TSTP Solution File: NUM923+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM923+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 : Mon Jul 18 13:33:09 EDT 2022
% Result : Timeout 300.08s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM923+3 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.35 % DateTime : Thu Jul 7 01:45:10 EDT 2022
% 0.12/0.35 % CPUTime :
% 1.52/1.89 ============================== Prover9 ===============================
% 1.52/1.89 Prover9 (32) version 2009-11A, November 2009.
% 1.52/1.89 Process 20332 was started by sandbox on n011.cluster.edu,
% 1.52/1.89 Thu Jul 7 01:45:11 2022
% 1.52/1.89 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20037_n011.cluster.edu".
% 1.52/1.89 ============================== end of head ===========================
% 1.52/1.89
% 1.52/1.89 ============================== INPUT =================================
% 1.52/1.89
% 1.52/1.89 % Reading from file /tmp/Prover9_20037_n011.cluster.edu
% 1.52/1.89
% 1.52/1.89 set(prolog_style_variables).
% 1.52/1.89 set(auto2).
% 1.52/1.89 % set(auto2) -> set(auto).
% 1.52/1.89 % set(auto) -> set(auto_inference).
% 1.52/1.89 % set(auto) -> set(auto_setup).
% 1.52/1.89 % set(auto_setup) -> set(predicate_elim).
% 1.52/1.89 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.52/1.89 % set(auto) -> set(auto_limits).
% 1.52/1.89 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.52/1.89 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.52/1.89 % set(auto) -> set(auto_denials).
% 1.52/1.89 % set(auto) -> set(auto_process).
% 1.52/1.89 % set(auto2) -> assign(new_constants, 1).
% 1.52/1.89 % set(auto2) -> assign(fold_denial_max, 3).
% 1.52/1.89 % set(auto2) -> assign(max_weight, "200.000").
% 1.52/1.89 % set(auto2) -> assign(max_hours, 1).
% 1.52/1.89 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.52/1.89 % set(auto2) -> assign(max_seconds, 0).
% 1.52/1.89 % set(auto2) -> assign(max_minutes, 5).
% 1.52/1.89 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.52/1.89 % set(auto2) -> set(sort_initial_sos).
% 1.52/1.89 % set(auto2) -> assign(sos_limit, -1).
% 1.52/1.89 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.52/1.89 % set(auto2) -> assign(max_megs, 400).
% 1.52/1.89 % set(auto2) -> assign(stats, some).
% 1.52/1.89 % set(auto2) -> clear(echo_input).
% 1.52/1.89 % set(auto2) -> set(quiet).
% 1.52/1.89 % set(auto2) -> clear(print_initial_clauses).
% 1.52/1.89 % set(auto2) -> clear(print_given).
% 1.52/1.89 assign(lrs_ticks,-1).
% 1.52/1.89 assign(sos_limit,10000).
% 1.52/1.89 assign(order,kbo).
% 1.52/1.89 set(lex_order_vars).
% 1.52/1.89 clear(print_given).
% 1.52/1.89
% 1.52/1.89 % formulas(sos). % not echoed (1211 formulas)
% 1.52/1.89
% 1.52/1.89 ============================== end of input ==========================
% 1.52/1.89
% 1.52/1.89 % From the command line: assign(max_seconds, 300).
% 1.52/1.89
% 1.52/1.89 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.52/1.89
% 1.52/1.89 % Formulas that are not ordinary clauses:
% 1.52/1.89 1 (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].
% 1.52/1.89 2 (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].
% 1.52/1.89 3 (all B_1_1 all B_2_1 is_bool(hAPP_real_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 4 (all B_1_1 all B_2_1 is_bool(hAPP_P603027463t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 5 (all B_1_1 all B_2_1 is_bool(hAPP_P178748804t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Int__Oint_Mtc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 6 (all B_1_1 all B_2_1 is_bool(member_real(B_1_1,B_2_1))) # label(gsy_c_member_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 7 (all A all R all B all M all C all D_1 all N_1 hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(A),hAPP_int_int(times_times_int(R),B))),M)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(C),hAPP_int_int(times_times_int(R),D_1))),N_1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A),M)),hAPP_int_int(times_times_int(C),N_1))),hAPP_int_int(times_times_int(R),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),M)),hAPP_int_int(times_times_int(D_1),N_1))))) # label(fact_0_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 8 (all X_46 all Y_46 all A_117 all B_92 hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X_46),Y_46)),hAPP_int_int(times_times_int(A_117),B_92)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_46),hAPP_int_int(minus_minus_int(Y_46),B_92))),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(X_46),A_117)),B_92))) # label(fact_1_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 9 (all X_46 all Y_46 all A_117 all B_92 hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(X_46),Y_46)),hAPP_real_real(times_times_real(A_117),B_92)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_46),hAPP_real_real(minus_minus_real(Y_46),B_92))),hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(X_46),A_117)),B_92))) # label(fact_2_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 10 (all X_1 all Y_1 all A_116 all B_91 hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(X_1),Y_1)),hAPP_real_real(times_times_real(A_116),B_91)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(X_1),A_116)),hAPP_real_real(minus_minus_real(Y_1),B_91))),hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(X_1),A_116)),B_91))),hAPP_real_real(times_times_real(A_116),hAPP_real_real(minus_minus_real(Y_1),B_91)))) # label(fact_3_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 11 (all Aa all E_1 all C_1 all Ba all D_2 (hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),E_1)),C_1) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Ba),E_1)),D_2) <-> C_1 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Ba),Aa)),E_1)),D_2))) # label(fact_4_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 12 (all Aa all E_1 all C_1 all Ba all D_2 (hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),E_1)),C_1) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Ba),E_1)),D_2) <-> C_1 = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(Ba),Aa)),E_1)),D_2))) # label(fact_5_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 13 (all Aa all E_1 all C_1 all Ba all D_2 (hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),E_1)),C_1) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Ba),E_1)),D_2) <-> hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Aa),Ba)),E_1)),C_1) = D_2)) # label(fact_6_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 14 (all Aa all E_1 all C_1 all Ba all D_2 (hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),E_1)),C_1) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Ba),E_1)),D_2) <-> hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(Aa),Ba)),E_1)),C_1) = D_2)) # label(fact_7_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 15 (all X_1 (hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X_1)) <-> (exists A_49 exists B_65 twoSqu1241645765sum2sq(product_Pair_int_int(A_49,B_65)) = X_1))) # label(fact_8_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 16 (all A all B all C (hAPP_int_int(minus_minus_int(A),B) = C -> A = hAPP_int_int(plus_plus_int(C),B))) # label(fact_9_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 17 (all W_1 all Z1 all Z2 hAPP_int_int(times_times_int(W_1),hAPP_int_int(minus_minus_int(Z1),Z2)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(W_1),Z1)),hAPP_int_int(times_times_int(W_1),Z2))) # label(fact_10_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 18 (all Z1 all Z2 all W_1 hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Z1),Z2)),W_1) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(Z1),W_1)),hAPP_int_int(times_times_int(Z2),W_1))) # label(fact_11_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 19 (all W_1 all Z1 all Z2 hAPP_int_int(times_times_int(W_1),hAPP_int_int(plus_plus_int(Z1),Z2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W_1),Z1)),hAPP_int_int(times_times_int(W_1),Z2))) # label(fact_12_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 20 (all Z1 all Z2 all W_1 hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(Z1),Z2)),W_1) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Z1),W_1)),hAPP_int_int(times_times_int(Z2),W_1))) # label(fact_13_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 21 (all A_115 all B_90 hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(A_115),B_90)),B_90) = A_115) # label(fact_14_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 22 (all A_115 all B_90 hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(A_115),B_90)),B_90) = A_115) # label(fact_15_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 23 (all A_114 all B_89 all C_54 hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(A_114),B_89)),C_54) = hAPP_int_int(times_times_int(A_114),hAPP_int_int(times_times_int(B_89),C_54))) # label(fact_16_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 24 (all A_114 all B_89 all C_54 hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(A_114),B_89)),C_54) = hAPP_real_real(times_times_real(A_114),hAPP_real_real(times_times_real(B_89),C_54))) # label(fact_17_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 25 (all A_114 all B_89 all C_54 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(A_114),B_89)),C_54) = hAPP_nat_nat(times_times_nat(A_114),hAPP_nat_nat(times_times_nat(B_89),C_54))) # label(fact_18_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 26 (all B_88 all A_113 all C_53 (hAPP_int_int(plus_plus_int(B_88),A_113) = hAPP_int_int(plus_plus_int(C_53),A_113) -> B_88 = C_53)) # label(fact_19_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 27 (all B_88 all A_113 all C_53 (hAPP_real_real(plus_plus_real(B_88),A_113) = hAPP_real_real(plus_plus_real(C_53),A_113) -> B_88 = C_53)) # label(fact_20_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 28 (all B_88 all A_113 all C_53 (hAPP_nat_nat(plus_plus_nat(B_88),A_113) = hAPP_nat_nat(plus_plus_nat(C_53),A_113) -> B_88 = C_53)) # label(fact_21_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 29 (all A_112 all B_87 all C_52 (hAPP_int_int(plus_plus_int(A_112),B_87) = hAPP_int_int(plus_plus_int(A_112),C_52) -> B_87 = C_52)) # label(fact_22_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 30 (all A_112 all B_87 all C_52 (hAPP_real_real(plus_plus_real(A_112),B_87) = hAPP_real_real(plus_plus_real(A_112),C_52) -> B_87 = C_52)) # label(fact_23_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 31 (all A_112 all B_87 all C_52 (hAPP_nat_nat(plus_plus_nat(A_112),B_87) = hAPP_nat_nat(plus_plus_nat(A_112),C_52) -> B_87 = C_52)) # label(fact_24_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 32 (all A_111 all B_86 all C_51 (hAPP_int_int(plus_plus_int(A_111),B_86) = hAPP_int_int(plus_plus_int(A_111),C_51) -> B_86 = C_51)) # label(fact_25_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 33 (all A_111 all B_86 all C_51 (hAPP_real_real(plus_plus_real(A_111),B_86) = hAPP_real_real(plus_plus_real(A_111),C_51) -> B_86 = C_51)) # label(fact_26_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 34 (all A_111 all B_86 all C_51 (hAPP_nat_nat(plus_plus_nat(A_111),B_86) = hAPP_nat_nat(plus_plus_nat(A_111),C_51) -> B_86 = C_51)) # label(fact_27_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 35 (all Ba all Aa all C_1 (hAPP_int_int(plus_plus_int(Ba),Aa) = hAPP_int_int(plus_plus_int(C_1),Aa) <-> Ba = C_1)) # label(fact_28_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 36 (all Ba all Aa all C_1 (hAPP_real_real(plus_plus_real(Ba),Aa) = hAPP_real_real(plus_plus_real(C_1),Aa) <-> Ba = C_1)) # label(fact_29_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 37 (all Ba all Aa all C_1 (hAPP_nat_nat(plus_plus_nat(Ba),Aa) = hAPP_nat_nat(plus_plus_nat(C_1),Aa) <-> Ba = C_1)) # label(fact_30_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 38 (all Aa all Ba all C_1 (hAPP_int_int(plus_plus_int(Aa),Ba) = hAPP_int_int(plus_plus_int(Aa),C_1) <-> Ba = C_1)) # label(fact_31_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 39 (all Aa all Ba all C_1 (hAPP_real_real(plus_plus_real(Aa),Ba) = hAPP_real_real(plus_plus_real(Aa),C_1) <-> Ba = C_1)) # label(fact_32_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 40 (all Aa all Ba all C_1 (hAPP_nat_nat(plus_plus_nat(Aa),Ba) = hAPP_nat_nat(plus_plus_nat(Aa),C_1) <-> Ba = C_1)) # label(fact_33_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 41 (all A_110 all B_85 all C_50 hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_110),B_85)),C_50) = hAPP_int_int(plus_plus_int(A_110),hAPP_int_int(plus_plus_int(B_85),C_50))) # label(fact_34_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 42 (all A_110 all B_85 all C_50 hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_110),B_85)),C_50) = hAPP_real_real(plus_plus_real(A_110),hAPP_real_real(plus_plus_real(B_85),C_50))) # label(fact_35_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 43 (all A_110 all B_85 all C_50 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_110),B_85)),C_50) = hAPP_nat_nat(plus_plus_nat(A_110),hAPP_nat_nat(plus_plus_nat(B_85),C_50))) # label(fact_36_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 44 (all Aa all Ba all C_1 all D_2 (hAPP_int_int(minus_minus_int(Aa),Ba) = hAPP_int_int(minus_minus_int(C_1),D_2) -> (Aa = Ba <-> C_1 = D_2))) # label(fact_37_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 45 (all Aa all Ba all C_1 all D_2 (hAPP_real_real(minus_minus_real(Aa),Ba) = hAPP_real_real(minus_minus_real(C_1),D_2) -> (Aa = Ba <-> C_1 = D_2))) # label(fact_38_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 46 (all Z1 all Z2 all Z3 hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Z1),Z2)),Z3) = hAPP_int_int(times_times_int(Z1),hAPP_int_int(times_times_int(Z2),Z3))) # label(fact_39_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 47 (all Z_1 all W_1 hAPP_int_int(times_times_int(Z_1),W_1) = hAPP_int_int(times_times_int(W_1),Z_1)) # label(fact_40_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 48 (all Z1 all Z2 all Z3 hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(Z1),Z2)),Z3) = hAPP_int_int(plus_plus_int(Z1),hAPP_int_int(plus_plus_int(Z2),Z3))) # label(fact_41_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 49 (all X all Y all Z_1 hAPP_int_int(plus_plus_int(X),hAPP_int_int(plus_plus_int(Y),Z_1)) = hAPP_int_int(plus_plus_int(Y),hAPP_int_int(plus_plus_int(X),Z_1))) # label(fact_42_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 50 (all Z_1 all W_1 hAPP_int_int(plus_plus_int(Z_1),W_1) = hAPP_int_int(plus_plus_int(W_1),Z_1)) # label(fact_43_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 51 (all A_109 all E_2 all B_84 all C_49 hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_109),E_2)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_84),E_2)),C_49)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_109),B_84)),E_2)),C_49)) # label(fact_44_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 52 (all A_109 all E_2 all B_84 all C_49 hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_109),E_2)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(B_84),E_2)),C_49)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_109),B_84)),E_2)),C_49)) # label(fact_45_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 53 (all A_109 all E_2 all B_84 all C_49 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_109),E_2)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(B_84),E_2)),C_49)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_109),B_84)),E_2)),C_49)) # label(fact_46_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 54 (all X_45 all Y_45 all Ya_1 hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X_45),Y_45)),Ya_1) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_45),Ya_1)),hAPP_real_real(times_times_real(Y_45),Ya_1))) # label(fact_47_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 55 (all A_108 all A_107 all B_83 hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_108),A_107)),B_83) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_108),B_83)),hAPP_real_real(times_times_real(A_107),B_83))) # label(fact_48_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 56 (all A_106 all B_82 all C_48 hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_106),B_82)),C_48) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_106),C_48)),hAPP_int_int(times_times_int(B_82),C_48))) # label(fact_49_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 57 (all A_106 all B_82 all C_48 hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_106),B_82)),C_48) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_106),C_48)),hAPP_real_real(times_times_real(B_82),C_48))) # label(fact_50_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 58 (all A_106 all B_82 all C_48 