fun_int_bool))) -> hAPP_f1594865479ol_int(partial_flat_lub_int(Ba),A) = Ba) & (-hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),bot_bot_fun_int_bool))) -> hAPP_f1594865479ol_int(partial_flat_lub_int(Ba),A) = hAPP_f1594865479ol_int(the_int,hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Ba),bot_bot_fun_int_bool))))))) # label(fact_932_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 952 (all A all Ba ((hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),bot_bo797238721a_bool))) -> hAPP_f1693662087iple_a(partia1949573335iple_a(Ba),A) = Ba) & (-hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),bot_bo797238721a_bool))) -> hAPP_f1693662087iple_a(partia1949573335iple_a(Ba),A) = hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Ba),bot_bo797238721a_bool))))))) # label(fact_933_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 953 (all A all Ba ((hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool))) -> hAPP_f22106695ol_nat(partial_flat_lub_nat(Ba),A) = Ba) & (-hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool))) -> hAPP_f22106695ol_nat(partial_flat_lub_nat(Ba),A) = hAPP_f22106695ol_nat(the_nat,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Ba),bot_bot_fun_nat_bool))))))) # label(fact_934_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 954 (all N_1 all Q_1 all Pa ((all X_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(Q_1,X_2)),hAPP_nat_nat(Pa,X_2)))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,Pa),hAPP_n1699378549t_bool(ord_lessThan_nat,N_1))),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,Q_1),hAPP_n1699378549t_bool(ord_lessThan_nat,N_1))) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1914919701at_nat(hAPP_f1408247010at_nat(cOMBS_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,minus_minus_nat),Pa)),Q_1)),hAPP_n1699378549t_bool(ord_lessThan_nat,N_1)))) # label(fact_935_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 955 (all B all A (A != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f1594865479ol_int(finite_fold1_int(ord_min_int),B)),hAPP_f1594865479ol_int(finite_fold1_int(ord_min_int),A))))))) # label(fact_936_fold1__antimono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 956 (all B all A (A != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_fold1_nat(ord_min_nat),B)),hAPP_f22106695ol_nat(finite_fold1_nat(ord_min_nat),A))))))) # label(fact_937_fold1__antimono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 957 (all Q_1 all Pa ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Q_1,X_2)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Pa),Q_1)))) # label(fact_938_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 958 (all Q_1 all Pa ((all X_2 (hBOOL(hAPP_nat_bool(Pa,X_2)) -> hBOOL(hAPP_nat_bool(Q_1,X_2)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1)))) # label(fact_939_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 959 (all Q_1 all Pa ((all X_2 (hBOOL(hAPP_int_bool(Pa,X_2)) -> hBOOL(hAPP_int_bool(Q_1,X_2)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(collect_int,Pa)),hAPP_f1805168059t_bool(collect_int,Q_1))))) # label(fact_940_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 960 (all Q_1 all Pa ((all X_2 (hBOOL(hAPP_H1037229737a_bool(Pa,X_2)) -> hBOOL(hAPP_H1037229737a_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(ord_le1523781517a_bool,hAPP_f20753329a_bool(collec351493750iple_a,Pa)),hAPP_f20753329a_bool(collec351493750iple_a,Q_1))))) # label(fact_941_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 961 (all Q_1 all Pa ((all X_2 (hBOOL(hAPP_nat_bool(Pa,X_2)) -> hBOOL(hAPP_nat_bool(Q_1,X_2)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(collect_nat,Pa)),hAPP_f800510211t_bool(collect_nat,Q_1))))) # label(fact_942_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 962 (all M_3 all N_3 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,M_3),N_3)) -> (M_3 != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,N_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f1594865479ol_int(big_linorder_Min_int,N_3)),hAPP_f1594865479ol_int(big_linorder_Min_int,M_3))))))) # label(fact_943_Min__antimono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 963 (all M_3 all N_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,M_3),N_3)) -> (M_3 != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(big_linorder_Min_nat,N_3)),hAPP_f22106695ol_nat(big_linorder_Min_nat,M_3))))))) # label(fact_944_Min__antimono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 964 (all M_3 all N_3 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,M_3),N_3)) -> (M_3 != bot_bot_fun_int_bool -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,N_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_f1594865479ol_int(big_linorder_Max_int,M_3)),hAPP_f1594865479ol_int(big_linorder_Max_int,N_3))))))) # label(fact_945_Max__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 965 (all M_3 all N_3 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,M_3),N_3)) -> (M_3 != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(big_linorder_Max_nat,M_3)),hAPP_f22106695ol_nat(big_linorder_Max_nat,N_3))))))) # label(fact_946_Max__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 966 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_lessThan_nat,K_1)))) # label(fact_947_finite__lessThan) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 967 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K_1))))) # label(fact_948_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 968 (all N_3 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) <-> (exists M_1 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),M_1)))))) # label(fact_949_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 969 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_1),hAPP_f1594865479ol_int(big_linorder_Min_int,A)) = hAPP_f1594865479ol_int(big_linorder_Min_int,A)))) # label(fact_950_Min_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 970 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_1),hAPP_f22106695ol_nat(big_linorder_Min_nat,A)) = hAPP_f22106695ol_nat(big_linorder_Min_nat,A)))) # label(fact_951_Min_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 971 (all X_18 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_18),X_18) = X_18) # label(fact_952_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 972 (all X_17 all Y_12 all Z_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_17),Y_12)),Z_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_17),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_12),Z_7))) # label(fact_953_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 973 (all A_11 all B_10 all C_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_11),B_10)),C_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_10),C_3))) # label(fact_954_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 974 (all X_16 all Y_11 all Z_6 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_16),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_11),Z_6)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_16),Z_6))) # label(fact_955_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 975 (all B_9 all A_10 all C_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_10),C_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_10),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_9),C_2))) # label(fact_956_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 976 (all X_15 all Y_10 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_15),Y_10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_15),Y_10)) # label(fact_957_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 977 (all A_9 all B_8 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_9),B_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_9),B_8)) # label(fact_958_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 978 (all X_14 all Y_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_14),Y_9) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_9),X_14)) # label(fact_959_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 979 (all A_8 all B_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_8),B_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_7),A_8)) # label(fact_960_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 980 (all A_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_7),A_7) = A_7) # label(fact_961_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 981 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_1),Y_1)),Z_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),Z_1)))) # label(fact_962_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 982 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_1),Y_1)),Z_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Z_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),Z_1)))) # label(fact_963_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 983 (all X_13 all A_6 all B_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_6),B_6))) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),A_6)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),B_6))))) # label(fact_964_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 984 (all X_13 all A_6 all B_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_13),hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,A_6),B_6))) -> -(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_13),A_6)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_13),B_6))))) # label(fact_965_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 985 (all B_5 all D all A_5 all C_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_5),C_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),D)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_5),B_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,C_1),D)))))) # label(fact_966_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 986 (all B_5 all D all A_5 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_5),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_5),D)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,A_5),B_5)),hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,C_1),D)))))) # label(fact_967_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 987 (all Z_5 all X_12 all Y_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Y_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Z_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_8),Z_5)))))) # label(fact_968_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 988 (all Z_5 all X_12 all Y_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_12),Y_8)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_12),Z_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_12),hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,Y_8),Z_5)))))) # label(fact_969_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 989 (all B_4 all X_11 all A_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),A_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),B_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_4),B_4)))))) # label(fact_970_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 990 (all B_4 all X_11 all A_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),A_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),B_4)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,A_4),B_4)))))) # label(fact_971_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 991 (all Y_7 all X_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_10)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_10),Y_7) = Y_7)) # label(fact_972_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 992 (all Y_7 all X_10 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_7),X_10)) -> hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_10),Y_7) = Y_7)) # label(fact_973_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 993 (all X_9 all Y_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_6)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_9),Y_6) = X_9)) # label(fact_974_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 994 (all X_9 all Y_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_9),Y_6)) -> hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_9),Y_6) = X_9)) # label(fact_975_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 995 (all A_3 all B_3 all X_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_3),X_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_3),B_3)),X_8)))) # label(fact_976_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 996 (all A_3 all B_3 all X_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_3),X_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,A_3),B_3)),X_8)))) # label(fact_977_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 997 (all B_2 all A_2 all X_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),X_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_2),B_2)),X_7)))) # label(fact_978_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 998 (all B_2 all A_2 all X_7 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),X_7)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,A_2),B_2)),X_7)))) # label(fact_979_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 999 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_1),Z_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,X_1),Z_1)))) # label(fact_980_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1000 (all X_1 all Y_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,Y_1),Z_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,X_1),Z_1)))) # label(fact_981_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1001 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_1),Y_1) = X_1)) # label(fact_982_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1002 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_1),Y_1) = X_1)) # label(fact_983_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1003 (all X_6 all Y_5 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_6),Y_5)),Y_5))) # label(fact_984_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1004 (all X_6 all Y_5 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_6),Y_5)),Y_5))) # label(fact_985_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1005 (all X_5 all Y_4 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_5),Y_4)),X_5))) # label(fact_986_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1006 (all X_5 all Y_4 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_5),Y_4)),X_5))) # label(fact_987_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1007 (all X_4 all Y_3 all Z_4 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_4),Y_3)),Z_4) = hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_4),Z_4)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y_3),Z_4))) # label(fact_988_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1008 (all X_4 all Y_3 all Z_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_4),Y_3)),Z_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_4),Z_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_3),Z_4))) # label(fact_989_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1009 (all X_3 all Y_2 all Z_3 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,X_3),Y_2)),Z_3) = hAPP_int_int(hAPP_int_fun_int_int(ord_min_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_3),Z_3)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Y_2),Z_3))) # label(fact_990_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1010 (all U all F ((all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(F,N_2)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,ord_less_eq_nat),F)),U)))))) # label(fact_991_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1011 (all N_1 all K_1 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))))) # label(fact_992_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1012 (all K all L_1 all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),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),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),L_1)))))) # label(fact_993_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1013 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),J))))) # label(fact_994_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1014 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K))))) # label(fact_995_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1015 (all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),M))))) # label(fact_996_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1016 (all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),M)))) # label(fact_997_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1017 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N))) # label(fact_998_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1018 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)))) # label(fact_999_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1019 (all M all N (M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1000_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1020 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K))))) # label(fact_1001_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1021 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> M = N))) # label(fact_1002_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1022 (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(plus_plus_nat,M),K)),N)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))))) # label(fact_1003_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1023 (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(plus_plus_nat,M),K)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1004_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.20 1024 (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(plus_plus_nat,M),K)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)))) # label(fact_1005_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1025 (all K all L_1 all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),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),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))))) # label(fact_1006_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1026 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))))) # label(fact_1007_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1027 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),J))))) # label(fact_1008_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1028 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M))))) # label(fact_1009_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1029 (all K_1 all M_2 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,K_1),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_1010_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1030 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) <-> (exists K_2 N_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)))) # label(fact_1011_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1031 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)))) # label(fact_1012_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1032 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)))) # label(fact_1013_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1033 (all M all I all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),I)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),N)),I)) # label(fact_1014_min__diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1034 (all K all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_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))) # label(fact_1015_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1035 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)),N) = M) # label(fact_1016_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1036 (all N all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)),N) = M) # label(fact_1017_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1037 (all I all J all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))) # label(fact_1018_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1038 (all I all J all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),K)),J)) # label(fact_1019_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1039 (all M all N all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_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))) # label(fact_1020_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1040 (all K all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_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)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) # label(fact_1021_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1041 (all M all K all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,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)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) # label(fact_1022_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1042 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),M))) # label(fact_1023_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1043 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),J))) # label(fact_1024_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1044 (all J_1 all K_1 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_1)),I_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1))))) # label(fact_1025_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1045 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)),K))))) # label(fact_1026_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1046 (all L_1 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(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M))))) # label(fact_1027_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1047 (all L_1 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(hAPP_nat_fun_nat_nat(minus_minus_nat,M),L_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),L_1))))) # label(fact_1028_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1048 (all I all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),I)) = I)) # label(fact_1029_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1049 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) = M)) # label(fact_1030_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1050 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),K))) # label(fact_1031_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1051 (all I_1 all K_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_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)),J_1))))) # label(fact_1032_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1052 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),N) = M)) # label(fact_1033_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1053 (all K_1 all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_1) = K_1 <-> J_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),I_1)))) # label(fact_1034_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1054 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)))) # label(fact_1035_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1055 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),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)),I) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I)),K))) # label(fact_1036_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1056 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),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)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)),I))) # label(fact_1037_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1057 (all N_1 all K_1 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1) <-> M_2 = N_1)))) # label(fact_1038_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1058 (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,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)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)))) # label(fact_1039_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1059 (all U all M_2 all N_1 all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_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)),M_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),N_1) <-> M_2 = 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_1),I_1)),U)),N_1)))) # label(fact_1040_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1060 (all U_1 all M all N all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),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),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),U_1)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_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),I)),U_1)),N)))) # label(fact_1041_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1061 (all U all M_2 all N_1 all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hBOOL(hAPP_nat_bool(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_1),U)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),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_1),I_1)),U)),N_1)))))) # label(fact_1042_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1062 (all U all M_2 all N_1 all J_1 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_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)),M_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),N_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,I_1),J_1)),U)),M_2) = N_1))) # label(fact_1043_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1063 (all U_1 all M all N all J all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I)) -> 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),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),U_1)),N)) = 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),J)),U_1)),M)),N))) # label(fact_1044_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1064 (all M all N all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K))) # label(fact_1045_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1065 