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_106),B_82)),C_48) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_106),C_48)),hAPP_nat_nat(times_times_nat(B_82),C_48))) # label(fact_51_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 59 (all Xa_1 all X_44 all Y_44 hAPP_real_real(times_times_real(Xa_1),hAPP_real_real(plus_plus_real(X_44),Y_44)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Xa_1),X_44)),hAPP_real_real(times_times_real(Xa_1),Y_44))) # label(fact_52_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 60 (all A_105 all B_81 all B_80 hAPP_real_real(times_times_real(A_105),hAPP_real_real(plus_plus_real(B_81),B_80)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_105),B_81)),hAPP_real_real(times_times_real(A_105),B_80))) # label(fact_53_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 61 (all X_43 all Y_43 all Ya hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(X_43),Y_43)),Ya) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(X_43),Ya)),hAPP_real_real(times_times_real(Y_43),Ya))) # label(fact_54_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 62 (all A_104 all A_103 all B_79 hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(A_104),A_103)),B_79) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(A_104),B_79)),hAPP_real_real(times_times_real(A_103),B_79))) # label(fact_55_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 63 (all Xa all X_42 all Y_42 hAPP_real_real(times_times_real(Xa),hAPP_real_real(minus_minus_real(X_42),Y_42)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(Xa),X_42)),hAPP_real_real(times_times_real(Xa),Y_42))) # label(fact_56_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 64 (all A_102 all B_78 all B_77 hAPP_real_real(times_times_real(A_102),hAPP_real_real(minus_minus_real(B_78),B_77)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(A_102),B_78)),hAPP_real_real(times_times_real(A_102),B_77))) # label(fact_57_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 65 (all A_101 all C_47 all B_76 all D_12 hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(A_101),C_47)),hAPP_int_int(plus_plus_int(B_76),D_12)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(A_101),B_76)),hAPP_int_int(minus_minus_int(C_47),D_12))) # label(fact_58_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 66 (all A_101 all C_47 all B_76 all D_12 hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(A_101),C_47)),hAPP_real_real(plus_plus_real(B_76),D_12)) = hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(A_101),B_76)),hAPP_real_real(minus_minus_real(C_47),D_12))) # label(fact_59_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 67 (all A_100 all B_75 hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(A_100),B_75)),B_75) = A_100) # label(fact_60_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 68 (all A_100 all B_75 hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(A_100),B_75)),B_75) = A_100) # label(fact_61_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 69 (all W all Y_1 all X_1 all Z (hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W),Y_1)),hAPP_int_int(times_times_int(X_1),Z)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W),Z)),hAPP_int_int(times_times_int(X_1),Y_1)) <-> W = X_1 | Y_1 = Z)) # label(fact_62_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 70 (all W all Y_1 all X_1 all Z (hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W),Y_1)),hAPP_real_real(times_times_real(X_1),Z)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W),Z)),hAPP_real_real(times_times_real(X_1),Y_1)) <-> W = X_1 | Y_1 = Z)) # label(fact_63_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 71 (all W all Y_1 all X_1 all Z (hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W),Y_1)),hAPP_nat_nat(times_times_nat(X_1),Z)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W),Z)),hAPP_nat_nat(times_times_nat(X_1),Y_1)) <-> W = X_1 | Y_1 = Z)) # label(fact_64_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 72 (all A_99 all M_7 all B_74 hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_99),M_7)),hAPP_int_int(times_times_int(B_74),M_7)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_99),B_74)),M_7)) # label(fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 73 (all A_99 all M_7 all B_74 hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_99),M_7)),hAPP_real_real(times_times_real(B_74),M_7)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_99),B_74)),M_7)) # label(fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 74 (all A_99 all M_7 all B_74 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_99),M_7)),hAPP_nat_nat(times_times_nat(B_74),M_7)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_99),B_74)),M_7)) # label(fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 75 (all A_98 all B_73 all C_46 hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_98),B_73)),C_46) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_98),C_46)),hAPP_int_int(times_times_int(B_73),C_46))) # label(fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 76 (all A_98 all B_73 all C_46 hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_98),B_73)),C_46) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_98),C_46)),hAPP_real_real(times_times_real(B_73),C_46))) # label(fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 77 (all A_98 all B_73 all C_46 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_98),B_73)),C_46) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_98),C_46)),hAPP_nat_nat(times_times_nat(B_73),C_46))) # label(fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 78 (all C_1 all D_2 all Aa all Ba (Aa != Ba & C_1 != D_2 <-> hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),C_1)),hAPP_int_int(times_times_int(Ba),D_2)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),D_2)),hAPP_int_int(times_times_int(Ba),C_1)))) # label(fact_71_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 79 (all C_1 all D_2 all Aa all Ba (Aa != Ba & C_1 != D_2 <-> hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),C_1)),hAPP_real_real(times_times_real(Ba),D_2)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),D_2)),hAPP_real_real(times_times_real(Ba),C_1)))) # label(fact_72_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 80 (all C_1 all D_2 all Aa all Ba (Aa != Ba & C_1 != D_2 <-> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(Aa),C_1)),hAPP_nat_nat(times_times_nat(Ba),D_2)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(Aa),D_2)),hAPP_nat_nat(times_times_nat(Ba),C_1)))) # label(fact_73_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 81 (all X_41 all Y_41 all Z_17 hAPP_int_int(times_times_int(X_41),hAPP_int_int(plus_plus_int(Y_41),Z_17)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_41),Y_41)),hAPP_int_int(times_times_int(X_41),Z_17))) # label(fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 82 (all X_41 all Y_41 all Z_17 hAPP_real_real(times_times_real(X_41),hAPP_real_real(plus_plus_real(Y_41),Z_17)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_41),Y_41)),hAPP_real_real(times_times_real(X_41),Z_17))) # label(fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 83 (all X_41 all Y_41 all Z_17 hAPP_nat_nat(times_times_nat(X_41),hAPP_nat_nat(plus_plus_nat(Y_41),Z_17)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X_41),Y_41)),hAPP_nat_nat(times_times_nat(X_41),Z_17))) # label(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 84 (all A_97 all B_72 all A_96 all B_71 (product_Pair_int_int(A_97,B_72) = product_Pair_int_int(A_96,B_71) -> -(A_97 = A_96 -> B_72 != B_71))) # label(fact_77_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 85 (all A_97 all B_72 all A_96 all B_71 (produc282740534nt_int(A_97,B_72) = produc282740534nt_int(A_96,B_71) -> -(A_97 = A_96 -> B_72 != B_71))) # label(fact_78_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 86 (all Aa all Ba all A_95 all B_70 (product_Pair_int_int(Aa,Ba) = product_Pair_int_int(A_95,B_70) <-> Aa = A_95 & Ba = B_70)) # label(fact_79_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 87 (all Aa all Ba all A_95 all B_70 (produc282740534nt_int(Aa,Ba) = produc282740534nt_int(A_95,B_70) <-> Aa = A_95 & Ba = B_70)) # label(fact_80_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 88 (all P_1 ((all X1 hBOOL(hAPP_P603027463t_bool(P_1,X1))) <-> (all A_49 all B_65 hBOOL(hAPP_P603027463t_bool(P_1,product_Pair_int_int(A_49,B_65)))))) # label(fact_81_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 89 (all P_1 ((all X1 hBOOL(hAPP_P178748804t_bool(P_1,X1))) <-> (all A_49 all B_65 hBOOL(hAPP_P178748804t_bool(P_1,produc282740534nt_int(A_49,B_65)))))) # label(fact_82_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 90 (all A_94 all B_69 all C_45 all D_11 hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_94),B_69)),hAPP_int_int(plus_plus_int(C_45),D_11)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_94),C_45)),hAPP_int_int(plus_plus_int(B_69),D_11))) # label(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 91 (all A_94 all B_69 all C_45 all D_11 hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_94),B_69)),hAPP_real_real(plus_plus_real(C_45),D_11)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_94),C_45)),hAPP_real_real(plus_plus_real(B_69),D_11))) # label(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 92 (all A_94 all B_69 all C_45 all D_11 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_94),B_69)),hAPP_nat_nat(plus_plus_nat(C_45),D_11)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_94),C_45)),hAPP_nat_nat(plus_plus_nat(B_69),D_11))) # label(fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 93 (all A_93 all B_68 all C_44 hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_93),B_68)),C_44) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_93),C_44)),B_68)) # label(fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 94 (all A_93 all B_68 all C_44 hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_93),B_68)),C_44) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_93),C_44)),B_68)) # label(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 95 (all A_93 all B_68 all C_44 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_93),B_68)),C_44) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_93),C_44)),B_68)) # label(fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 96 (all A_92 all B_67 hAPP_int_int(times_times_int(A_92),B_67) = hAPP_int_int(times_times_int(B_67),A_92)) # label(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 97 (all A_92 all B_67 hAPP_real_real(times_times_real(A_92),B_67) = hAPP_real_real(times_times_real(B_67),A_92)) # label(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 98 (all A_92 all B_67 hAPP_nat_nat(times_times_nat(A_92),B_67) = hAPP_nat_nat(times_times_nat(B_67),A_92)) # label(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 99 (all Lx_6 all Rx_6 all Ry_4 hAPP_int_int(times_times_int(Lx_6),hAPP_int_int(times_times_int(Rx_6),Ry_4)) = hAPP_int_int(times_times_int(Rx_6),hAPP_int_int(times_times_int(Lx_6),Ry_4))) # label(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 100 (all Lx_6 all Rx_6 all Ry_4 hAPP_real_real(times_times_real(Lx_6),hAPP_real_real(times_times_real(Rx_6),Ry_4)) = hAPP_real_real(times_times_real(Rx_6),hAPP_real_real(times_times_real(Lx_6),Ry_4))) # label(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 101 (all Lx_6 all Rx_6 all Ry_4 hAPP_nat_nat(times_times_nat(Lx_6),hAPP_nat_nat(times_times_nat(Rx_6),Ry_4)) = hAPP_nat_nat(times_times_nat(Rx_6),hAPP_nat_nat(times_times_nat(Lx_6),Ry_4))) # label(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 102 (all Lx_5 all Rx_5 all Ry_3 hAPP_int_int(times_times_int(Lx_5),hAPP_int_int(times_times_int(Rx_5),Ry_3)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_5),Rx_5)),Ry_3)) # label(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 103 (all Lx_5 all Rx_5 all Ry_3 hAPP_real_real(times_times_real(Lx_5),hAPP_real_real(times_times_real(Rx_5),Ry_3)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_5),Rx_5)),Ry_3)) # label(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 104 (all Lx_5 all Rx_5 all Ry_3 hAPP_nat_nat(times_times_nat(Lx_5),hAPP_nat_nat(times_times_nat(Rx_5),Ry_3)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_5),Rx_5)),Ry_3)) # label(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 105 (all Lx_4 all Ly_4 all Rx_4 hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_4),Ly_4)),Rx_4) = hAPP_int_int(times_times_int(Lx_4),hAPP_int_int(times_times_int(Ly_4),Rx_4))) # label(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 106 (all Lx_4 all Ly_4 all Rx_4 hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_4),Ly_4)),Rx_4) = hAPP_real_real(times_times_real(Lx_4),hAPP_real_real(times_times_real(Ly_4),Rx_4))) # label(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 107 (all Lx_4 all Ly_4 all Rx_4 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_4),Ly_4)),Rx_4) = hAPP_nat_nat(times_times_nat(Lx_4),hAPP_nat_nat(times_times_nat(Ly_4),Rx_4))) # label(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 108 (all Lx_3 all Ly_3 all Rx_3 hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_3),Ly_3)),Rx_3) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_3),Rx_3)),Ly_3)) # label(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 109 (all Lx_3 all Ly_3 all Rx_3 hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_3),Ly_3)),Rx_3) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_3),Rx_3)),Ly_3)) # label(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 110 (all Lx_3 all Ly_3 all Rx_3 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_3),Ly_3)),Rx_3) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_3),Rx_3)),Ly_3)) # label(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 111 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_2),Ly_2)),hAPP_int_int(times_times_int(Rx_2),Ry_2)) = hAPP_int_int(times_times_int(Lx_2),hAPP_int_int(times_times_int(Ly_2),hAPP_int_int(times_times_int(Rx_2),Ry_2)))) # label(fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 112 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_2),Ly_2)),hAPP_real_real(times_times_real(Rx_2),Ry_2)) = hAPP_real_real(times_times_real(Lx_2),hAPP_real_real(times_times_real(Ly_2),hAPP_real_real(times_times_real(Rx_2),Ry_2)))) # label(fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 113 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_2),Ly_2)),hAPP_nat_nat(times_times_nat(Rx_2),Ry_2)) = hAPP_nat_nat(times_times_nat(Lx_2),hAPP_nat_nat(times_times_nat(Ly_2),hAPP_nat_nat(times_times_nat(Rx_2),Ry_2)))) # label(fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 114 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_1),Ly_1)),hAPP_int_int(times_times_int(Rx_1),Ry_1)) = hAPP_int_int(times_times_int(Rx_1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_1),Ly_1)),Ry_1))) # label(fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 115 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_1),Ly_1)),hAPP_real_real(times_times_real(Rx_1),Ry_1)) = hAPP_real_real(times_times_real(Rx_1),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_1),Ly_1)),Ry_1))) # label(fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 116 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_1),Ly_1)),hAPP_nat_nat(times_times_nat(Rx_1),Ry_1)) = hAPP_nat_nat(times_times_nat(Rx_1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_1),Ly_1)),Ry_1))) # label(fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 117 (all Lx all Ly all Rx all Ry hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx),Ly)),hAPP_int_int(times_times_int(Rx),Ry)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx),Rx)),hAPP_int_int(times_times_int(Ly),Ry))) # label(fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 118 (all Lx all Ly all Rx all Ry hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx),Ly)),hAPP_real_real(times_times_real(Rx),Ry)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx),Rx)),hAPP_real_real(times_times_real(Ly),Ry))) # label(fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 119 (all Lx all Ly all Rx all Ry hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx),Ly)),hAPP_nat_nat(times_times_nat(Rx),Ry)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx),Rx)),hAPP_nat_nat(times_times_nat(Ly),Ry))) # label(fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 120 (all A_91 all C_43 hAPP_int_int(plus_plus_int(A_91),C_43) = hAPP_int_int(plus_plus_int(C_43),A_91)) # label(fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 121 (all A_91 all C_43 hAPP_real_real(plus_plus_real(A_91),C_43) = hAPP_real_real(plus_plus_real(C_43),A_91)) # label(fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 122 (all A_91 all C_43 hAPP_nat_nat(plus_plus_nat(A_91),C_43) = hAPP_nat_nat(plus_plus_nat(C_43),A_91)) # label(fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 123 (all A_90 all C_42 all D_10 hAPP_int_int(plus_plus_int(A_90),hAPP_int_int(plus_plus_int(C_42),D_10)) = hAPP_int_int(plus_plus_int(C_42),hAPP_int_int(plus_plus_int(A_90),D_10))) # label(fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 124 (all A_90 all C_42 all D_10 hAPP_real_real(plus_plus_real(A_90),hAPP_real_real(plus_plus_real(C_42),D_10)) = hAPP_real_real(plus_plus_real(C_42),hAPP_real_real(plus_plus_real(A_90),D_10))) # label(fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 125 (all A_90 all C_42 all D_10 hAPP_nat_nat(plus_plus_nat(A_90),hAPP_nat_nat(plus_plus_nat(C_42),D_10)) = hAPP_nat_nat(plus_plus_nat(C_42),hAPP_nat_nat(plus_plus_nat(A_90),D_10))) # label(fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 126 (all A_89 all C_41 all D_9 hAPP_int_int(plus_plus_int(A_89),hAPP_int_int(plus_plus_int(C_41),D_9)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_89),C_41)),D_9)) # label(fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 127 (all A_89 all C_41 all D_9 hAPP_real_real(plus_plus_real(A_89),hAPP_real_real(plus_plus_real(C_41),D_9)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_89),C_41)),D_9)) # label(fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 128 (all A_89 all C_41 all D_9 hAPP_nat_nat(plus_plus_nat(A_89),hAPP_nat_nat(plus_plus_nat(C_41),D_9)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_89),C_41)),D_9)) # label(fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 129 (all A_88 all B_66 all C_40 hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_88),B_66)),C_40) = hAPP_int_int(plus_plus_int(A_88),hAPP_int_int(plus_plus_int(B_66),C_40))) # label(fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 130 (all A_88 all B_66 all C_40 hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_88),B_66)),C_40) = hAPP_real_real(plus_plus_real(A_88),hAPP_real_real(plus_plus_real(B_66),C_40))) # label(fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 131 (all A_88 all B_66 all C_40 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_88),B_66)),C_40) = hAPP_nat_nat(plus_plus_nat(A_88),hAPP_nat_nat(plus_plus_nat(B_66),C_40))) # label(fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 132 (all P_1 ((exists X1 hBOOL(hAPP_P603027463t_bool(P_1,X1))) <-> (exists A_49 exists B_65 hBOOL(hAPP_P603027463t_bool(P_1,product_Pair_int_int(A_49,B_65)))))) # label(fact_125_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 133 (all P_1 ((exists X1 hBOOL(hAPP_P178748804t_bool(P_1,X1))) <-> (exists A_49 exists B_65 hBOOL(hAPP_P178748804t_bool(P_1,produc282740534nt_int(A_49,B_65)))))) # label(fact_126_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 134 (all X_1 all P_1 ((all A_49 all B_65 all C_39 hBOOL(hAPP_P178748804t_bool(P_1,produc282740534nt_int(A_49,product_Pair_int_int(B_65,C_39))))) -> hBOOL(hAPP_P178748804t_bool(P_1,X_1)))) # label(fact_127_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 135 (all Y_40 -(all A_49 all B_65 all C_39 Y_40 != produc282740534nt_int(A_49,product_Pair_int_int(B_65,C_39)))) # label(fact_128_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 136 (all P_3 -(all X_2 all Y_2 P_3 != product_Pair_int_int(X_2,Y_2))) # label(fact_129_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 137 (all P_3 -(all X_2 all Y_2 P_3 != produc282740534nt_int(X_2,Y_2))) # label(fact_130_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 138 (all X_1 all A_87 (hBOOL(member_real(X_1,A_87)) <-> hBOOL(hAPP_real_bool(A_87,X_1)))) # label(fact_131_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 139 (all Y_39 -(all A_49 all B_65 Y_39 != product_Pair_int_int(A_49,B_65))) # label(fact_132_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 140 (all Y_39 -(all A_49 all B_65 Y_39 != produc282740534nt_int(A_49,B_65))) # label(fact_133_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 141 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(F,product_Pair_int_int(Aa,Ba))) -> hBOOL(hAPP_int_bool(produc262399358t_bool(F,Aa),Ba)))) # label(fact_134_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 142 (all F all Aa all Ba (hBOOL(hAPP_P178748804t_bool(F,produc282740534nt_int(Aa,Ba))) -> hBOOL(hAPP_P603027463t_bool(produc97574839t_bool(F,Aa),Ba)))) # label(fact_135_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 143 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),E_1)),C_1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Ba),E_1)),D_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Aa),Ba)),E_1)),C_1)),D_2)))) # label(fact_136_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 144 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),E_1)),C_1)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Ba),E_1)),D_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(Aa),Ba)),E_1)),C_1)),D_2)))) # label(fact_137_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 145 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),E_1)),C_1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Ba),E_1)),D_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Ba),Aa)),E_1)),D_2))))) # label(fact_138_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 146 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),E_1)),C_1)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Ba),E_1)),D_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_1),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(Ba),Aa)),E_1)),D_2))))) # label(fact_139_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 147 (all X_40 hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(X_40),X_40)),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(X_40),one_one_int)),hAPP_int_int(minus_minus_int(X_40),one_one_int))) # label(fact_140_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 148 (all X_40 hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(X_40),X_40)),one_one_real) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(X_40),one_one_real)),hAPP_real_real(minus_minus_real(X_40),one_one_real))) # label(fact_141_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 149 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),E_1)),C_1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Ba),E_1)),D_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Aa),Ba)),E_1)),C_1)),D_2)))) # label(fact_142_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 150 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),E_1)),C_1)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Ba),E_1)),D_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(Aa),Ba)),E_1)),C_1)),D_2)))) # label(fact_143_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 151 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Aa),E_1)),C_1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Ba),E_1)),D_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Ba),Aa)),E_1)),D_2))))) # label(fact_144_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 152 (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Aa),E_1)),C_1)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Ba),E_1)),D_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_1),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(Ba),Aa)),E_1)),D_2))))) # label(fact_145_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 153 (all V_17 all W_11 all C_38 hAPP_int_int(plus_plus_int(number_number_of_int(V_17)),hAPP_int_int(minus_minus_int(number_number_of_int(W_11)),C_38)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(V_17),W_11))),C_38)) # label(fact_146_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 154 (all V_17 all W_11 all C_38 hAPP_real_real(plus_plus_real(number267125858f_real(V_17)),hAPP_real_real(minus_minus_real(number267125858f_real(W_11)),C_38)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(V_17),W_11))),C_38)) # label(fact_147_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 155 (all F all Aa all Ba (hBOOL(hAPP_int_bool(produc262399358t_bool(F,Aa),Ba)) <-> hBOOL(hAPP_P603027463t_bool(F,product_Pair_int_int(Aa,Ba))))) # label(fact_148_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 156 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(produc97574839t_bool(F,Aa),Ba)) <-> hBOOL(hAPP_P178748804t_bool(F,produc282740534nt_int(Aa,Ba))))) # label(fact_149_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 157 (all N_3 all M_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M_6)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),N_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(M_6),N_3)))))) # label(fact_150_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 158 (all N_3 all M_6 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),M_6)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),N_3)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(M_6),N_3)))))) # label(fact_151_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 159 (all N_3 all M_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),M_6)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(M_6),N_3)))))) # label(fact_152_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 160 (all A_86 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_86),hAPP_int_int(plus_plus_int(A_86),one_one_int)))) # label(fact_153_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 161 (all A_86 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_86),hAPP_real_real(plus_plus_real(A_86),one_one_real)))) # label(fact_154_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 162 (all A_86 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_86),hAPP_nat_nat(plus_plus_nat(A_86),one_one_nat)))) # label(fact_155_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 163 (all C_37 all D_8 all A_85 all B_64 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_85),B_64)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_37),D_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_85),C_37)),hAPP_int_int(plus_plus_int(B_64),D_8)))))) # label(fact_156_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 164 (all C_37 all D_8 all A_85 all B_64 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_85),B_64)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_37),D_8)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_85),C_37)),hAPP_real_real(plus_plus_real(B_64),D_8)))))) # label(fact_157_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 165 (all C_37 all D_8 all A_85 all B_64 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_85),B_64)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_37),D_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(A_85),C_37)),hAPP_nat_nat(plus_plus_nat(B_64),D_8)))))) # label(fact_158_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.89 166 (all C_36 all D_7 all A_84 all B_63 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_84),B_63)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_36),D_7)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_84),C_36)),hAPP_int_int(plus_plus_int(B_63),D_7)))))) # label(fact_159_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 167 (all C_36 all D_7 all A_84 all B_63 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_84),B_63)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_36),D_7)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_84),C_36)),hAPP_real_real(plus_plus_real(B_63),D_7)))))) # label(fact_160_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 168 (all C_36 all D_7 all A_84 all B_63 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_84),B_63)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_36),D_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(A_84),C_36)),hAPP_nat_nat(plus_plus_nat(B_63),D_7)))))) # label(fact_161_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 169 (all X_1 (one_one_int = X_1 <-> X_1 = one_one_int)) # label(fact_162_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 170 (all X_1 (one_one_real = X_1 <-> X_1 = one_one_real)) # label(fact_163_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 171 (all X_1 (one_one_nat = X_1 <-> X_1 = one_one_nat)) # label(fact_164_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 172 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),hAPP_int_int(plus_plus_int(Z),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z)))) # label(fact_165_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 173 (all W all X_1 (number_number_of_int(W) = X_1 <-> X_1 = number_number_of_int(W))) # label(fact_166_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 174 (all W all X_1 (number267125858f_real(W) = X_1 <-> X_1 = number267125858f_real(W))) # label(fact_167_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 175 (all W all X_1 (number_number_of_nat(W) = X_1 <-> X_1 = number_number_of_nat(W))) # label(fact_168_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 176 (all V_1 all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_1)),number_number_of_int(W))) <-> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(W)),number_number_of_int(V_1))))) # label(fact_169_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 177 (all V_1 all W (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(V_1)),number267125858f_real(W))) <-> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(W)),number267125858f_real(V_1))))) # label(fact_170_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 178 (all V_1 all W (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_1)),number_number_of_nat(W))) <-> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(W)),number_number_of_nat(V_1))))) # label(fact_171_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 179 (all X_1 all Y_1 (number_number_of_int(X_1) = number_number_of_int(Y_1) <-> X_1 = Y_1)) # label(fact_172_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 180 (all X_1 all Y_1 (number267125858f_real(X_1) = number267125858f_real(Y_1) <-> X_1 = Y_1)) # label(fact_173_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 181 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_1)),number_number_of_int(Y_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)))) # label(fact_174_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 182 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_1)),number267125858f_real(Y_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)))) # label(fact_175_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 183 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_1)),number_number_of_int(Y_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)))) # label(fact_176_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 184 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_1)),number267125858f_real(Y_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)))) # label(fact_177_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 185 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(W),one_one_int)),Z)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)))) # label(fact_178_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 186 (all X_39 all Y_38 (X_39 != Y_38 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_39),Y_38)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_38),X_39))))) # label(fact_179_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 187 (all X_39 all Y_38 (X_39 != Y_38 -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_39),Y_38)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_38),X_39))))) # label(fact_180_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 188 (all W_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(W_1),one_one_int)),Z_1)))) # label(fact_181_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 189 (all X_38 all Y_37 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_38),Y_37)) -> (X_38 != Y_37 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_38),Y_37))))) # label(fact_182_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 190 (all X_38 all Y_37 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_38),Y_37)) -> (X_38 != Y_37 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_38),Y_37))))) # label(fact_183_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 191 (all X_38 all Y_37 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_38),Y_37)) -> (X_38 != Y_37 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_38),Y_37))))) # label(fact_184_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 192 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),hAPP_int_int(minus_minus_int(Z),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)))) # label(fact_185_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 193 (all Z_16 all Z_1 all W_10 