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M)) # label(fact_1046_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1066 (all M_2 all K_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1) <-> M_2 = N_1)) # label(fact_1047_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1067 (all K_1 all M_2 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1) <-> M_2 = N_1)) # label(fact_1048_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1068 (all M all N all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K))) # label(fact_1049_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1069 (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_1050_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1070 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)) # label(fact_1051_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1071 (all K all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_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))) # label(fact_1052_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1072 (all M all N all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_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))) # label(fact_1053_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1073 (all I all U_1 all J all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_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_1)),K)) = 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),J)),U_1)),K)) # label(fact_1054_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1074 (all U all M_2 all N_1 all J_1 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_1)) -> (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_1),U)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),N_1))) <-> 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_1),J_1)),U)),M_2)),N_1))))) # label(fact_1055_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1075 (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_1056_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1076 (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_1057_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1077 (all N all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,N),M)) # label(fact_1058_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1078 (all U hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(ord_lessThan_nat,U)) = U) # label(fact_1059_card__lessThan) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1079 (all M_2 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_1) = one_one_nat <-> M_2 = one_one_nat & N_1 = one_one_nat)) # label(fact_1060_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1080 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),one_one_nat) = N) # label(fact_1061_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1081 (all M_2 all N_1 (one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_1) <-> M_2 = one_one_nat & N_1 = one_one_nat)) # label(fact_1062_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1082 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N) = N) # label(fact_1063_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1083 (all M all N all Z hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,N)),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),N))),Z)) # label(fact_1064_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1084 (all M all N hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) # label(fact_1065_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1085 (all M_2 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M_2)),hAPP_nat_int(semiri1621563631at_int,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)))) # label(fact_1066_zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1086 (all M all N hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N))) # label(fact_1067_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1087 (all M all N hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N))) # label(fact_1068_int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1088 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)))) # label(fact_1070_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1089 (all N all M hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,N))),hAPP_nat_int(semiri1621563631at_int,M)))) # label(fact_1071_negative__zle) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1090 (all L all U hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U)))) # label(fact_1072_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1091 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K_1))))) # label(fact_1073_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1092 (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_1074_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1093 (all M all N hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M),N)) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M)),N)) # label(fact_1075_int__power) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1094 (all M all N hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M)),N) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M),N))) # label(fact_1076_zpower__int) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1095 (all M_2 all N_1 (hAPP_nat_int(semiri1621563631at_int,M_2) = hAPP_nat_int(semiri1621563631at_int,N_1) <-> M_2 = N_1)) # label(fact_1077_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1096 (all Z all W_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(uminus_uminus_int,Z)),W_1) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),W_1))) # label(fact_1078_zmult__zminus) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1097 (all Z all W_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),hAPP_int_int(uminus_uminus_int,W_1)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z),W_1)) # label(fact_1079_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1098 (all Z all W_1 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z),W_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),hAPP_int_int(uminus_uminus_int,W_1))) # label(fact_1080_diff__int__def) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1099 (all Z all W_1 hAPP_int_int(uminus_uminus_int,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,hAPP_int_int(uminus_uminus_int,Z)),hAPP_int_int(uminus_uminus_int,W_1))) # label(fact_1081_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1100 (all W_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),W_1))) # label(fact_1082_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1101 (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_1083_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1102 (all K all I all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),J)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),K)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K))))) # label(fact_1084_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1103 (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_1085_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1104 (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_1086_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1105 (all X all Y all Z hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Y)),Z) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Y),Z))) # label(fact_1087_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1106 (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_1088_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1107 (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_1089_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1108 (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_1090_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1109 (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_1091_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1110 (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_1092_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1111 (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_1093_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1112 (all X all Y all Z hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Y)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Z))) # label(fact_1094_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1113 (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_1095_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1114 (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_1096_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1115 (all K all I all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),J)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K),I)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K),J))))) # label(fact_1097_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1116 (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].
% 1.95/2.21 1117 (all Z hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),Z) = Z) # label(fact_1099_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1118 (all I all J all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)))) # label(fact_1100_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1119 (all M all N all K all L_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),L_1) = 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_1101_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1120 (all K all L_1 all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))))) # label(fact_1102_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1121 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))))) # label(fact_1103_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1122 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),J))))) # label(fact_1104_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1123 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M))))) # label(fact_1105_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1124 (all K_1 all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_2)),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_2),N_1)))) # label(fact_1106_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1125 (all J all I -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I)),I))) # label(fact_1107_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1126 (all I all J -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),I))) # label(fact_1108_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1127 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) & M_2 != N_1)) # label(fact_1109_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1128 (all M_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) | M_2 = N_1)) # label(fact_1110_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1129 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1111_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1130 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (M != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_1112_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1131 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_1113_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1132 (all N all J all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N)),K)))) # label(fact_1114_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1133 (all L_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L_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)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M)))))) # label(fact_1115_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1134 (all Pa all M_2 all N_1 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M_2))) -> ((M_2 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M_2))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M_2))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M_2)))))) # label(fact_1116_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1135 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_1117_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1136 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> M != N)) # label(fact_1118_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1137 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_1119_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1138 (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_1120_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1139 (all M_2 all N_1 (M_2 != N_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2)))) # label(fact_1121_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1140 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_1122_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1141 (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_1123_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1142 (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_1124_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1143 (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_1125_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1144 (all K_1 all I_1 all J_1 image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(I_1),J_1)) = hAPP_n1699378549t_bool(ord_at238088361st_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_1),K_1))) # label(fact_1126_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1145 (all N_3 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) <-> (exists M_1 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),M_1)))))) # label(fact_1127_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1146 (all Pa all I_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),Pa)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))))) # label(fact_1128_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1147 (all N_1 hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),N_1))) = N_1) # label(fact_1129_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1148 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) = M)) # label(fact_1130_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1149 (all I_1 all J_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),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),K_1)),J_1)))) # label(fact_1131_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1150 (all N_1 all K_1 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)))))) # label(fact_1132_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1151 (all C all A_1 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_1),C)))))) # label(fact_1133_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1152 (all U all M_2 all N_1 all J_1 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_1)) -> (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_1),U)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),N_1))) <-> 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_1),J_1)),U)),M_2)),N_1))))) # label(fact_1134_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1153 (all U all M_2 all N_1 all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hBOOL(hAPP_nat_bool(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_1),U)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),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_1),I_1)),U)),N_1)))))) # label(fact_1135_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1154 (all N all M -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,N)),hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,M))))) # label(fact_1136_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1155 (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_1137_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1156 (all K all I all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),J)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),K)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,J),K))))) # label(fact_1138_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1157 (all Z hAPP_int_int(uminus_uminus_int,hAPP_int_int(uminus_uminus_int,Z)) = Z) # label(fact_1139_zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1158 (all Z_2 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_2),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_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),Z)))))) # label(fact_1140_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1159 (all M_2 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_2)),hAPP_nat_int(semiri1621563631at_int,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)))) # label(fact_1141_zless__int) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1160 (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_1142_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1161 (all M_2 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),N_1))) -> hAPP_i1948725293t_bool(ord_at875362053st_int(M_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),N_1)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),N_1)),hAPP_i1948725293t_bool(ord_at875362053st_int(M_2),N_1)))) # label(fact_1143_atLeastAtMostPlus1__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1162 (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_1144_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1163 (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_1145_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1164 (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_1146_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1165 (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_1147_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1166 (all Pa all I_1 all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1)) -> (hBOOL(hAPP_int_bool(Pa,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K_1)) -> (hBOOL(hAPP_int_bool(Pa,I_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_1)))))) # label(fact_1148_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1167 (all L all U hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(ord_at875362053st_int(L),U)))) # label(fact_1149_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1168 (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_1150_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1169 (all J_1 all I_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J_1),I_1)) -> hAPP_i1948725293t_bool(ord_at875362053st_int(I_1),J_1) = bot_bot_fun_int_bool) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J_1),I_1)) -> hAPP_i1948725293t_bool(ord_at875362053st_int(I_1),J_1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,I_1),hAPP_i1948725293t_bool(ord_at875362053st_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_1),one_one_int)),J_1))))) # label(fact_1151_simp__from__to) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1170 (all Pa all I_1 all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),K_1)) -> (hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_1),one_one_int))) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K_1)) -> (hBOOL(hAPP_int_bool(Pa,I_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_1)))))) # label(fact_1152_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1171 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,A))))) # label(fact_1153_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1172 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))))) # label(fact_1154_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1173 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X_1)),image_nat_int(semiri1621563631at_int,A))))) # label(fact_1155_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1174 (all A all B (A = B <-> image_nat_int(semiri1621563631at_int,A) = image_nat_int(semiri1621563631at_int,B))) # label(fact_1156_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1175 (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_1157_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1176 (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_1158_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1177 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))))) # label(fact_1159_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1178 (all A hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,A))) # label(fact_1160_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1179 (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_1162_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1180 (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_1163_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1181 (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_1164_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1182 (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_1165_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1183 (all X all N hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,X)),N) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N))) # label(fact_1167_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1184 (all Pa all K_1 all I_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),I_1)) -> (hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),one_one_int))) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(Pa,I_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_1)))))) # label(fact_1168_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1185 (all Pa all K_1 all I_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_1)) -> (hBOOL(hAPP_int_bool(Pa,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(Pa,I_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_1)))))) # label(fact_1169_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1186 (all M_2 all K_1 all F ((all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_1)),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_2)),K_1)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)))))) # label(fact_1170_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1187 (all N_1 all N_3 ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),N_1)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)))) # label(fact_1171_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1188 (all Z -(all M_1 all N_2 Z != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_2)))) # label(fact_1172_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1189 (all I_1 all J_1 all F ((all I_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_2))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1)))))) # label(fact_1173_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1190 (all I_1 all Pa all K_1 (hBOOL(hAPP_int_bool(Pa,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(Pa,I_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)))))) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K_1)) -> (hBOOL(hAPP_int_bool(Pa,I_2)) -> hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(Pa,I_1)))))) # label(fact_1174_int__induct) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1191 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_1175_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1192 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_1176_le0) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1193 (all L all U hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U)))) # label(fact_1177_finite__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1194 (all N 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),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),N))))) # label(fact_1178_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1195 (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_1179_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1196 (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_1180_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1197 (all Z hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z)))) # label(fact_1181_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1198 (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_1183_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1199 (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_1184_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1200 (all K -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K)),zero_zero_int))) # label(fact_1186_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1201 (all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_1187_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1202 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_1),L)),zero_zero_int)))) # label(fact_1188_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1203 (all K all I all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),J)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),I)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),J)))))) # label(fact_1189_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1204 (all X_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_1)) | N_1 = zero_zero_nat)) # label(fact_1191_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1205 (all M all N all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),I)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,I),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,I),N))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_1192_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1206 (all N (N != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_1193_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1207 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> N != zero_zero_nat)) # label(fact_1194_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1208 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_1195_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1209 (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_1196_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1210 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_1197_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1211 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1212 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1213 (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].
% 1.95/2.21 1214 (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].
% 1.95/2.21 1215 (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].
% 1.95/2.21 1216 (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].
% 1.95/2.21 1217 (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].
% 1.95/2.21 1218 (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].
% 1.95/2.21 1219 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1220 (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].
% 1.95/2.21 1221 (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].
% 1.95/2.21 1222 (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].
% 1.95/2.21 1223 (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].
% 1.95/2.21 1224 (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].
% 1.95/2.21 1225 (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].
% 1.95/2.21 1226 (all P hAPP_int_int(cOMBI_int,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1227 (all P hAPP_nat_nat(cOMBI_nat,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1228 (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].
% 1.95/2.21 1229 (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].
% 1.95/2.21 1230 (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].
% 1.95/2.21 1231 (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].
% 1.95/2.21 1232 (all X all Y (-hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1233 (all X all Y (X != Y | hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1234 (all P all Q hAPP_int_int(hAPP_int_fun_int_int(cOMBK_int_int,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1235 (all P all Q hAPP_nat_int(hAPP_int_fun_nat_int(cOMBK_int_nat,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1236 (all P all Q hAPP_int_nat(hAPP_nat_fun_int_nat(cOMBK_nat_int,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1237 (all P all Q hAPP_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1238 (all P all Q (is_bool(P) -> hAPP_int_bool(hAPP_b396694332t_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].
% 1.95/2.21 1239 (all P all Q (is_bool(P) -> hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1240 (all P all Q (is_bool(P) -> hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1241 (all X all Y (-hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1242 (all X all Y (X != Y | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1243 (all X all Y (-hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1244 (all X all Y (X != Y | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1245 (all P all Q all R hAPP_nat_int(hAPP_f1139079189at_int(hAPP_f1431025877at_int(cOMBB_int_int_nat,P),Q),R) = hAPP_int_int(P,hAPP_nat_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Int__Oint_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1246 (all P all Q all R hAPP_int_int(hAPP_f147134065nt_int(hAPP_f1673907925nt_int(cOMBB_nat_int_int,P),Q),R) = hAPP_nat_int(P,hAPP_int_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Int__Oint_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1247 (all P all Q all R hAPP_int_nat(hAPP_f2132704789nt_nat(hAPP_f901215189nt_nat(cOMBB_nat_nat_int,P),Q),R) = hAPP_nat_nat(P,hAPP_int_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1248 (all P all Q all R hAPP_nat_nat(hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,P),Q),R) = hAPP_nat_nat(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1249 (all P all Q all R hAPP_int_nat(hAPP_int_fun_int_nat(hAPP_f909851349nt_nat(cOMBC_int_int_nat,P),Q),R) = hAPP_int_nat(hAPP_int_fun_int_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1250 (all P all Q all R hAPP_int_nat(hAPP_nat_fun_int_nat(hAPP_f879494613nt_nat(cOMBC_int_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_int_fun_nat_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1251 (all P all Q all R hAPP_nat_nat(hAPP_int_fun_nat_nat(hAPP_f446977493at_nat(cOMBC_nat_int_nat,P),Q),R) = hAPP_int_nat(hAPP_nat_fun_int_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1252 (all P all Q all R hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1253 (all P all Q all R hAPP_int_nat(hAPP_f2132704789nt_nat(hAPP_f1399363134nt_nat(cOMBS_int_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_int_fun_nat_nat(P,R),hAPP_int_nat(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1254 (all P all Q all R hAPP_nat_nat(hAPP_f1914919701at_nat(hAPP_f1408247010at_nat(cOMBS_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),hAPP_nat_nat(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1255 (all P all Q all R hAPP_int_bool(hAPP_i1948725293t_bool(hAPP_f428220345t_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].
% 1.95/2.21 1256 (all P all Q all R hAPP_int_bool(hAPP_n1082236369t_bool(hAPP_f175561985t_bool(cOMBC_int_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_i418383825t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1257 (all P all Q all R hAPP_nat_bool(hAPP_i418383825t_bool(hAPP_f482008321t_bool(cOMBC_nat_int_bool,P),Q),R) = hAPP_int_bool(hAPP_n1082236369t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1258 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1259 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f627970963t_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].
% 1.95/2.21 1260 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.21 1261 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f727283836t_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].
% 1.95/2.22 1262 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1263 (all P all Q hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1264 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1265 (all P all Q all R hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1266 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1267 (all P all Q all R hAPP_state_state(hAPP_f871651461_state(hAPP_f851239890_state(cOMBS_777315357_state,P),Q),R) = hAPP_nat_state(hAPP_s1892499976_state(P,R),hAPP_state_nat(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__Nat__Onat_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1268 (all P all Q all R hAPP_state_bool(hAPP_f746301080e_bool(hAPP_f162060345e_bool(cOMBB_844853809_state,P),Q),R) = hAPP_state_bool(P,hAPP_state_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Ostate_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1269 (all P all Q all R hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1270 (all P hAPP_H905846293iple_a(cOMBI_1301683934iple_a,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_U) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1271 (all X all Y (-hBOOL(hAPP_H1037229737a_bool(hAPP_H426895267a_bool(fequal963300192iple_a,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1272 (all X all Y (X != Y | hBOOL(hAPP_H1037229737a_bool(hAPP_H426895267a_bool(fequal963300192iple_a,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1273 (all P all Q all R hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1274 (all P all Q hAPP_H1229305626_a_int(hAPP_i1475897073_a_int(cOMBK_1007576201iple_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1275 (all P all Q hAPP_H592031934_a_nat(hAPP_n1653940209_a_nat(cOMBK_1028443109iple_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1276 (all P all Q (is_bool(P) -> hAPP_H1037229737a_bool(hAPP_b1882817719a_bool(cOMBK_235286536iple_a,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1277 (all P all Q all R hAPP_int_fun_nat_nat(hAPP_f1463450952at_nat(hAPP_f1087393429at_nat(cOMBB_1601129847at_int,P),Q),R) = hAPP_nat_fun_nat_nat(P,hAPP_int_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1278 (all P all Q all R hAPP_nat_fun_nat_nat(hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,P),Q),R) = hAPP_nat_fun_nat_nat(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_003) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1279 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f1791153283t_bool(hAPP_f1399575567t_bool(cOMBB_118231410ol_int,P),Q),R) = hAPP_i1948725293t_bool(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1280 (all P all Q all R hAPP_n1082236369t_bool(hAPP_f1533130627t_bool(hAPP_f879109391t_bool(cOMBB_1628441366ol_nat,P),Q),R) = hAPP_i1948725293t_bool(P,hAPP_nat_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__004) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1281 (all P all Q all R hAPP_i418383825t_bool(hAPP_f876579787t_bool(hAPP_f2026117279t_bool(cOMBB_1437810218ol_int,P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_int_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1282 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1283 (all P all Q all R hAPP_int_nat(hAPP_f1134349059nt_nat(hAPP_f2100446809nt_nat(cOMBB_2018621492at_int,P),Q),R) = hAPP_f957591787ol_nat(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Nat__Ona) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1284 (all P all Q all R hAPP_nat_nat(hAPP_f389300155at_nat(hAPP_f109563153at_nat(cOMBB_1381347800at_nat,P),Q),R) = hAPP_f957591787ol_nat(P,hAPP_n1082236369t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Nat__Ona_006) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1285 (all P all Q all R hAPP_int_nat(hAPP_f1161717855nt_nat(hAPP_f1964560145nt_nat(cOMBB_1125113304at_int,P),Q),R) = hAPP_f22106695ol_nat(P,hAPP_i418383825t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1286 (all P all Q all R hAPP_int_nat(hAPP_f787214110nt_nat(hAPP_f261731407nt_nat(cOMBC_462113011ol_nat,P),Q),R) = hAPP_f22106695ol_nat(hAPP_i1530422220ol_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1287 (all P all Q all R hAPP_nat_nat(hAPP_f1473602334at_nat(hAPP_f630508183at_nat(cOMBC_1505178355ol_nat,P),Q),R) = hAPP_f957591787ol_nat(hAPP_n259507732ol_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1288 (all P all Q all R hAPP_int_nat(hAPP_f1134349059nt_nat(hAPP_f446447448nt_nat(cOMBS_1999073191ol_nat,P),Q),R) = hAPP_f957591787ol_nat(hAPP_i318423664ol_nat(P,R),hAPP_i1948725293t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1289 (all P all Q all R hAPP_int_nat(hAPP_f1161717855nt_nat(hAPP_f369809936nt_nat(cOMBS_1063588099ol_nat,P),Q),R) = hAPP_f22106695ol_nat(hAPP_i1530422220ol_nat(P,R),hAPP_i418383825t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1290 (all P all Q all R hAPP_nat_nat(hAPP_f389300155at_nat(hAPP_f1750007732at_nat(cOMBS_2106653443ol_nat,P),Q),R) = hAPP_f957591787ol_nat(hAPP_n259507732ol_nat(P,R),hAPP_n1082236369t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1291 (all P all Q all R hAPP_int_bool(hAPP_f2119767738t_bool(hAPP_f423804115t_bool(cOMBB_1418110531ol_int,P),Q),R) = hAPP_f448129468l_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1292 (all P all Q all R hAPP_nat_bool(hAPP_f158894502t_bool(hAPP_f1777703707t_bool(cOMBB_955900739ol_nat,P),Q),R) = hAPP_f54304608l_bool(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1293 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f202917053t_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].