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_10),W_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_16),Z_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(W_10),Z_16)),hAPP_int_int(plus_plus_int(W_1),Z_1)))))) # label(fact_186_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 194 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),hAPP_int_int(plus_plus_int(Z),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)) | W = Z)) # label(fact_187_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 195 (all Aa all C_1 all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(Aa),C_1)),hAPP_int_int(plus_plus_int(Ba),C_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)))) # label(fact_188_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 196 (all Aa all C_1 all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(Aa),C_1)),hAPP_real_real(plus_plus_real(Ba),C_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)))) # label(fact_189_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 197 (all Aa all C_1 all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(Aa),C_1)),hAPP_nat_nat(plus_plus_nat(Ba),C_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_190_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 198 (all C_1 all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(C_1),Aa)),hAPP_int_int(plus_plus_int(C_1),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)))) # label(fact_191_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 199 (all C_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(C_1),Aa)),hAPP_real_real(plus_plus_real(C_1),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)))) # label(fact_192_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 200 (all C_1 all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(C_1),Aa)),hAPP_nat_nat(plus_plus_nat(C_1),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_193_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 201 (all C_35 all A_83 all B_62 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_83),B_62)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_83),C_35)),hAPP_int_int(plus_plus_int(B_62),C_35))))) # label(fact_194_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 202 (all C_35 all A_83 all B_62 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_83),B_62)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_83),C_35)),hAPP_real_real(plus_plus_real(B_62),C_35))))) # label(fact_195_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 203 (all C_35 all A_83 all B_62 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_83),B_62)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(A_83),C_35)),hAPP_nat_nat(plus_plus_nat(B_62),C_35))))) # label(fact_196_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 204 (all C_34 all A_82 all B_61 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_82),B_61)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(C_34),A_82)),hAPP_int_int(plus_plus_int(C_34),B_61))))) # label(fact_197_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 205 (all C_34 all A_82 all B_61 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_82),B_61)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(C_34),A_82)),hAPP_real_real(plus_plus_real(C_34),B_61))))) # label(fact_198_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 206 (all C_34 all A_82 all B_61 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_82),B_61)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(C_34),A_82)),hAPP_nat_nat(plus_plus_nat(C_34),B_61))))) # label(fact_199_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 207 (all C_33 all D_6 all A_81 all B_60 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_81),B_60)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_33),D_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_81),C_33)),hAPP_int_int(plus_plus_int(B_60),D_6)))))) # label(fact_200_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 208 (all C_33 all D_6 all A_81 all B_60 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_81),B_60)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_33),D_6)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_81),C_33)),hAPP_real_real(plus_plus_real(B_60),D_6)))))) # label(fact_201_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 209 (all C_33 all D_6 all A_81 all B_60 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_81),B_60)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_33),D_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(A_81),C_33)),hAPP_nat_nat(plus_plus_nat(B_60),D_6)))))) # label(fact_202_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 210 (all A_80 all C_32 all B_59 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_80),C_32)),hAPP_int_int(plus_plus_int(B_59),C_32))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_80),B_59)))) # label(fact_203_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 211 (all A_80 all C_32 all B_59 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_80),C_32)),hAPP_real_real(plus_plus_real(B_59),C_32))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_80),B_59)))) # label(fact_204_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 212 (all A_80 all C_32 all B_59 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(A_80),C_32)),hAPP_nat_nat(plus_plus_nat(B_59),C_32))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_80),B_59)))) # label(fact_205_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 213 (all C_31 all A_79 all B_58 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(C_31),A_79)),hAPP_int_int(plus_plus_int(C_31),B_58))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_79),B_58)))) # label(fact_206_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 214 (all C_31 all A_79 all B_58 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(C_31),A_79)),hAPP_real_real(plus_plus_real(C_31),B_58))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_79),B_58)))) # label(fact_207_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 215 (all C_31 all A_79 all B_58 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(C_31),A_79)),hAPP_nat_nat(plus_plus_nat(C_31),B_58))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_79),B_58)))) # label(fact_208_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 216 (all A_78 hAPP_int_int(times_times_int(one_one_int),A_78) = A_78) # label(fact_209_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 217 (all A_78 hAPP_real_real(times_times_real(one_one_real),A_78) = A_78) # label(fact_210_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 218 (all A_78 hAPP_nat_nat(times_times_nat(one_one_nat),A_78) = A_78) # label(fact_211_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 219 (all A_77 hAPP_int_int(times_times_int(A_77),one_one_int) = A_77) # label(fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 220 (all A_77 hAPP_real_real(times_times_real(A_77),one_one_real) = A_77) # label(fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 221 (all A_77 hAPP_nat_nat(times_times_nat(A_77),one_one_nat) = A_77) # label(fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 222 (all A_76 hAPP_int_int(times_times_int(one_one_int),A_76) = A_76) # label(fact_215_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 223 (all A_76 hAPP_real_real(times_times_real(one_one_real),A_76) = A_76) # label(fact_216_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 224 (all A_76 hAPP_nat_nat(times_times_nat(one_one_nat),A_76) = A_76) # label(fact_217_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 225 (all A_75 hAPP_int_int(times_times_int(one_one_int),A_75) = A_75) # label(fact_218_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 226 (all A_75 hAPP_real_real(times_times_real(one_one_real),A_75) = A_75) # label(fact_219_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 227 (all A_75 hAPP_nat_nat(times_times_nat(one_one_nat),A_75) = A_75) # label(fact_220_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 228 (all A_74 hAPP_int_int(times_times_int(A_74),one_one_int) = A_74) # label(fact_221_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 229 (all A_74 hAPP_real_real(times_times_real(A_74),one_one_real) = A_74) # label(fact_222_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 230 (all A_74 hAPP_nat_nat(times_times_nat(A_74),one_one_nat) = A_74) # label(fact_223_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 231 (all A_73 hAPP_int_int(times_times_int(A_73),one_one_int) = A_73) # label(fact_224_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 232 (all A_73 hAPP_real_real(times_times_real(A_73),one_one_real) = A_73) # label(fact_225_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 233 (all A_73 hAPP_nat_nat(times_times_nat(A_73),one_one_nat) = A_73) # label(fact_226_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 234 (all Aa all Ba all C_1 all D_2 (hAPP_int_int(minus_minus_int(Aa),Ba) = hAPP_int_int(minus_minus_int(C_1),D_2) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_1),D_2))))) # label(fact_227_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 235 (all Aa all Ba all C_1 all D_2 (hAPP_real_real(minus_minus_real(Aa),Ba) = hAPP_real_real(minus_minus_real(C_1),D_2) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_1),D_2))))) # label(fact_228_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 236 (all Aa all C_1 all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(Aa),C_1)),hAPP_int_int(plus_plus_int(Ba),C_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)))) # label(fact_229_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 237 (all Aa all C_1 all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(Aa),C_1)),hAPP_real_real(plus_plus_real(Ba),C_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)))) # label(fact_230_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 238 (all Aa all C_1 all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(Aa),C_1)),hAPP_nat_nat(plus_plus_nat(Ba),C_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_231_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 239 (all C_1 all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(C_1),Aa)),hAPP_int_int(plus_plus_int(C_1),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)))) # label(fact_232_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 240 (all C_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(C_1),Aa)),hAPP_real_real(plus_plus_real(C_1),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)))) # label(fact_233_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 241 (all C_1 all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(C_1),Aa)),hAPP_nat_nat(plus_plus_nat(C_1),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_234_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 242 (all C_30 all A_72 all B_57 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_72),B_57)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(A_72),C_30)),hAPP_int_int(plus_plus_int(B_57),C_30))))) # label(fact_235_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 243 (all C_30 all A_72 all B_57 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_72),B_57)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(A_72),C_30)),hAPP_real_real(plus_plus_real(B_57),C_30))))) # label(fact_236_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 244 (all C_30 all A_72 all B_57 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_72),B_57)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(A_72),C_30)),hAPP_nat_nat(plus_plus_nat(B_57),C_30))))) # label(fact_237_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 245 (all C_29 all A_71 all B_56 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_71),B_56)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(C_29),A_71)),hAPP_int_int(plus_plus_int(C_29),B_56))))) # label(fact_238_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 246 (all C_29 all A_71 all B_56 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_71),B_56)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(C_29),A_71)),hAPP_real_real(plus_plus_real(C_29),B_56))))) # label(fact_239_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 247 (all C_29 all A_71 all B_56 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_71),B_56)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(C_29),A_71)),hAPP_nat_nat(plus_plus_nat(C_29),B_56))))) # label(fact_240_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 248 (all C_28 all D_5 all A_70 all B_55 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_70),B_55)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_28),D_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(A_70),C_28)),hAPP_int_int(plus_plus_int(B_55),D_5)))))) # label(fact_241_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 249 (all C_28 all D_5 all A_70 all B_55 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_70),B_55)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_28),D_5)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(A_70),C_28)),hAPP_real_real(plus_plus_real(B_55),D_5)))))) # label(fact_242_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 250 (all C_28 all D_5 all A_70 all B_55 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_70),B_55)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_28),D_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(A_70),C_28)),hAPP_nat_nat(plus_plus_nat(B_55),D_5)))))) # label(fact_243_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 251 (all A_69 all C_27 all B_54 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(A_69),C_27)),hAPP_int_int(plus_plus_int(B_54),C_27))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_69),B_54)))) # label(fact_244_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 252 (all A_69 all C_27 all B_54 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(A_69),C_27)),hAPP_real_real(plus_plus_real(B_54),C_27))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_69),B_54)))) # label(fact_245_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 253 (all A_69 all C_27 all B_54 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(A_69),C_27)),hAPP_nat_nat(plus_plus_nat(B_54),C_27))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_69),B_54)))) # label(fact_246_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 254 (all C_26 all A_68 all B_53 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(C_26),A_68)),hAPP_int_int(plus_plus_int(C_26),B_53))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_68),B_53)))) # label(fact_247_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 255 (all C_26 all A_68 all B_53 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(C_26),A_68)),hAPP_real_real(plus_plus_real(C_26),B_53))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_68),B_53)))) # label(fact_248_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 256 (all C_26 all A_68 all B_53 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(C_26),A_68)),hAPP_nat_nat(plus_plus_nat(C_26),B_53))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_68),B_53)))) # label(fact_249_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 257 (all Aa all Ba all C_1 all D_2 (hAPP_int_int(minus_minus_int(Aa),Ba) = hAPP_int_int(minus_minus_int(C_1),D_2) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_1),D_2))))) # label(fact_250_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 258 (all Aa all Ba all C_1 all D_2 (hAPP_real_real(minus_minus_real(Aa),Ba) = hAPP_real_real(minus_minus_real(C_1),D_2) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_1),D_2))))) # label(fact_251_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 259 (all V all W_1 hAPP_int_int(times_times_int(number_number_of_int(V)),number_number_of_int(W_1)) = number_number_of_int(hAPP_int_int(times_times_int(V),W_1))) # label(fact_252_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 260 (all V all W_1 hAPP_int_int(plus_plus_int(number_number_of_int(V)),number_number_of_int(W_1)) = number_number_of_int(hAPP_int_int(plus_plus_int(V),W_1))) # label(fact_253_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 261 (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(plus_plus_int(I),K)),hAPP_int_int(plus_plus_int(J),K))))) # label(fact_254_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 262 (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(plus_plus_int(K),I)),hAPP_int_int(plus_plus_int(K),J))))) # label(fact_255_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 263 (all Z_1 hAPP_int_int(times_times_int(one_one_int),Z_1) = Z_1) # label(fact_256_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 264 (all Z_1 hAPP_int_int(times_times_int(Z_1),one_one_int) = Z_1) # label(fact_257_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 265 (all V_16 all B_52 all C_25 