% 1.95/2.22 1294 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1295 (all P all Q all R hAPP_i68813070l_bool(hAPP_f2144054103l_bool(hAPP_f1734373249l_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].
% 1.95/2.22 1296 (all P all Q all R hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1297 (all P all Q all R hAPP_s58564346l_bool(hAPP_f1259673775l_bool(hAPP_f1561913689l_bool(cOMBB_188601460_state,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1298 (all P all Q all R hAPP_s1892499976_state(hAPP_v365393659_state(hAPP_f1542232213_state(cOMBC_1193272608_state,P),Q),R) = hAPP_v594194232_state(hAPP_s712361723_state(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ovname_000tc__fun_Itc__Nat__) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1299 (all X all Y (-hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(fequal874423448a_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1300 (all X all Y (X != Y | hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(fequal874423448a_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1301 (all P all Q all R hAPP_H592031934_a_nat(hAPP_f106743253_a_nat(hAPP_f500900629_a_nat(cOMBB_1250632933iple_a,P),Q),R) = hAPP_nat_nat(P,hAPP_H592031934_a_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Hoare____Mirabelle) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1302 (all P all Q all R hAPP_H592031934_a_nat(hAPP_i1313984149_a_nat(hAPP_f183615253_a_nat(cOMBC_2020858056nt_nat,P),Q),R) = hAPP_int_nat(hAPP_H978941973nt_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1303 (all P all Q all R hAPP_H592031934_a_nat(hAPP_n1653940209_a_nat(hAPP_f1903462933_a_nat(cOMBC_667342884at_nat,P),Q),R) = hAPP_nat_nat(hAPP_H1772910449at_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_009) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1304 (all P all Q all R hAPP_int_nat(hAPP_H978941973nt_nat(hAPP_f1451619093nt_nat(cOMBC_1917249810_a_nat,P),Q),R) = hAPP_H592031934_a_nat(hAPP_i1313984149_a_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1305 (all P all Q all R hAPP_nat_nat(hAPP_H1772910449at_nat(hAPP_f2146713109at_nat(cOMBC_441305270_a_nat,P),Q),R) = hAPP_H592031934_a_nat(hAPP_n1653940209_a_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1306 (all P all Q all R hAPP_H1229305626_a_int(hAPP_f1561000661_a_int(hAPP_f789902073_a_int(cOMBS_1600277268nt_int,P),Q),R) = hAPP_int_int(hAPP_H1140854897nt_int(P,R),hAPP_H1229305626_a_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1307 (all P all Q all R hAPP_H592031934_a_nat(hAPP_f106743253_a_nat(hAPP_f1418102009_a_nat(cOMBS_1756972052at_nat,P),Q),R) = hAPP_nat_nat(hAPP_H1772910449at_nat(P,R),hAPP_H592031934_a_nat(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_010) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1308 (all P all Q all R hAPP_H1037229737a_bool(hAPP_i611776424a_bool(hAPP_f920351535a_bool(cOMBC_1530706207t_bool,P),Q),R) = hAPP_int_bool(hAPP_H1675210280t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_011) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1309 (all P all Q all R hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hAPP_f228417655a_bool(cOMBC_364739t_bool,P),Q),R) = hAPP_nat_bool(hAPP_H144868812t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_012) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1310 (all P all Q all R hAPP_int_bool(hAPP_H1675210280t_bool(hAPP_f936407855t_bool(cOMBC_1719122773a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_i611776424a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Hoare____Mirabelle____uwgpyvfjxg__O_013) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1311 (all P all Q all R hAPP_nat_bool(hAPP_H144868812t_bool(hAPP_f1886543991t_bool(cOMBC_533513393a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Hoare____Mirabelle____uwgpyvfjxg__O_014) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1312 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f604201481a_bool(cOMBB_1882975613iple_a,P),Q),R) = hAPP_bool_bool(P,hAPP_H1037229737a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1313 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H2130837971l_bool(P,R),hAPP_H1037229737a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_015) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1314 (all P all Q all R hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1315 (all P all Q all R hAPP_a2036067514e_bool(hAPP_f100967412e_bool(hAPP_f1460451647e_bool(cOMBC_524597097e_bool,P),Q),R) = hAPP_f746301080e_bool(hAPP_a1224971408e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__Com__Ostate_J_000t) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1316 (all P all Q all R hAPP_int_fun_nat_nat(hAPP_f1169617132at_nat(hAPP_f701299925at_nat(cOMBC_1294079849at_nat,P),Q),R) = hAPP_f1914919701at_nat(hAPP_i1876697324at_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1317 (all P all Q all R hAPP_nat_fun_int_nat(hAPP_f237327688nt_nat(hAPP_f1633513941nt_nat(cOMBC_1218031117nt_nat,P),Q),R) = hAPP_f2132704789nt_nat(hAPP_n74706760nt_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__Nat__Onat_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1318 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,P),Q),R) = hAPP_f1805168059t_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1319 (all P all Q all R hAPP_n1082236369t_bool(hAPP_f2022049025t_bool(hAPP_f1986088027t_bool(cOMBB_2101530536ol_nat,P),Q),R) = hAPP_f1805168059t_bool(P,hAPP_n1082236369t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__016) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1320 (all P all Q all R hAPP_i418383825t_bool(hAPP_f783004929t_bool(hAPP_f1410409747t_bool(cOMBB_1746576572ol_int,P),Q),R) = hAPP_f800510211t_bool(P,hAPP_i418383825t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1321 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(hAPP_f472159229t_bool(cOMBC_1683390479t_bool,P),Q),R) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__017) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1322 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,P),Q),R) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__018) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1323 (all P all Q all R hAPP_f448129468l_bool(hAPP_f284875647l_bool(hAPP_f1399552105l_bool(cOMBC_605892544l_bool,P),Q),R) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1324 (all P all Q all R hAPP_f54304608l_bool(hAPP_f103356543l_bool(hAPP_f643944041l_bool(cOMBC_1693257480l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1325 (all P all Q hAPP_H905846293iple_a(hAPP_H2085992369iple_a(cOMBK_2052406350iple_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1326 (all P all Q all R hAPP_H1140854897nt_int(hAPP_f231878828nt_int(hAPP_f1621780181nt_int(cOMBB_1885471694iple_a,P),Q),R) = hAPP_int_fun_int_int(P,hAPP_H1229305626_a_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1327 (all P all Q all R hAPP_H1772910449at_nat(hAPP_f429024520at_nat(hAPP_f703420885at_nat(cOMBB_789959282iple_a,P),Q),R) = hAPP_nat_fun_nat_nat(P,hAPP_H592031934_a_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_019) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1328 (all P all Q all R hAPP_H1675210280t_bool(hAPP_f2142913731t_bool(hAPP_f1329415375t_bool(cOMBB_1505691757iple_a,P),Q),R) = hAPP_i1948725293t_bool(P,hAPP_H1229305626_a_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__020) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1329 (all P all Q all R hAPP_H144868812t_bool(hAPP_f1872860171t_bool(hAPP_f1981448543t_bool(cOMBB_1391527205iple_a,P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_H592031934_a_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__021) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1330 (all P all Q all R hAPP_nat_nat(hAPP_f966999552at_nat(hAPP_f724467227at_nat(cOMBB_161916371at_nat,P),Q),R) = hAPP_f2097660464ol_nat(P,hAPP_n1919155532a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1331 (all P all Q all R hAPP_H592031934_a_nat(hAPP_f342603021_a_nat(hAPP_f575660003_a_nat(cOMBB_1357028143iple_a,P),Q),R) = hAPP_f957591787ol_nat(P,hAPP_H1675210280t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Nat__Ona_022) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1332 (all P all Q all R hAPP_H592031934_a_nat(hAPP_f2085403241_a_nat(hAPP_f734830747_a_nat(cOMBB_1107515603iple_a,P),Q),R) = hAPP_f22106695ol_nat(P,hAPP_H144868812t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona_023) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1333 (all P all Q all R hAPP_H592031934_a_nat(hAPP_f1464798435_a_nat(hAPP_f1012303887_a_nat(cOMBC_1159891896ol_nat,P),Q),R) = hAPP_f22106695ol_nat(hAPP_H1993634375ol_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_024) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1334 (all P all Q all R hAPP_nat_nat(hAPP_f2122367971at_nat(hAPP_f870149665at_nat(cOMBC_2036134968ol_nat,P),Q),R) = hAPP_f2097660464ol_nat(hAPP_n130255193ol_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1335 (all P all Q all R hAPP_H592031934_a_nat(hAPP_f342603021_a_nat(hAPP_f270087133_a_nat(cOMBS_1333400172ol_nat,P),Q),R) = hAPP_f957591787ol_nat(hAPP_H781635819ol_nat(P,R),hAPP_H1675210280t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_025) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1336 (all P all Q all R hAPP_H592031934_a_nat(hAPP_f2085403241_a_nat(hAPP_f1052116629_a_nat(cOMBS_397915080ol_nat,P),Q),R) = hAPP_f22106695ol_nat(hAPP_H1993634375ol_nat(P,R),hAPP_H144868812t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_026) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1337 (all P all Q all R hAPP_int_nat(hAPP_f2050777416nt_nat(hAPP_f1895921634nt_nat(cOMBS_202713324ol_nat,P),Q),R) = hAPP_f2097660464ol_nat(hAPP_i51375541ol_nat(P,R),hAPP_i611776424a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__fun_Itc__Hoare____Mirabelle____uwgp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1338 (all P all Q all R hAPP_nat_nat(hAPP_f966999552at_nat(hAPP_f264818750at_nat(cOMBS_1274158152ol_nat,P),Q),R) = hAPP_f2097660464ol_nat(hAPP_n130255193ol_nat(P,R),hAPP_n1919155532a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1339 (all P all Q all R hAPP_H2130837971l_bool(hAPP_f146754017l_bool(hAPP_f239971723l_bool(cOMBB_1866391387iple_a,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1037229737a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_027) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1340 (all P all Q all R hAPP_a849909144l_bool(hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_a2036067514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1341 (all P all Q all R hAPP_i318423664ol_nat(hAPP_f1548925761ol_nat(hAPP_f1331458699ol_nat(cOMBB_2091167284at_int,P),Q),R) = hAPP_f1109019371ol_nat(P,hAPP_int_fun_int_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Nat__Onat_J_000tc__fun_Itc__) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1342 (all P all Q all R hAPP_n259507732ol_nat(hAPP_f299305025ol_nat(hAPP_f1632710027ol_nat(cOMBB_1453893592at_nat,P),Q),R) = hAPP_f1109019371ol_nat(P,hAPP_nat_fun_int_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Nat__Onat_J_000tc__fun_Itc___028) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1343 (all P all Q all R hAPP_i1530422220ol_nat(hAPP_f1501159417ol_nat(hAPP_f1029311995ol_nat(cOMBB_1562322300at_int,P),Q),R) = hAPP_f782000547ol_nat(P,hAPP_int_fun_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__fun_Itc__) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1344 (all P all Q all R hAPP_H1037229737a_bool(hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_H426895267a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_029) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1345 (all P all Q all R hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(hAPP_f194616807t_bool(cOMBC_922884543t_bool,P),Q),R) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__030) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1346 (all P all Q all R hAPP_f800510211t_bool(hAPP_f1730770594t_bool(hAPP_f1311642927t_bool(cOMBC_646315179t_bool,P),Q),R) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__031) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1347 (all P all Q all R hAPP_H1772910449at_nat(hAPP_f221335601at_nat(hAPP_f388255893at_nat(cOMBC_1038836708at_nat,P),Q),R) = hAPP_f1914919701at_nat(hAPP_H1651200817at_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_032) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1348 (all P all Q all R hAPP_H1675210280t_bool(hAPP_f138254639t_bool(hAPP_f1998609161t_bool(cOMBB_1870764287iple_a,P),Q),R) = hAPP_f1805168059t_bool(P,hAPP_H1675210280t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__033) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1349 (all P all Q all R hAPP_H144868812t_bool(hAPP_f27379319t_bool(hAPP_f196067081t_bool(cOMBB_437532599iple_a,P),Q),R) = hAPP_f800510211t_bool(P,hAPP_H144868812t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__034) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1350 (all P all Q all R hAPP_a723219176e_bool(hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,P),Q),R) = hAPP_f167292325e_bool(P,hAPP_a849909144l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1351 (all P all Q all R hAPP_n74706760nt_nat(hAPP_f2080483477nt_nat(hAPP_f1701814485nt_nat(cOMBB_737513486at_nat,P),Q),R) = hAPP_f901215189nt_nat(P,hAPP_nat_fun_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__fun_Itc___035) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1352 (all P all Q all R hAPP_i1876697324at_nat(hAPP_f1033905301at_nat(hAPP_f1315855317at_nat(cOMBB_891709290at_int,P),Q),R) = hAPP_f1585078997at_nat(P,hAPP_int_fun_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__fun_Itc___036) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1353 (all P all Q all R hAPP_a1224971408e_bool(hAPP_f1406200875e_bool(hAPP_f635443597e_bool(cOMBB_2139825703bool_a,P),Q),R) = hAPP_f162060345e_bool(P,hAPP_a2036067514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_037) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1354 (all P all Q all R hAPP_i611776424a_bool(hAPP_f298605433a_bool(hAPP_f1421841531a_bool(cOMBB_1700417404ol_int,P),Q),R) = hAPP_H426895267a_bool(P,hAPP_i240634960iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1355 (all P all Q all R hAPP_n1919155532a_bool(hAPP_f260875897a_bool(hAPP_f1930382715a_bool(cOMBB_1063143712ol_nat,P),Q),R) = hAPP_H426895267a_bool(P,hAPP_n261501868iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_038) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1356 (all P all Q all R hAPP_i1529485324t_bool(hAPP_f1468280982t_bool(hAPP_f1596157055t_bool(cOMBB_765314529ol_int,P),Q),R) = hAPP_f1223193598t_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__039) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1357 (all P all Q all R hAPP_n1512601776t_bool(hAPP_f10625010t_bool(hAPP_f1115950719t_bool(cOMBB_1654519265ol_nat,P),Q),R) = hAPP_f1730770594t_bool(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__040) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1358 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f1194757675a_bool(hAPP_f1697223433a_bool(cOMBB_1610959875iple_a,P),Q),R) = hAPP_f1695230391l_bool(P,hAPP_H426895267a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_041) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1359 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_H622608077l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_042) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1360 (all P all Q all R hAPP_H781635819ol_nat(hAPP_f224922881ol_nat(hAPP_f543861963ol_nat(cOMBB_1075417391iple_a,P),Q),R) = hAPP_f1109019371ol_nat(P,hAPP_H978941973nt_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Nat__Onat_J_000tc__fun_Itc___043) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1361 (all P all Q all R hAPP_H1993634375ol_nat(hAPP_f1669765561ol_nat(hAPP_f1073041467ol_nat(cOMBB_10565751iple_a,P),Q),R) = hAPP_f782000547ol_nat(P,hAPP_H1772910449at_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__fun_Itc___044) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1362 (all P all Q all R hAPP_a1200519163e_bool(hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,P),Q),R) = hAPP_f644196280e_bool(P,hAPP_a849909144l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_045) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1363 (all P all Q all R hAPP_n1653940209_a_nat(hAPP_f1393576712_a_nat(hAPP_f145529813_a_nat(cOMBC_309106125_a_nat,P),Q),R) = hAPP_f106743253_a_nat(hAPP_n352002696_a_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp_046) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1364 (all P all Q all R hAPP_i611776424a_bool(hAPP_f1718504751a_bool(hAPP_f481410067a_bool(cOMBB_1028320654ol_int,P),Q),R) = hAPP_f20753329a_bool(P,hAPP_i611776424a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_047) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1365 (all P all Q all R hAPP_n1919155532a_bool(hAPP_f2087582327a_bool(hAPP_f1396758363a_bool(cOMBB_391046962ol_nat,P),Q),R) = hAPP_f20753329a_bool(P,hAPP_n1919155532a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_048) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.22 1366 (all P all Q all R hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1367 (all P all Q all R hAPP_H1651200817at_nat(hAPP_f1879857877at_nat(hAPP_f481016213at_nat(cOMBB_1672982117iple_a,P),Q),R) = hAPP_f1585078997at_nat(P,hAPP_H1772910449at_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__fun_Itc___049) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1368 (all P all Q all R hAPP_H426895267a_bool(hAPP_f960023481a_bool(hAPP_f1786170683a_bool(cOMBB_683172471iple_a,P),Q),R) = hAPP_H426895267a_bool(P,hAPP_H905846293iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_050) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1369 (all P all Q all R hAPP_i51375541ol_nat(hAPP_f1442126667ol_nat(hAPP_f1072896543ol_nat(cOMBB_206396714at_int,P),Q),R) = hAPP_f1371399797ol_nat(P,hAPP_i1313984149_a_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_051) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1370 (all P all Q all R hAPP_n130255193ol_nat(hAPP_f883871819ol_nat(hAPP_f424754463ol_nat(cOMBB_1716606670at_nat,P),Q),R) = hAPP_f1371399797ol_nat(P,hAPP_n1653940209_a_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_052) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1371 (all P all Q all R hAPP_H426895267a_bool(hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_053) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1372 (all P all Q all R hAPP_n352002696_a_nat(hAPP_f1485673429_a_nat(hAPP_f2006236373_a_nat(cOMBB_2005430478at_nat,P),Q),R) = hAPP_f500900629_a_nat(P,hAPP_nat_fun_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__fun_Itc___054) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1373 (all P all Q all R hAPP_f20753329a_bool(hAPP_f1706700729a_bool(hAPP_f957014749a_bool(cOMBC_288844080a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_055) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67 1374 (all P all Q all R hAPP_H1743777351a_bool(hAPP_f550111323a_bool(hAPP_f615286271a_bool(cOMBB_1176122337iple_a,P),Q),R) = hAPP_f1706700729a_bool(P,hAPP_H426895267a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_056) # label(axiom) # label(non_clause). [assumption].
% 3.47/3.67
% 3.47/3.67 ============================== end of process non-clausal formulas ===
% 3.47/3.67
% 3.47/3.67 ============================== PROCESS INITIAL CLAUSES ===============
% 3.47/3.67
% 3.47/3.67 ============================== PREDICATE ELIMINATION =================
% 3.47/3.67
% 3.47/3.67 ============================== end predicate elimination =============
% 3.47/3.67
% 3.47/3.67 Auto_denials: (non-Horn, no changes).