hAPP_int_int(times_times_int(number_number_of_int(V_16)),hAPP_int_int(plus_plus_int(B_52),C_25)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(V_16)),B_52)),hAPP_int_int(times_times_int(number_number_of_int(V_16)),C_25))) # label(fact_258_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 266 (all V_16 all B_52 all C_25 hAPP_real_real(times_times_real(number267125858f_real(V_16)),hAPP_real_real(plus_plus_real(B_52),C_25)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(number267125858f_real(V_16)),B_52)),hAPP_real_real(times_times_real(number267125858f_real(V_16)),C_25))) # label(fact_259_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 267 (all V_16 all B_52 all C_25 hAPP_nat_nat(times_times_nat(number_number_of_nat(V_16)),hAPP_nat_nat(plus_plus_nat(B_52),C_25)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(V_16)),B_52)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_16)),C_25))) # label(fact_260_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 268 (all A_67 all B_51 all V_15 hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_67),B_51)),number_number_of_int(V_15)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_67),number_number_of_int(V_15))),hAPP_int_int(times_times_int(B_51),number_number_of_int(V_15)))) # label(fact_261_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 269 (all A_67 all B_51 all V_15 hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_67),B_51)),number267125858f_real(V_15)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_67),number267125858f_real(V_15))),hAPP_real_real(times_times_real(B_51),number267125858f_real(V_15)))) # label(fact_262_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 270 (all A_67 all B_51 all V_15 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_67),B_51)),number_number_of_nat(V_15)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_67),number_number_of_nat(V_15))),hAPP_nat_nat(times_times_nat(B_51),number_number_of_nat(V_15)))) # label(fact_263_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 271 (all V_14 all B_50 all C_24 hAPP_int_int(times_times_int(number_number_of_int(V_14)),hAPP_int_int(minus_minus_int(B_50),C_24)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(V_14)),B_50)),hAPP_int_int(times_times_int(number_number_of_int(V_14)),C_24))) # label(fact_264_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 272 (all V_14 all B_50 all C_24 hAPP_real_real(times_times_real(number267125858f_real(V_14)),hAPP_real_real(minus_minus_real(B_50),C_24)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(V_14)),B_50)),hAPP_real_real(times_times_real(number267125858f_real(V_14)),C_24))) # label(fact_265_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 273 (all A_66 all B_49 all V_13 hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(A_66),B_49)),number_number_of_int(V_13)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(A_66),number_number_of_int(V_13))),hAPP_int_int(times_times_int(B_49),number_number_of_int(V_13)))) # label(fact_266_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 274 (all A_66 all B_49 all V_13 hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(A_66),B_49)),number267125858f_real(V_13)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(A_66),number267125858f_real(V_13))),hAPP_real_real(times_times_real(B_49),number267125858f_real(V_13)))) # label(fact_267_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 275 (all V_12 all W_9 number_number_of_int(hAPP_int_int(times_times_int(V_12),W_9)) = hAPP_int_int(times_times_int(number_number_of_int(V_12)),number_number_of_int(W_9))) # label(fact_268_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 276 (all V_12 all W_9 number267125858f_real(hAPP_int_int(times_times_int(V_12),W_9)) = hAPP_real_real(times_times_real(number267125858f_real(V_12)),number267125858f_real(W_9))) # label(fact_269_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 277 (all V_11 all W_8 hAPP_int_int(times_times_int(number_number_of_int(V_11)),number_number_of_int(W_8)) = number_number_of_int(hAPP_int_int(times_times_int(V_11),W_8))) # label(fact_270_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 278 (all V_11 all W_8 hAPP_real_real(times_times_real(number267125858f_real(V_11)),number267125858f_real(W_8)) = number267125858f_real(hAPP_int_int(times_times_int(V_11),W_8))) # label(fact_271_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 279 (all V_10 all W_7 all Z_15 hAPP_int_int(times_times_int(number_number_of_int(V_10)),hAPP_int_int(times_times_int(number_number_of_int(W_7)),Z_15)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(V_10),W_7))),Z_15)) # label(fact_272_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 280 (all V_10 all W_7 all Z_15 hAPP_real_real(times_times_real(number267125858f_real(V_10)),hAPP_real_real(times_times_real(number267125858f_real(W_7)),Z_15)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(V_10),W_7))),Z_15)) # label(fact_273_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 281 (all V_9 all W_6 number_number_of_int(hAPP_int_int(plus_plus_int(V_9),W_6)) = hAPP_int_int(plus_plus_int(number_number_of_int(V_9)),number_number_of_int(W_6))) # label(fact_274_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 282 (all V_9 all W_6 number267125858f_real(hAPP_int_int(plus_plus_int(V_9),W_6)) = hAPP_real_real(plus_plus_real(number267125858f_real(V_9)),number267125858f_real(W_6))) # label(fact_275_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 283 (all V_8 all W_5 hAPP_int_int(plus_plus_int(number_number_of_int(V_8)),number_number_of_int(W_5)) = number_number_of_int(hAPP_int_int(plus_plus_int(V_8),W_5))) # label(fact_276_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 284 (all V_8 all W_5 hAPP_real_real(plus_plus_real(number267125858f_real(V_8)),number267125858f_real(W_5)) = number267125858f_real(hAPP_int_int(plus_plus_int(V_8),W_5))) # label(fact_277_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 285 (all V_7 all W_4 all Z_14 hAPP_int_int(plus_plus_int(number_number_of_int(V_7)),hAPP_int_int(plus_plus_int(number_number_of_int(W_4)),Z_14)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(V_7),W_4))),Z_14)) # label(fact_278_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 286 (all V_7 all W_4 all Z_14 hAPP_real_real(plus_plus_real(number267125858f_real(V_7)),hAPP_real_real(plus_plus_real(number267125858f_real(W_4)),Z_14)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(V_7),W_4))),Z_14)) # label(fact_279_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 287 (all V_6 all W_3 number_number_of_int(hAPP_int_int(minus_minus_int(V_6),W_3)) = hAPP_int_int(minus_minus_int(number_number_of_int(V_6)),number_number_of_int(W_3))) # label(fact_280_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 288 (all V_6 all W_3 number267125858f_real(hAPP_int_int(minus_minus_int(V_6),W_3)) = hAPP_real_real(minus_minus_real(number267125858f_real(V_6)),number267125858f_real(W_3))) # label(fact_281_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 289 (all M_5 hAPP_int_int(plus_plus_int(M_5),M_5) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),M_5)) # label(fact_282_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 290 (all M_5 hAPP_real_real(plus_plus_real(M_5),M_5) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),M_5)) # label(fact_283_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 291 (all M_5 hAPP_nat_nat(plus_plus_nat(M_5),M_5) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),M_5)) # label(fact_284_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 292 (all M_4 all A_65 hAPP_int_int(plus_plus_int(M_4),hAPP_int_int(times_times_int(A_65),M_4)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_65),one_one_int)),M_4)) # label(fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 293 (all M_4 all A_65 hAPP_real_real(plus_plus_real(M_4),hAPP_real_real(times_times_real(A_65),M_4)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_65),one_one_real)),M_4)) # label(fact_286_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 294 (all M_4 all A_65 hAPP_nat_nat(plus_plus_nat(M_4),hAPP_nat_nat(times_times_nat(A_65),M_4)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_65),one_one_nat)),M_4)) # label(fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 295 (all A_64 all M_3 hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_64),M_3)),M_3) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_64),one_one_int)),M_3)) # label(fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 296 (all A_64 all M_3 hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_64),M_3)),M_3) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_64),one_one_real)),M_3)) # label(fact_289_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 297 (all A_64 all M_3 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_64),M_3)),M_3) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_64),one_one_nat)),M_3)) # label(fact_290_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 298 (all F all Aa all Ba (hBOOL(hAPP_int_bool(produc262399358t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P603027463t_bool(F,product_Pair_int_int(Aa,Ba))))) # label(fact_291_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 299 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(produc97574839t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P178748804t_bool(F,produc282740534nt_int(Aa,Ba))))) # label(fact_292_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 300 (all F all Aa all Ba (hBOOL(hAPP_int_bool(produc262399358t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P603027463t_bool(F,product_Pair_int_int(Aa,Ba))))) # label(fact_293_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 301 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(produc97574839t_bool(F,Aa),Ba)) -> hBOOL(hAPP_P178748804t_bool(F,produc282740534nt_int(Aa,Ba))))) # label(fact_294_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 302 (all X_37 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_37),X_37))) # label(fact_295_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 303 (all X_37 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_37),X_37))) # label(fact_296_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 304 (all X_37 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_37),X_37))) # label(fact_297_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 305 (all Z_13 all Y_36 all X_36 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_36),X_36)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_13),Y_36)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_13),X_36))))) # label(fact_298_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 306 (all Z_13 all Y_36 all X_36 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_36),X_36)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_13),Y_36)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_13),X_36))))) # label(fact_299_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 307 (all Z_13 all Y_36 all X_36 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_36),X_36)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_13),Y_36)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_13),X_36))))) # label(fact_300_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 308 (all Z_12 all X_35 all Y_35 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_35),Y_35)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_35),Z_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_35),Z_12))))) # label(fact_301_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 309 (all Z_12 all X_35 all Y_35 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_35),Y_35)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_35),Z_12)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_35),Z_12))))) # label(fact_302_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 310 (all Z_12 all X_35 all Y_35 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_35),Y_35)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_35),Z_12)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_35),Z_12))))) # label(fact_303_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 311 (all Z_11 all Y_34 all X_34 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_34),X_34)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_11),Y_34)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_11),X_34))))) # label(fact_304_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 312 (all Z_11 all Y_34 all X_34 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_34),X_34)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_11),Y_34)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_11),X_34))))) # label(fact_305_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 313 (all Z_11 all Y_34 all X_34 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_34),X_34)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_11),Y_34)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_11),X_34))))) # label(fact_306_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 314 (all Z_10 all X_33 all Y_33 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_33),Y_33)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_33),Z_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_33),Z_10))))) # label(fact_307_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 315 (all Z_10 all X_33 all Y_33 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_33),Y_33)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_33),Z_10)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_33),Z_10))))) # label(fact_308_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 316 (all Z_10 all X_33 all Y_33 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_33),Y_33)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_33),Z_10)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_33),Z_10))))) # label(fact_309_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 317 (all B_48 all A_63 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_48),A_63)) -> (A_63 != B_48 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_48),A_63))))) # label(fact_310_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 318 (all B_48 all A_63 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_48),A_63)) -> (A_63 != B_48 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_48),A_63))))) # label(fact_311_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 319 (all B_48 all A_63 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_48),A_63)) -> (A_63 != B_48 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_48),A_63))))) # label(fact_312_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 320 (all A_62 all B_47 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_62),B_47)) -> (A_62 != B_47 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_62),B_47))))) # label(fact_313_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 321 (all A_62 all B_47 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_62),B_47)) -> (A_62 != B_47 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_62),B_47))))) # label(fact_314_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 322 (all A_62 all B_47 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_62),B_47)) -> (A_62 != B_47 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_62),B_47))))) # label(fact_315_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 323 (all X_32 all Y_32 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_32),Y_32)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_32),Y_32)) | X_32 = Y_32)) # label(fact_316_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 324 (all X_32 all Y_32 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_32),Y_32)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_32),Y_32)) | X_32 = Y_32)) # label(fact_317_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 325 (all X_32 all Y_32 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_32),Y_32)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_32)) | X_32 = Y_32)) # label(fact_318_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 326 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_319_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 327 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_320_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 328 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_321_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 329 (all X_31 all Y_31 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_31),Y_31)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_31),Y_31)))) # label(fact_322_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 330 (all X_31 all Y_31 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_31),Y_31)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_31),Y_31)))) # label(fact_323_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 331 (all X_31 all Y_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_31)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_31),Y_31)))) # label(fact_324_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 332 (all W_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),W_1))) # label(fact_325_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 333 (all K number_number_of_int(K) = K) # label(fact_326_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 334 (all Z_1 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_1)))) # label(fact_327_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 335 (all Z all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),W)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) & Z != W)) # label(fact_328_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 336 (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_329_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 337 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K_1)),number_number_of_int(L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)))) # label(fact_330_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 338 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K_1)),number_number_of_int(L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)))) # label(fact_331_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 339 (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_332_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 340 (all Z_1 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_1)) -> Z_1 = W_1))) # label(fact_333_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 341 (all X_30 all Y_30 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_30),Y_30)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_30),X_30)))) # label(fact_334_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 342 (all X_30 all Y_30 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_30),Y_30)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_30),X_30)))) # label(fact_335_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 343 (all X_30 all Y_30 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_30),Y_30)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_30),X_30)))) # label(fact_336_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 344 (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_337_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 345 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),X_1)))) # label(fact_338_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 346 (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_339_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 347 (all X_29 all Y_29 (X_29 = Y_29 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_29)))) # label(fact_340_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 348 (all X_29 all Y_29 (X_29 = Y_29 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_29),Y_29)))) # label(fact_341_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 349 (all X_29 all Y_29 (X_29 = Y_29 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_29),Y_29)))) # label(fact_342_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 350 (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_343_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 351 (all Y_1 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_344_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 352 (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_345_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 353 (all C_23 all A_61 all B_46 (A_61 = B_46 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_46),C_23)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_61),C_23))))) # label(fact_346_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 354 (all C_23 all A_61 all B_46 (A_61 = B_46 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_46),C_23)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_61),C_23))))) # label(fact_347_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 355 (all C_23 all A_61 all B_46 (A_61 = B_46 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_46),C_23)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_61),C_23))))) # label(fact_348_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 356 (all C_22 all A_60 all B_45 (A_60 = B_45 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_22),B_45)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_22),A_60))))) # label(fact_349_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 357 (all C_22 all A_60 all B_45 (A_60 = B_45 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_22),B_45)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_22),A_60))))) # label(fact_350_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 358 (all C_22 all A_60 all B_45 (A_60 = B_45 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_22),B_45)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_22),A_60))))) # label(fact_351_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 359 (all C_21 all A_59 all B_44 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_59),B_44)) -> (B_44 = C_21 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_59),C_21))))) # label(fact_352_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 360 (all C_21 all A_59 all B_44 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_59),B_44)) -> (B_44 = C_21 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_59),C_21))))) # label(fact_353_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 361 (all C_21 all A_59 all B_44 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_59),B_44)) -> (B_44 = C_21 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_59),C_21))))) # label(fact_354_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 362 (all C_20 all B_43 all A_58 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_43),A_58)) -> (B_43 = C_20 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_20),A_58))))) # label(fact_355_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 363 (all C_20 all B_43 all A_58 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_43),A_58)) -> (B_43 = C_20 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_20),A_58))))) # label(fact_356_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 364 (all C_20 all B_43 all A_58 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_43),A_58)) -> (B_43 = C_20 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_58))))) # label(fact_357_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 365 (all X_28 all Y_28 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_28),Y_28)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_28),X_28)) -> X_28 = Y_28))) # label(fact_358_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 366 (all X_28 all Y_28 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_28),Y_28)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_28),X_28)) -> X_28 = Y_28))) # label(fact_359_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 367 (all X_28 all Y_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_28),Y_28)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_28),X_28)) -> X_28 = Y_28))) # label(fact_360_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 368 (all Z_9 all X_27 all Y_27 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_27),Y_27)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_27),Z_9)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_27),Z_9))))) # label(fact_361_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 369 (all Z_9 all X_27 all Y_27 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_27),Y_27)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_27),Z_9)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_27),Z_9))))) # label(fact_362_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 370 (all Z_9 all X_27 all Y_27 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_27),Y_27)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_27),Z_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_27),Z_9))))) # label(fact_363_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 371 (all Y_26 all X_26 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_26),X_26)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_26),Y_26)) -> X_26 = Y_26))) # label(fact_364_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 372 (all Y_26 all X_26 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_26),X_26)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_26),Y_26)) -> X_26 = Y_26))) # label(fact_365_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 373 (all Y_26 all X_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_26),X_26)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_26),Y_26)) -> X_26 = Y_26))) # label(fact_366_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 374 (all Z_8 all Y_25 all X_25 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_25),X_25)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_8),Y_25)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_8),X_25))))) # label(fact_367_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 375 (all Z_8 all Y_25 all X_25 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_25),X_25)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_8),Y_25)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_8),X_25))))) # label(fact_368_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 376 (all Z_8 all Y_25 all X_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_25),X_25)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_8),Y_25)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_8),X_25))))) # label(fact_369_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 377 (all X_24 all Y_24 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_24),Y_24)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_24),X_24)))) # label(fact_370_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 378 (all X_24 all Y_24 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_24),Y_24)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_24),X_24)))) # label(fact_371_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 379 (all X_24 all Y_24 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_24),Y_24)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_24),X_24)))) # label(fact_372_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 380 (all X_23 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_23),X_23))) # label(fact_373_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 381 (all X_23 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_23),X_23))) # label(fact_374_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 382 (all X_23 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),X_23))) # label(fact_375_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 383 (all X_1 all Y_1 (X_1 != Y_1 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)))) # label(fact_376_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 384 (all X_1 all Y_1 (X_1 != Y_1 <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),X_1)))) # label(fact_377_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 385 (all X_1 all Y_1 (X_1 != Y_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)))) # label(fact_378_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 386 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) | X_1 = Y_1)) # label(fact_379_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 387 (all X_1 all Y_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),X_1)) | X_1 = Y_1)) # label(fact_380_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 388 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) | X_1 = Y_1)) # label(fact_381_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 389 (all X_22 all Y_23 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_22),Y_23)) | X_22 = Y_23 | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_23),X_22)))) # label(fact_382_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 390 (all X_22 all Y_23 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_22),Y_23)) | X_22 = Y_23 | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_23),X_22)))) # label(fact_383_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 391 (all X_22 all Y_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_23)) | X_22 = Y_23 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_22)))) # label(fact_384_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 392 (all Y_1 all X_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_385_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 393 (all Y_1 all X_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),X_1)) -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_386_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 394 (all Y_1 all X_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_387_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 395 (all X_21 all Y_22 (X_21 != Y_22 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_21),Y_22)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_22),X_21))))) # label(fact_388_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 396 (all X_21 all Y_22 (X_21 != Y_22 -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_21),Y_22)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_22),X_21))))) # label(fact_389_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 397 (all X_21 all Y_22 (X_21 != Y_22 -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),Y_22)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_22),X_21))))) # label(fact_390_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 398 (all X_20 all Y_21 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_21)) -> X_20 != Y_21)) # label(fact_391_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 399 (all X_20 all Y_21 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_20),Y_21)) -> X_20 != Y_21)) # label(fact_392_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 400 (all X_20 all Y_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_20),Y_21)) -> X_20 != Y_21)) # label(fact_393_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 401 (all X_19 all Y_20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_19),Y_20)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_20),X_19)))) # label(fact_394_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 402 (all X_19 all Y_20 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_19),Y_20)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_20),X_19)))) # label(fact_395_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 403 (all X_19 all Y_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_19),Y_20)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_19)))) # label(fact_396_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 404 (all X_18 all Y_19 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_18),Y_19)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_19),X_18)))) # label(fact_397_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 405 (all X_18 all Y_19 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_18),Y_19)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_19),X_18)))) # label(fact_398_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 406 (all X_18 all Y_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_18),Y_19)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_19),X_18)))) # label(fact_399_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 407 (all X_17 all Y_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_17),Y_18)) -> X_17 != Y_18)) # label(fact_400_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 408 (all X_17 all Y_18 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_17),Y_18)) -> X_17 != Y_18)) # label(fact_401_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 409 (all X_17 all Y_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_17),Y_18)) -> X_17 != Y_18)) # label(fact_402_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 410 (all X_16 all Y_17 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_16),Y_17)) -> Y_17 != X_16)) # label(fact_403_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 411 (all X_16 all Y_17 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_16),Y_17)) -> Y_17 != X_16)) # label(fact_404_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 412 (all X_16 all Y_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_16),Y_17)) -> Y_17 != X_16)) # label(fact_405_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 413 (all P_1 all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)) -> hBOOL(P_1)))) # label(fact_406_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 414 (all P_1 