% 3.47/3.67
% 3.47/3.67 Term ordering decisions:
% 3.47/3.67 Function symbol KB weights: plus_plus_nat=1. ord_less_eq_nat=1. insert956547291iple_a=1. insert_nat=1. insert_int=1. times_times_nat=1. bot_bo797238721a_bool=1. member_nat=1. bot_bot_fun_nat_bool=1. bot_bot_fun_int_bool=1. member_int=1. member1797258804iple_a=1. plus_plus_int=1. finite_finite_nat=1. finite_finite_int=1. ord_less_eq_int=1. times_times_int=1. finite1738664244iple_a=1. ord_le951220754t_bool=1. ord_le1568362934t_bool=1. minus_minus_nat=1. semiri1621563631at_int=1. ord_less_nat=1. minus_1449998731t_bool=1. minus_2067140911t_bool=1. ord_le1523781517a_bool=1. minus_85316870a_bool=1. big_co387207925at_nat=1. big_co1740723097nt_nat=1. big_co1340561246_a_nat=1. fconj=1. ord_min_nat=1. minus_minus_int=1. collect_nat=1. ord_less_int=1. collect_int=1. collec351493750iple_a=1. one_one_int=1. cOMBB_1652995168ol_int=1. cOMBS_int_bool_bool=1. ord_min_int=1. bot_bot_bool=1. cOMBB_1015721476ol_nat=1. cOMBS_nat_bool_bool=1. cOMBB_1866391387iple_a=1. cOMBS_154988028l_bool=1. cOMBC_94739984l_bool=1. fequal963300192iple_a=1. fequal_int=1. fequal_nat=1. zero_zero_int=1. big_co1977834938_a_int=1. cOMBC_226598744l_bool=1. cOMBC_1519416966l_bool=1. cOMBC_nat_nat_bool=1. fdisj=1. fimplies=1. one_one_nat=1. ord_less_eq_bool=1. big_co1024481617at_int=1. the_Ho830102290iple_a=1. the_int=1. the_nat=1. cOMBC_int_int_bool=1. zero_zero_nat=1. ord_lessThan_nat=1. cOMBC_1940896922a_bool=1. fNot=1. big_co230513141nt_int=1. minus_minus_bool=1. power_power_int=1. uminus_uminus_int=1. power_power_nat=1. bot_bot_nat=1. cOMBB_1746576572ol_int=1. cOMBB_1870764287iple_a=1. cOMBB_1882975613iple_a=1. cOMBB_2101530536ol_nat=1. cOMBB_391046962ol_nat=1. cOMBB_437532599iple_a=1. cOMBB_591320580ol_int=1. cOMBB_963856155at_nat=1. cOMBB_bool_bool_int=1. cOMBB_bool_bool_nat=1. fFalse=1. cOMBB_10565751iple_a=1. cOMBB_1453893592at_nat=1. cOMBB_1562322300at_int=1. cOMBB_1716606670at_nat=1. cOMBB_789959282iple_a=1. cOMBB_1028320654ol_int=1. cOMBB_1601129847at_int=1. ord_lessThan_int=1. big_linorder_Min_int=1. big_linorder_Min_nat=1. cOMBB_nat_nat_nat=1. cOMBC_1159891896ol_nat=1. cOMBC_1505178355ol_nat=1. cOMBC_1570214144a_bool=1. cOMBC_1683390479t_bool=1. cOMBC_1719122773a_bool=1. cOMBC_178881787t_bool=1. cOMBC_2036134968ol_nat=1. cOMBC_364739t_bool=1. cOMBC_462113011ol_nat=1. cOMBC_533513393a_bool=1. cOMBC_667342884at_nat=1. cOMBC_int_nat_bool=1. cOMBC_int_nat_nat=1. cOMBC_nat_int_bool=1. cOMBK_1028443109iple_a=1. cOMBK_2052406350iple_a=1. cOMBK_int_int=1. cOMBK_int_nat=1. cOMBK_nat_int=1. cOMBK_nat_nat=1. cOMBS_1756972052at_nat=1. cOMBS_nat_nat_nat=1. fTrue=1. cOMBB_1063143712ol_nat=1. cOMBB_1075417391iple_a=1. cOMBB_1176122337iple_a=1. cOMBB_118231410ol_int=1. cOMBB_1250632933iple_a=1. cOMBB_1348041619bool_a=1. cOMBB_1355796797bool_a=1. cOMBB_1391527205iple_a=1. cOMBB_1437810218ol_int=1. cOMBB_1628441366ol_nat=1. cOMBB_1654519265ol_nat=1. cOMBB_1700417404ol_int=1. cOMBB_1885471694iple_a=1. cOMBB_188601460_state=1. cOMBB_206396714at_int=1. cOMBB_2091167284at_int=1. cOMBB_765314529ol_int=1. cOMBB_800536526ol_nat=1. cOMBB_nat_nat_int=1. cOMBC_1530706207t_bool=1. cOMBC_231445413l_bool=1. cOMBC_288844080a_bool=1. cOMBC_41962815e_bool=1. cOMBC_441305270_a_nat=1. cOMBC_646315179t_bool=1. cOMBC_922884543t_bool=1. cOMBC_nat_int_nat=1. cOMBC_nat_nat_nat=1. cOMBK_1458035955bool_a=1. cOMBS_1063588099ol_nat=1. cOMBS_1274158152ol_nat=1. cOMBS_1333400172ol_nat=1. cOMBS_1600277268nt_int=1. cOMBS_1999073191ol_nat=1. cOMBS_202713324ol_nat=1. cOMBS_2106653443ol_nat=1. cOMBS_397915080ol_nat=1. cOMBS_int_nat_nat=1. fequal874423448a_bool=1. fequal_fun_int_bool=1. fequal_fun_nat_bool=1. fequal_state=1. finite_card_nat=1. big_linorder_Max_int=1. big_linorder_Max_nat=1. cOMBB_1107515603iple_a=1. cOMBB_1125113304at_int=1. cOMBB_1357028143iple_a=1. cOMBB_1381347800at_nat=1. cOMBB_1418110531ol_int=1. cOMBB_1505691757iple_a=1. cOMBB_1610959875iple_a=1. cOMBB_161916371at_nat=1. cOMBB_1672982117iple_a=1. cOMBB_2005430478at_nat=1. cOMBB_2018621492at_int=1. cOMBB_2139825703bool_a=1. cOMBB_683172471iple_a=1. cOMBB_737513486at_nat=1. cOMBB_844853809_state=1. cOMBB_891709290at_int=1. cOMBB_955900739ol_nat=1. cOMBB_int_int_nat=1. cOMBB_nat_int_int=1. cOMBC_1038836708at_nat=1. cOMBC_1193272608_state=1. cOMBC_1218031117nt_nat=1. cOMBC_1294079849at_nat=1. cOMBC_1693257480l_bool=1. cOMBC_1917249810_a_nat=1. cOMBC_2020858056nt_nat=1. cOMBC_2027030106e_bool=1. cOMBC_309106125_a_nat=1. cOMBC_524597097e_bool=1. cOMBC_605892544l_bool=1. cOMBC_627599030l_bool=1. cOMBC_int_int_nat=1. cOMBI_1301683934iple_a=1. cOMBI_int=1. cOMBI_nat=1. cOMBK_1007576201iple_a=1. cOMBK_235286536iple_a=1. cOMBK_bool_int=1. cOMBK_bool_nat=1. cOMBS_777315357_state=1. ord_le1912455174t_bool=1. ord_le382113706t_bool=1. the_el1519802624iple_a=1. the_elem_int=1. the_elem_nat=1. cOMBB_145932198bool_a=1. cOMBB_160679318_state=1. cOMBC_892787026e_bool=1. cOMBK_bool_state=1. cOMBS_1378840469l_bool=1. collec999179778a_bool=1. collect_fun_int_bool=1. collect_fun_nat_bool=1. finite1395289673t_bool=1. finite2012431853t_bool=1. finite268574148a_bool=1. finite_card_int=1. ord_max_nat=1. skip=1. the_fu1555441254a_bool=1. the_fun_int_bool=1. the_fun_nat_bool=1. update=1. b=1. c=1. g=1. p=1. hAPP_nat_nat=1. hAPP_nat_fun_nat_nat=1. hAPP_f54304608l_bool=1. hAPP_f448129468l_bool=1. hAPP_f1695230391l_bool=1. hAPP_int_int=1. hAPP_nat_bool=1. hAPP_f20753329a_bool=1. hAPP_f800510211t_bool=1. hAPP_f1805168059t_bool=1. hAPP_int_fun_int_int=1. hAPP_int_bool=1. hAPP_n1699378549t_bool=1. hAPP_H1743777351a_bool=1. hAPP_n1512601776t_bool=1. hAPP_i1529485324t_bool=1. hAPP_i1948725293t_bool=1. hAPP_n215258509l_bool=1. hAPP_i2112223885l_bool=1. hAPP_f22106695ol_nat=1. hAPP_H622608077l_bool=1. hAPP_f284875647l_bool=1. hAPP_f103356543l_bool=1. hAPP_nat_int=1. hAPP_H1037229737a_bool=1. hAPP_f1594865479ol_int=1. hAPP_f1767618879l_bool=1. hAPP_f1223193598t_bool=1. hAPP_f1730770594t_bool=1. hAPP_f1706700729a_bool=1. hAPP_f957591787ol_nat=1. hAPP_f2097660464ol_nat=1. hAPP_f782000547ol_nat=1. hAPP_f1109019371ol_nat=1. hAPP_f1693662087iple_a=1. image_nat_int=1. hAPP_f1371399797ol_nat=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. image_int_int=1. image_nat_nat=1. image_533441733iple_a=1. hAPP_H905846293iple_a=1. hAPP_H592031934_a_nat=1. hAPP_int_nat=1. hAPP_f587450508ol_int=1. hAPP_H2085992369iple_a=1. hAPP_f1734373249l_bool=1. hAPP_f2144054103l_bool=1. hAPP_f727283836t_bool=1. hAPP_H426895267a_bool=1. hAPP_state_bool=1. hAPP_f1080886329l_bool=1. hAPP_f1146629647l_bool=1. hAPP_f561022312t_bool=1. hAPP_f146754017l_bool=1. hAPP_f239971723l_bool=1. hAPP_f607497069a_bool=1. hAPP_f659380387ol_int=1. hAPP_H1229305626_a_int=1. hAPP_f202917053t_bool=1. hAPP_f428220345t_bool=1. finite_fold_int_int=1. finite_fold_nat_nat=1. finite1205970312iple_a=1. hAPP_a2036067514e_bool=1. finite1215486064a_bool=1. finite1578363458t_bool=1. finite1827710202t_bool=1. hAPP_f1544320301ol_int=1. hAPP_f1722879237t_bool=1. hAPP_f229349961t_bool=1. hAPP_f247708275a_bool=1. hAPP_f1599440987ol_int=1. hAPP_int_fun_nat_int=1. image_48635758_a_nat=1. hAPP_f920293029a_bool=1. hAPP_f1926459811ol_int=1. finite1621280049iple_a=1. finite_fold1Set_int=1. finite_fold1Set_nat=1. image_1865589340iple_a=1. image_685909450_a_int=1. image_int_nat=1. finite1626084323ne_int=1. finite1753440478iple_a=1. finite988810631ne_nat=1. hAPP_n1653940209_a_nat=1. hAPP_nat_fun_int_nat=1. image_1844722432iple_a=1. hAPP_H144868812t_bool=1. hAPP_H1675210280t_bool=1. hAPP_f1914919701at_nat=1. hAPP_i418383825t_bool=1. hAPP_n1082236369t_bool=1. hAPP_n1919155532a_bool=1. ass=1. finite1033474011iple_a=1. finite1432773856em_int=1. finite795500164em_nat=1. hAPP_H1772910449at_nat=1. hAPP_f106743253_a_nat=1. hAPP_f138254639t_bool=1. hAPP_f1396758363a_bool=1. hAPP_f1410409747t_bool=1. hAPP_f1639111240at_nat=1. hAPP_f1731313045at_nat=1. hAPP_f196067081t_bool=1. hAPP_f1986088027t_bool=1. hAPP_f1998609161t_bool=1. hAPP_f2022049025t_bool=1. hAPP_f2087582327a_bool=1. hAPP_f27379319t_bool=1. hAPP_f604201481a_bool=1. hAPP_f627970963t_bool=1. hAPP_f654702867t_bool=1. hAPP_f783004929t_bool=1. hAPP_f894608603t_bool=1. hAPP_i611776424a_bool=1. hAPP_int_fun_nat_nat=1. hAPP_n261501868iple_a=1. semi=1. hAPP_f1029311995ol_nat=1. hAPP_f1073041467ol_nat=1. hAPP_f1501159417ol_nat=1. hAPP_f1632710027ol_nat=1. hAPP_f1669765561ol_nat=1. hAPP_f2132704789nt_nat=1. hAPP_f299305025ol_nat=1. hAPP_f424754463ol_nat=1. hAPP_f429024520at_nat=1. hAPP_f703420885at_nat=1. hAPP_f883871819ol_nat=1. hAPP_i240634960iple_a=1. hAPP_f1087393429at_nat=1. hAPP_f1134349059nt_nat=1. hAPP_f1161717855nt_nat=1. hAPP_f1463450952at_nat=1. hAPP_f1718504751a_bool=1. hAPP_f2085403241_a_nat=1. hAPP_f342603021_a_nat=1. hAPP_f389300155at_nat=1. hAPP_f481410067a_bool=1. hAPP_f966999552at_nat=1. hAPP_s1806633685e_bool=1. hAPP_f1012303887_a_nat=1. hAPP_f1048215610t_bool=1. hAPP_f1181346091a_bool=1. hAPP_f1408247010at_nat=1. hAPP_f1418102009_a_nat=1. hAPP_f1464798435_a_nat=1. hAPP_f1473602334at_nat=1. hAPP_f1570313510t_bool=1. hAPP_f1585078997at_nat=1. hAPP_f175561985t_bool=1. hAPP_f1886543991t_bool=1. hAPP_f1903462933_a_nat=1. hAPP_f2122367971at_nat=1. hAPP_f228417655a_bool=1. hAPP_f261731407nt_nat=1. hAPP_f472159229t_bool=1. hAPP_f482008321t_bool=1. hAPP_f571476211a_bool=1. hAPP_f630508183at_nat=1. hAPP_f688831301t_bool=1. hAPP_f762886889e_bool=1. hAPP_f787214110nt_nat=1. hAPP_f870149665at_nat=1. hAPP_f879494613nt_nat=1. hAPP_f936407855t_bool=1. hAPP_H1993634375ol_nat=1. hAPP_H978941973nt_nat=1. hAPP_a849909144l_bool=1. hAPP_b2019457360e_bool=1. hAPP_b540892988e_bool=1. hAPP_f1006724181e_bool=1. hAPP_f1052116629_a_nat=1. hAPP_f10625010t_bool=1. hAPP_f1072896543ol_nat=1. hAPP_f1115950719t_bool=1. hAPP_f1178339559l_bool=1. hAPP_f1266913334l_bool=1. hAPP_f1311642927t_bool=1. hAPP_f1331458699ol_nat=1. hAPP_f1399363134nt_nat=1. hAPP_f1399575567t_bool=1. hAPP_f1421841531a_bool=1. hAPP_f1442126667ol_nat=1. hAPP_f1468280982t_bool=1. hAPP_f1505651103t_bool=1. hAPP_f1509969235l_bool=1. hAPP_f1533130627t_bool=1. hAPP_f1548925761ol_nat=1. hAPP_f1561000661_a_int=1. hAPP_f1561913689l_bool=1. hAPP_f1577095245l_bool=1. hAPP_f1596157055t_bool=1. hAPP_f1621780181nt_int=1. hAPP_f1634429330l_bool=1. hAPP_f1750007732at_nat=1. hAPP_f1759915619e_bool=1. hAPP_f1791153283t_bool=1. hAPP_f1824947087e_bool=1. hAPP_f1872860171t_bool=1. hAPP_f1895921634nt_nat=1. hAPP_f1930382715a_bool=1. hAPP_f194616807t_bool=1. hAPP_f1981448543t_bool=1. hAPP_f2026117279t_bool=1. hAPP_f2050777416nt_nat=1. hAPP_f2146713109at_nat=1. hAPP_f224922881ol_nat=1. hAPP_f231878828nt_int=1. hAPP_f260875897a_bool=1. hAPP_f264818750at_nat=1. hAPP_f270087133_a_nat=1. hAPP_f298605433a_bool=1. hAPP_f340725611e_bool=1. hAPP_f369809936nt_nat=1. hAPP_f416620757at_nat=1. hAPP_f446447448nt_nat=1. hAPP_f446977493at_nat=1. hAPP_f500900629_a_nat=1. hAPP_f543861963ol_nat=1. hAPP_f550111323a_bool=1. hAPP_f615286271a_bool=1. hAPP_f618557131t_bool=1. hAPP_f789902073_a_int=1. hAPP_f876579787t_bool=1. hAPP_f879109391t_bool=1. hAPP_f901215189nt_nat=1. hAPP_f920351535a_bool=1. hAPP_f957014749a_bool=1. hAPP_i1313984149_a_nat=1. hAPP_i1530422220ol_nat=1. hAPP_int_fun_int_nat=1. hAPP_n130255193ol_nat=1. hAPP_n259507732ol_nat=1. hAPP_s58564346l_bool=1. big_se1603268663iple_a=1. big_se275732192ig_nat=1. big_se913005884ig_int=1. hAPP_H1140854897nt_int=1. hAPP_H1651200817at_nat=1. hAPP_H2130837971l_bool=1. hAPP_H781635819ol_nat=1. hAPP_a1200519163e_bool=1. hAPP_a1224971408e_bool=1. hAPP_a723219176e_bool=1. hAPP_b1013836512t_bool=1. hAPP_b1882817719a_bool=1. hAPP_b396694332t_bool=1. hAPP_f100967412e_bool=1. hAPP_f1033905301at_nat=1. hAPP_f109563153at_nat=1. hAPP_f1139079189at_int=1. hAPP_f1169617132at_nat=1. hAPP_f1194757675a_bool=1. hAPP_f1259673775l_bool=1. hAPP_f1315855317at_nat=1. hAPP_f1329415375t_bool=1. hAPP_f1393576712_a_nat=1. hAPP_f1399552105l_bool=1. hAPP_f1406200875e_bool=1. hAPP_f1431025877at_int=1. hAPP_f1451619093nt_nat=1. hAPP_f145529813_a_nat=1. hAPP_f1460451647e_bool=1. hAPP_f147134065nt_int=1. hAPP_f1485673429_a_nat=1. hAPP_f1542232213_state=1. hAPP_f158894502t_bool=1. hAPP_f162060345e_bool=1. hAPP_f1633513941nt_nat=1. hAPP_f1637334154l_bool=1. hAPP_f167292325e_bool=1. hAPP_f1673907925nt_int=1. hAPP_f1697223433a_bool=1. hAPP_f1701814485nt_nat=1. hAPP_f1777703707t_bool=1. hAPP_f1786170683a_bool=1. hAPP_f183615253_a_nat=1. hAPP_f1879857877at_nat=1. hAPP_f1964560145nt_nat=1. hAPP_f2006236373_a_nat=1. hAPP_f2080483477nt_nat=1. hAPP_f2100446809nt_nat=1. hAPP_f2100528361l_bool=1. hAPP_f2110825313l_bool=1. hAPP_f2119767738t_bool=1. hAPP_f2142913731t_bool=1. hAPP_f215623910l_bool=1. hAPP_f221335601at_nat=1. hAPP_f237327688nt_nat=1. hAPP_f388255893at_nat=1. hAPP_f423804115t_bool=1. hAPP_f481016213at_nat=1. hAPP_f575660003_a_nat=1. hAPP_f635443597e_bool=1. hAPP_f643944041l_bool=1. hAPP_f644196280e_bool=1. hAPP_f701299925at_nat=1. hAPP_f724467227at_nat=1. hAPP_f734830747_a_nat=1. hAPP_f746301080e_bool=1. hAPP_f817621513e_bool=1. hAPP_f851239890_state=1. hAPP_f871651461_state=1. hAPP_f909851349nt_nat=1. hAPP_f960023481a_bool=1. hAPP_i1475897073_a_int=1. hAPP_i1876697324at_nat=1. hAPP_i318423664ol_nat=1. hAPP_i51375541ol_nat=1. hAPP_i68813070l_bool=1. hAPP_n1006566506l_bool=1. hAPP_n352002696_a_nat=1. hAPP_n74706760nt_nat=1. hAPP_s1892499976_state=1. hAPP_state_state=1. hAPP_v365393659_state=1. hAPP_f1246832597l_bool=1. hAPP_f1261923407e_bool=1. hAPP_f1948010709l_bool=1. hAPP_f2073279419e_bool=1. hAPP_f258822235a_bool=1. hAPP_f375255701e_bool=1. hAPP_f396832789l_bool=1. hAPP_f582319405t_bool=1. hAPP_f631471077t_bool=1. hAPP_f963367678e_bool=1. hAPP_nat_state=1. hAPP_s712361723_state=1. hAPP_state_nat=1. hAPP_v594194232_state=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f59=1. f60=1. f61=1. f74=1. f75=1. f76=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. f110=1. f111=1. f112=1. f116=1. f117=1. f118=1. f128=1. f129=1. f130=1. f131=1. f132=1. f133=1. f134=1. f135=1. f136=1. f147=1. f148=1. f149=1. f150=1. f151=1. f152=1. f171=1. f172=1. f183=1. f184=1. f185=1. f197=1. f198=1. f200=1. f201=1. f202=1. f203=1. f204=1. f206=1. f207=1. f208=1. f209=1. f211=1. f218=1. hoare_2102800559rivs_a=1. finite772772422nt_int=1. finite929467206at_nat=1. finite90892550iple_a=1. finite1973466193nt_int=1. finite2130160977at_nat=1. finite1428139793iple_a=1. big_co1815942735_a_nat=1. big_co305732779_a_int=1. finite_fold1_int=1. finite_fold1_nat=1. big_co1705425894at_nat=1. big_co195215938at_int=1. finite1071749497t_bool=1. finite1321096241t_bool=1. finite2114894759a_bool=1. finite1803123436a_bool=1. finite1956789438t_bool=1. finite58652534t_bool=1. ord_at875362053st_int=1. finite1465856449iple_a=1. big_co1548731110nt_int=1. big_co911457418nt_nat=1. if_nat=1. finite1008073724t_bool=1. finite1152845682a_bool=1. finite1704255308nt_int=1. finite1860950092at_nat=1. finite648855052iple_a=1. finite758726980t_bool=1. ord_at238088361st_nat=1. partia1949573335iple_a=1. partial_flat_lub_int=1. partial_flat_lub_nat=1. ord_gr375877188st_nat=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f31=1. f32=1. f33=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f137=1. f138=1. f139=1. f140=1. f205=1. f210=1. f219=1. f220=1. f225=1. f226=1. f227=1. f228=1. hoare_1916936827iple_a=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f98=1. f99=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f113=1. f114=1. f115=1. f159=1. f160=1. f161=1. f162=1. f163=1. f164=1. f173=1. f174=1. f175=1. f176=1. f177=1. f178=1. f179=1. f180=1. f181=1. f182=1. f186=1. f187=1. f188=1. f189=1. f190=1. f191=1. f192=1. f193=1. f194=1. f195=1. f196=1. f199=1. f212=1. f213=1. f214=1. f215=1. f216=1. f217=1. f221=1. f222=1. f223=1. f224=1. f1=1. f2=1. f34=1. f35=1. f55=1. f56=1. f57=1. f58=1. f68=1. f69=1. f70=1. f71=1. f72=1. f73=1. f119=1. f120=1. f121=1. f122=1. f123=1. f124=1. f125=1. f126=1. f127=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f165=1. f166=1. f167=1. f168=1. f169=1. f170=1. f3=1. f4=1. f5=1. f6=1. f153=1. f154=1. f155=1. f156=1. f157=1. f158=1. f7=1. f8=1. f9=1. f36=1.