all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),X_1)) -> hBOOL(P_1)))) # label(fact_407_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 415 (all P_1 all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) -> hBOOL(P_1)))) # label(fact_408_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 416 (all A_57 all B_42 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_57),B_42)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_42),A_57)))) # label(fact_409_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 417 (all A_57 all B_42 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_57),B_42)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_42),A_57)))) # label(fact_410_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 418 (all A_57 all B_42 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_57),B_42)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_42),A_57)))) # label(fact_411_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 419 (all B_41 all A_56 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_41),A_56)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_56),B_41)))) # label(fact_412_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 420 (all B_41 all A_56 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_41),A_56)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_56),B_41)))) # label(fact_413_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 421 (all B_41 all A_56 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_41),A_56)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_56),B_41)))) # label(fact_414_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 422 (all C_19 all A_55 all B_40 (A_55 = B_40 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_40),C_19)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_55),C_19))))) # label(fact_415_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 423 (all C_19 all A_55 all B_40 (A_55 = B_40 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_40),C_19)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_55),C_19))))) # label(fact_416_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 424 (all C_19 all A_55 all B_40 (A_55 = B_40 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_40),C_19)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_55),C_19))))) # label(fact_417_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 425 (all C_18 all A_54 all B_39 (A_54 = B_39 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_18),B_39)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_18),A_54))))) # label(fact_418_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 426 (all C_18 all A_54 all B_39 (A_54 = B_39 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_18),B_39)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_18),A_54))))) # label(fact_419_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 427 (all C_18 all A_54 all B_39 (A_54 = B_39 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_18),B_39)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_18),A_54))))) # label(fact_420_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.90 428 (all C_17 all A_53 all B_38 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_53),B_38)) -> (B_38 = C_17 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_53),C_17))))) # label(fact_421_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 429 (all C_17 all A_53 all B_38 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_53),B_38)) -> (B_38 = C_17 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_53),C_17))))) # label(fact_422_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 430 (all C_17 all A_53 all B_38 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_53),B_38)) -> (B_38 = C_17 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_53),C_17))))) # label(fact_423_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 431 (all C_16 all B_37 all A_52 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_37),A_52)) -> (B_37 = C_16 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_16),A_52))))) # label(fact_424_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 432 (all C_16 all B_37 all A_52 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_37),A_52)) -> (B_37 = C_16 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_16),A_52))))) # label(fact_425_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 433 (all C_16 all B_37 all A_52 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_37),A_52)) -> (B_37 = C_16 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_16),A_52))))) # label(fact_426_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 434 (all Z_7 all X_15 all Y_16 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_15),Y_16)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_16),Z_7)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_15),Z_7))))) # label(fact_427_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 435 (all Z_7 all X_15 all Y_16 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_15),Y_16)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_16),Z_7)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_15),Z_7))))) # label(fact_428_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 436 (all Z_7 all X_15 all Y_16 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_15),Y_16)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_16),Z_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_15),Z_7))))) # label(fact_429_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 437 (all Z_6 all Y_15 all X_14 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_15),X_14)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_6),Y_15)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_6),X_14))))) # label(fact_430_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 438 (all Z_6 all Y_15 all X_14 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_15),X_14)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_6),Y_15)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_6),X_14))))) # label(fact_431_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 439 (all Z_6 all Y_15 all X_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_15),X_14)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_6),Y_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_6),X_14))))) # label(fact_432_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 440 (all X_13 all Y_14 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_13),Y_14)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_14),X_13)))) # label(fact_433_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 441 (all X_13 all Y_14 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_13),Y_14)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_14),X_13)))) # label(fact_434_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 442 (all X_13 all Y_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_14)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_14),X_13)))) # label(fact_435_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 443 (all X_12 all Y_13 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_12),Y_13)) -> (X_12 != Y_13 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_13),X_12))))) # label(fact_436_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 444 (all X_12 all Y_13 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_12),Y_13)) -> (X_12 != Y_13 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_13),X_12))))) # label(fact_437_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 445 (all X_12 all Y_13 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_12),Y_13)) -> (X_12 != Y_13 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_13),X_12))))) # label(fact_438_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 446 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)))) # label(fact_439_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 447 (all X_1 all Y_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),X_1)))) # label(fact_440_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 448 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)))) # label(fact_441_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 449 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1)))) # label(fact_442_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 450 (all X_1 all Y_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),X_1)))) # label(fact_443_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 451 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)))) # label(fact_444_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 452 (all X_11 all Y_12 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),Y_12)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_12),X_11)))) # label(fact_445_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 453 (all X_11 all Y_12 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_11),Y_12)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_12),X_11)))) # label(fact_446_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 454 (all X_11 all Y_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),Y_12)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_11)))) # label(fact_447_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 455 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) & X_1 != Y_1)) # label(fact_448_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 456 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) & X_1 != Y_1)) # label(fact_449_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 457 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) & X_1 != Y_1)) # label(fact_450_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 458 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) & -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)))) # label(fact_451_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 459 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) & -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),X_1)))) # label(fact_452_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 460 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)))) # label(fact_453_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 461 (all X_1 all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) | X_1 = Y_1)) # label(fact_454_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 462 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) | X_1 = Y_1)) # label(fact_455_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 463 (all X_1 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) | X_1 = Y_1)) # label(fact_456_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 464 (all X_10 all Y_11 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_10),Y_11)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_11),X_10)))) # label(fact_457_leI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 465 (all X_10 all Y_11 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_10),Y_11)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_11),X_10)))) # label(fact_458_leI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 466 (all X_10 all Y_11 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_10)))) # label(fact_459_leI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 467 (all Y_10 all X_9 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_10),X_9)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Y_10)))) # label(fact_460_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 468 (all Y_10 all X_9 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_10),X_9)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_9),Y_10)))) # label(fact_461_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 469 (all Y_10 all X_9 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_10)))) # label(fact_462_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 470 (all X_1 all Y_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_463_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 471 (all X_1 all Y_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_464_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 472 (all X_1 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_465_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 473 (all A_51 all B_36 (A_51 != B_36 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_51),B_36)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_51),B_36))))) # label(fact_466_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 474 (all A_51 all B_36 (A_51 != B_36 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_51),B_36)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_51),B_36))))) # label(fact_467_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 475 (all A_51 all B_36 (A_51 != B_36 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_51),B_36)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_51),B_36))))) # label(fact_468_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 476 (all A_50 all B_35 (A_50 != B_35 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_35),A_50)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_35),A_50))))) # label(fact_469_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 477 (all A_50 all B_35 (A_50 != B_35 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_35),A_50)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_35),A_50))))) # label(fact_470_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 478 (all A_50 all B_35 (A_50 != B_35 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_35),A_50)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_35),A_50))))) # label(fact_471_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 479 (all Y_9 all X_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_9),X_8)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_8),Y_9)))) # label(fact_472_leD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 480 (all Y_9 all X_8 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_9),X_8)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_8),Y_9)))) # label(fact_473_leD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 481 (all Y_9 all X_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_8)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_9)))) # label(fact_474_leD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 482 (all A all B (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),hAPP_int_int(minus_minus_int(B),one_one_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),B)))) # label(fact_475_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 483 (all P_1 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(P_1,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K_1)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(minus_minus_int(I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_476_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 484 (all P_1 all I_1 all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),K_1)) -> (hBOOL(hAPP_int_bool(P_1,hAPP_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(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(minus_minus_int(I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_477_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 485 (all P_1 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(P_1,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(plus_plus_int(I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_478_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 486 (all P_1 all K_1 all I_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),I_1)) -> (hBOOL(hAPP_int_bool(P_1,hAPP_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(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(plus_plus_int(I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_479_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 487 (all Z_5 all Y_8 ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_8)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Z_5)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_8),Z_5)))) # label(fact_480_dense__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 488 (all Z_4 all X_7 all Y_7 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_7),Y_7)) -> ((all W_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_7),W_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,W_2),Y_7)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W_2),Z_4))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_7),Z_4))))) # label(fact_481_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 489 (all I_1 all P_1 all K_1 (hBOOL(hAPP_int_bool(P_1,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_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(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(minus_minus_int(I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_482_int__induct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 