% 6.45/6.68
% 6.45/6.68 ============================== end of process initial clauses ========
% 6.45/6.68
% 6.45/6.68 ============================== CLAUSES FOR SEARCH ====================
% 6.45/6.68
% 6.45/6.68 ============================== end of clauses for search =============
% 6.45/6.68
% 6.45/6.68 ============================== SEARCH ================================
% 6.45/6.68
% 6.45/6.68 % Starting search at 1.76 seconds.
% 6.45/6.68
% 6.45/6.68 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 85 (0.00 of 2.59 sec).
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=59.000, iters=3604
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=49.000, iters=3404
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=45.000, iters=3334
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=40.000, iters=3348
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=39.000, iters=3544
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=36.000, iters=3366
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=35.000, iters=3370
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=34.000, iters=3373
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=33.000, iters=3386
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=32.000, iters=3343
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=31.000, iters=3427
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=30.000, iters=3373
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=29.000, iters=3341
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=28.000, iters=3340
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=27.000, iters=3418
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=26.000, iters=3358
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=25.000, iters=3339
% 6.45/6.68
% 6.45/6.68 Low Water (keep): wt=24.000, iters=3349
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=23.000, iters=3338
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=22.000, iters=3386
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=21.000, iters=3392
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=20.000, iters=3364
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=19.000, iters=3333
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=18.000, iters=3337
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=17.000, iters=3348
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=16.000, iters=3335
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=15.000, iters=3334
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=14.000, iters=3591
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=4536, wt=82.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5545, wt=77.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=4770, wt=76.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5635, wt=75.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5532, wt=71.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5236, wt=70.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=4526, wt=68.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5226, wt=66.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5582, wt=64.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=4842, wt=63.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5924, wt=62.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5982, wt=59.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=5989, wt=57.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=15243, wt=13.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=15510, wt=12.000
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=13.000, iters=3404
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=16035, wt=11.000
% 278.31/278.54
% 278.31/278.54 Low Water (displace): id=16042, wt=10.000
% 278.31/278.54
% 278.31/278.54 Low Water (keep): wt=12.000, iters=3376
% 278.31/278.54
% 278.31/278.54 ============================== STATISTICS ============================
% 278.31/278.54
% 278.31/278.54 Given=30905. Generated=10679334. Kept=59244. proofs=0.
% 278.31/278.54 Usable=29774. Sos=9927. Demods=3227. Limbo=227, Disabled=21240. Hints=0.
% 278.31/278.54 Kept_by_rule=0, Deleted_by_rule=0.
% 278.31/278.54 Forward_subsumed=5656069. Back_subsumed=33.
% 278.31/278.54 Sos_limit_deleted=4964020. Sos_displaced=16146. Sos_removed=0.
% 278.31/278.54 New_demodulators=3983 (11 lex), Back_demodulated=2942. Back_unit_deleted=195.
% 278.31/278.54 Demod_attempts=199857980. Demod_rewrites=8359030.
% 278.31/278.54 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 278.31/278.54 Nonunit_fsub_feature_tests=465509. Nonunit_bsub_feature_tests=4658.
% 278.31/278.54 Megabytes=419.43.
% 278.31/278.54 User_CPU=270.63, System_CPU=6.01, Wall_clock=277.
% 278.31/278.54
% 278.31/278.54 Megs malloced by palloc(): 400.
% 278.31/278.54 type (bytes each) gets frees in use bytes
% 278.31/278.54 chunk ( 104) 56978 56978 0 0.0 K
% 278.31/278.54 string_buf ( 8) 47954 47954 0 0.0 K
% 278.31/278.54 token ( 20) 127821 127821 0 0.0 K
% 278.31/278.54 pterm ( 16) 75414 75414 0 0.0 K
% 278.31/278.54 hashtab ( 8) 1374 1374 0 0.0 K
% 278.31/278.54 hashnode ( 8) 4843 4843 0 0.0 K
% 278.31/278.54 term ( 20) 339420026 338601226 818800 15992.2 K
% 278.31/278.54 term arg arrays: 3599.7 K
% 278.31/278.54 attribute ( 12) 10884 544 10340 121.2 K
% 278.31/278.54 ilist ( 8) 2196960820 2196688573 272247 2126.9 K
% 278.31/278.54 plist ( 8) 510934 392738 118196 923.4 K
% 278.31/278.54 i2list ( 12) 103046014 103046014 0 0.0 K
% 278.31/278.54 just ( 12) 18526682 18455388 71294 835.5 K
% 278.31/278.54 parajust ( 16) 4815596 4794464 21132 330.2 K
% 278.31/278.54 instancejust ( 8) 0 0 0 0.0 K
% 278.31/278.54 ivyjust ( 24) 0 0 0 0.0 K
% 278.31/278.54 formula ( 28) 50275 32133 18142 496.1 K
% 278.31/278.54 formula arg arrays: 60.1 K
% 278.31/278.54 topform ( 52) 10682632 10620089 62543 3176.0 K
% 278.31/278.54 clist_pos ( 20) 176313 111918 64395 1257.7 K
% 278.31/278.54 clist ( 16) 8 1 7 0.1 K
% 278.31/278.54 context ( 808) 46538837 46538834 3 2.4 K
% 278.31/278.54 trail ( 12) 39363954 39363952 2 0.0 K
% 278.31/278.54 ac_match_pos (70044) 0 0 0 0.0 K
% 278.31/278.54 ac_match_free_vars_pos (20020)
% 278.31/278.54 0 0 0 0.0 K
% 278.31/278.54 btm_state ( 60) 0 0 0 0.0 K
% 278.31/278.54 btu_state ( 60) 0 0 0 0.0 K
% 278.31/278.54 ac_position (285432) 0 0 0 0.0 K
% 278.31/278.54 fpa_trie ( 20) 513529 99652 413877 8083.5 K
% 278.31/278.54 fpa_state ( 28) 1356072 1356066 6 0.2 K
% 278.31/278.54 fpa_index ( 12) 10 0 10 0.1 K
% 278.31/278.54 fpa_chunk ( 20) 448163 251341 196822 3844.2 K
% 278.31/278.54 fpa_list ( 16) 231296 0 231296 3614.0 K
% 278.31/278.54 fpa_list chunks: 7298.9 K
% 278.31/278.54 discrim ( 12) 262565 116119 146446 1716.2 K
% 278.31/278.54 discrim_pos ( 16) 13778750 13778750 0 0.0 K
% 278.31/278.54 flat2 ( 32) 87997489 87997489 0 0.0 K
% 278.31/278.54 flat ( 48) 0 0 0 0.0 K
% 278.31/278.54 flatterm ( 32) 293671122 293671122 0 0.0 K
% 278.31/278.54 mindex ( 28) 13 0 13 0.4 K
% 278.31/278.54 mindex_pos ( 56) 25090618 25090617 1 0.1 K
% 278.31/278.54 lindex ( 12) 5 0 5 0.1 K
% 278.31/278.54 clash ( 40) 0 0 0 0.0 K
% 278.31/278.54 di_tree ( 12) 39527697 9266928 30260769 354618.4 K
% 278.31/278.54 avl_node ( 20) 116261 96407 19854 387.8 K
% 278.31/278.54
% 278.31/278.54 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 278.31/278.54 List 1, length 4, 0.0 K
% 278.31/278.54 List 2, length 3324, 26.0 K
% 278.31/278.54 List 3, length 2, 0.0 K
% 278.31/278.54 List 4, length 12, 0.2 K
% 278.31/278.54 List 8, length 63, 2.0 K
% 278.31/278.54 List 9, length 9, 0.3 K
% 278.31/278.54 List 10, length 4, 0.2 K
% 278.31/278.54 List 11, length 4, 0.2 K
% 278.31/278.54 List 14, length 1, 0.1 K
% 278.31/278.54 List 16, length 13, 0.8 K
% 278.31/278.54 List 26, length 107, 10.9 K
% 278.31/278.54 List 64, length 53, 13.2 K
% 278.31/278.54 List 202, length 1, 0.8 K
% 278.31/278.54
% 278.31/278.54 ============================== SELECTOR REPORT =======================
% 278.31/278.54 Sos_deleted=4964020, Sos_displaced=16146, Sos_size=9927
% 278.31/278.54 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 278.31/278.54 I 2147483647 high age 0 1590
% 278.31/278.54 H 1 high weight 0 0
% 278.31/278.54 A 1 low age 9927 3258
% 278.31/278.54 F 4 low weight 4709 13029
% 278.31/278.54 T 4 low weight 5218 13028
% 278.31/278.54 ============================== end of selector report ================
% 278.31/278.54
% 278.31/278.54 ============================== end of statistics =====================
% 278.31/278.54
% 278.31/278.54 Exiting with failure.
% 278.31/278.54
% 278.31/278.54 Process 28673 exit (max_megs) Sun Jun 5 00:16:20 2022
% 278.31/278.54 Prover9 interrupted
%------------------------------------------------------------------------------