490 (all B all A all C (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),C)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),C)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),B)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),A))))) # label(fact_483_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 491 (all X_1 all P_1 ((all A_49 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_49)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(minus_minus_int(A_49),one_one_int)))) -> hBOOL(hAPP_int_bool(P_1,A_49)))) -> hBOOL(hAPP_int_bool(P_1,X_1)))) # label(fact_484_d22set__induct__old) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 492 (all V_5 all U_2 all Y_6 all X_6 all A_48 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_6),A_48)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_6),A_48)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_5)) -> (hAPP_int_int(plus_plus_int(U_2),V_5) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_2),X_6)),hAPP_int_int(times_times_int(V_5),Y_6))),A_48)))))))) # label(fact_485_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 493 (all V_5 all U_2 all Y_6 all X_6 all A_48 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_6),A_48)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_6),A_48)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),V_5)) -> (hAPP_real_real(plus_plus_real(U_2),V_5) = one_one_real -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2),X_6)),hAPP_real_real(times_times_real(V_5),Y_6))),A_48)))))))) # label(fact_486_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 494 (all V_1 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_1)),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(minus_minus_real(number267125858f_real(V_1)),one_one_real)),X_1)))) # label(fact_487_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 495 (all X_1 all V_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_1)),number_number_of_int(V_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_real_real(minus_minus_real(number267125858f_real(V_1)),one_one_real))))) # label(fact_488_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 496 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)))) # label(fact_489_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 497 (all X_1 (zero_zero_int = X_1 <-> X_1 = zero_zero_int)) # label(fact_490_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 498 (all X_1 (zero_zero_real = X_1 <-> X_1 = zero_zero_real)) # label(fact_491_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 499 (all X_1 (zero_zero_nat = X_1 <-> X_1 = zero_zero_nat)) # label(fact_492_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 500 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X_1)),zero_zero_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real)))) # label(fact_494_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 501 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_1)),one_one_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real)))) # label(fact_495_ceiling__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 502 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)))) # label(fact_496_one__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 503 (all A_47 hAPP_nat_nat(times_times_nat(zero_zero_nat),A_47) = zero_zero_nat) # label(fact_497_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 504 (all A_47 hAPP_real_real(times_times_real(zero_zero_real),A_47) = zero_zero_real) # label(fact_498_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 505 (all A_47 hAPP_int_int(times_times_int(zero_zero_int),A_47) = zero_zero_int) # label(fact_499_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 506 (all A_46 hAPP_nat_nat(times_times_nat(A_46),zero_zero_nat) = zero_zero_nat) # label(fact_500_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 507 (all A_46 hAPP_real_real(times_times_real(A_46),zero_zero_real) = zero_zero_real) # label(fact_501_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 508 (all A_46 hAPP_int_int(times_times_int(A_46),zero_zero_int) = zero_zero_int) # label(fact_502_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 509 (all A_45 hAPP_nat_nat(times_times_nat(zero_zero_nat),A_45) = zero_zero_nat) # label(fact_503_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 510 (all A_45 hAPP_real_real(times_times_real(zero_zero_real),A_45) = zero_zero_real) # label(fact_504_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 511 (all A_45 hAPP_int_int(times_times_int(zero_zero_int),A_45) = zero_zero_int) # label(fact_505_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 512 (all B_34 hAPP_real_real(times_times_real(zero_zero_real),B_34) = zero_zero_real) # label(fact_506_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 513 (all Y_5 hAPP_real_real(times_times_real(zero_zero_real),Y_5) = zero_zero_real) # label(fact_507_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 514 (all A_44 hAPP_nat_nat(times_times_nat(A_44),zero_zero_nat) = zero_zero_nat) # label(fact_508_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 515 (all A_44 hAPP_real_real(times_times_real(A_44),zero_zero_real) = zero_zero_real) # label(fact_509_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 516 (all A_44 hAPP_int_int(times_times_int(A_44),zero_zero_int) = zero_zero_int) # label(fact_510_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 517 (all A_43 hAPP_real_real(times_times_real(A_43),zero_zero_real) = zero_zero_real) # label(fact_511_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 518 (all X_5 hAPP_real_real(times_times_real(X_5),zero_zero_real) = zero_zero_real) # label(fact_512_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 519 (all Aa all Ba (hAPP_real_real(times_times_real(Aa),Ba) = zero_zero_real <-> Aa = zero_zero_real | Ba = zero_zero_real)) # label(fact_513_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 520 (all Aa all Ba (hAPP_int_int(times_times_int(Aa),Ba) = zero_zero_int <-> Aa = zero_zero_int | Ba = zero_zero_int)) # label(fact_514_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 521 (all B_33 all A_42 (A_42 != zero_zero_nat -> (B_33 != zero_zero_nat -> hAPP_nat_nat(times_times_nat(A_42),B_33) != zero_zero_nat))) # label(fact_515_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 522 (all B_33 all A_42 (A_42 != zero_zero_real -> (B_33 != zero_zero_real -> hAPP_real_real(times_times_real(A_42),B_33) != zero_zero_real))) # label(fact_516_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 523 (all B_33 all A_42 (A_42 != zero_zero_int -> (B_33 != zero_zero_int -> hAPP_int_int(times_times_int(A_42),B_33) != zero_zero_int))) # label(fact_517_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 524 (all A_41 all B_32 (hAPP_nat_nat(times_times_nat(A_41),B_32) = zero_zero_nat -> A_41 = zero_zero_nat | B_32 = zero_zero_nat)) # label(fact_518_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 525 (all A_41 all B_32 (hAPP_real_real(times_times_real(A_41),B_32) = zero_zero_real -> A_41 = zero_zero_real | B_32 = zero_zero_real)) # label(fact_519_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 526 (all A_41 all B_32 (hAPP_int_int(times_times_int(A_41),B_32) = zero_zero_int -> A_41 = zero_zero_int | B_32 = zero_zero_int)) # label(fact_520_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 527 (all A_40 hAPP_nat_nat(plus_plus_nat(zero_zero_nat),A_40) = A_40) # label(fact_521_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 528 (all A_40 hAPP_real_real(plus_plus_real(zero_zero_real),A_40) = A_40) # label(fact_522_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 529 (all A_40 hAPP_int_int(plus_plus_int(zero_zero_int),A_40) = A_40) # label(fact_523_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 530 (all A_39 hAPP_nat_nat(plus_plus_nat(A_39),zero_zero_nat) = A_39) # label(fact_524_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 531 (all A_39 hAPP_real_real(plus_plus_real(A_39),zero_zero_real) = A_39) # label(fact_525_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 532 (all A_39 hAPP_int_int(plus_plus_int(A_39),zero_zero_int) = A_39) # label(fact_526_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 533 (all Ba all Aa (Ba = hAPP_nat_nat(plus_plus_nat(Ba),Aa) <-> Aa = zero_zero_nat)) # label(fact_527_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 534 (all Ba all Aa (Ba = hAPP_real_real(plus_plus_real(Ba),Aa) <-> Aa = zero_zero_real)) # label(fact_528_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 535 (all Ba all Aa (Ba = hAPP_int_int(plus_plus_int(Ba),Aa) <-> Aa = zero_zero_int)) # label(fact_529_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 536 (all A_38 hAPP_nat_nat(plus_plus_nat(zero_zero_nat),A_38) = A_38) # label(fact_530_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 537 (all A_38 hAPP_real_real(plus_plus_real(zero_zero_real),A_38) = A_38) # label(fact_531_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 538 (all A_38 hAPP_int_int(plus_plus_int(zero_zero_int),A_38) = A_38) # label(fact_532_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 539 (all A_37 hAPP_nat_nat(plus_plus_nat(zero_zero_nat),A_37) = A_37) # label(fact_533_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 540 (all A_37 hAPP_real_real(plus_plus_real(zero_zero_real),A_37) = A_37) # label(fact_534_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 541 (all A_37 hAPP_int_int(plus_plus_int(zero_zero_int),A_37) = A_37) # label(fact_535_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 542 (all Aa (zero_zero_real = hAPP_real_real(plus_plus_real(Aa),Aa) <-> Aa = zero_zero_real)) # label(fact_536_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 543 (all Aa (zero_zero_int = hAPP_int_int(plus_plus_int(Aa),Aa) <-> Aa = zero_zero_int)) # label(fact_537_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 544 (all A_36 hAPP_nat_nat(plus_plus_nat(A_36),zero_zero_nat) = A_36) # label(fact_538_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 545 (all A_36 hAPP_real_real(plus_plus_real(A_36),zero_zero_real) = A_36) # label(fact_539_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 546 (all A_36 hAPP_int_int(plus_plus_int(A_36),zero_zero_int) = A_36) # label(fact_540_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 547 (all A_35 hAPP_nat_nat(plus_plus_nat(A_35),zero_zero_nat) = A_35) # label(fact_541_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 548 (all A_35 hAPP_real_real(plus_plus_real(A_35),zero_zero_real) = A_35) # label(fact_542_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 549 (all A_35 hAPP_int_int(plus_plus_int(A_35),zero_zero_int) = A_35) # label(fact_543_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 550 (all Aa (hAPP_real_real(plus_plus_real(Aa),Aa) = zero_zero_real <-> Aa = zero_zero_real)) # label(fact_544_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 551 (all Aa (hAPP_int_int(plus_plus_int(Aa),Aa) = zero_zero_int <-> Aa = zero_zero_int)) # label(fact_545_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 552 (all A_34 hAPP_real_real(minus_minus_real(A_34),zero_zero_real) = A_34) # label(fact_552_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 553 (all A_34 hAPP_int_int(minus_minus_int(A_34),zero_zero_int) = A_34) # label(fact_553_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 554 (all A_33 hAPP_real_real(minus_minus_real(A_33),A_33) = zero_zero_real) # label(fact_554_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 555 (all A_33 hAPP_int_int(minus_minus_int(A_33),A_33) = zero_zero_int) # label(fact_555_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 556 (all Aa all Ba (Aa = Ba <-> hAPP_real_real(minus_minus_real(Aa),Ba) = zero_zero_real)) # label(fact_556_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 557 (all Aa all Ba (Aa = Ba <-> hAPP_int_int(minus_minus_int(Aa),Ba) = zero_zero_int)) # label(fact_557_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 558 (all Aa all Ba (hAPP_real_real(minus_minus_real(Aa),Ba) = zero_zero_real <-> Aa = Ba)) # label(fact_558_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 559 (all Aa all Ba (hAPP_int_int(minus_minus_int(Aa),Ba) = zero_zero_int <-> Aa = Ba)) # label(fact_559_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 560 (all Z_1 hAPP_int_int(plus_plus_int(zero_zero_int),Z_1) = Z_1) # label(fact_561_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 561 (all Z_1 hAPP_int_int(plus_plus_int(Z_1),zero_zero_int) = Z_1) # label(fact_562_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 562 (all X_4 all Y_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_4)),archim856651990g_real(Y_4))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_4),Y_4)))) # label(fact_563_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 563 (all Y_3 all X_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_3),X_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(Y_3)),archim856651990g_real(X_3))))) # label(fact_564_ceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 564 (all V_4 archim856651990g_real(number267125858f_real(V_4)) = number_number_of_int(V_4)) # label(fact_566_ceiling__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 565 (all A_32 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_32),A_32)))) # label(fact_567_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 566 (all A_32 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_32),A_32)))) # label(fact_568_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 567 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(Aa),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Ba)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Ba),zero_zero_real)))) # label(fact_569_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 568 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ba)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),zero_zero_int)))) # label(fact_570_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 569 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(Aa),Ba)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Ba),zero_zero_real)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Ba)))) # label(fact_571_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 570 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(Aa),Ba)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),zero_zero_int)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ba)))) # label(fact_572_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 571 (all B_31 all A_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_31)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_31)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_31),B_31)))))) # label(fact_573_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 572 (all B_31 all A_31 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_31)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_31)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_31),B_31)))))) # label(fact_574_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 573 (all B_31 all A_31 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_31)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_31)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_31),B_31)))))) # label(fact_575_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 574 (all B_30 all A_30 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_30)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_30),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_30),B_30)),zero_zero_nat))))) # label(fact_576_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 575 (all B_30 all A_30 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_30)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_30),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_30),B_30)),zero_zero_real))))) # label(fact_577_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 576 (all B_30 all A_30 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_30)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_30),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_30),B_30)),zero_zero_int))))) # label(fact_578_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 577 (all B_29 all A_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_29),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(B_29),A_29)),zero_zero_nat))))) # label(fact_579_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 578 (all B_29 all A_29 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_29)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_29),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(B_29),A_29)),zero_zero_real))))) # label(fact_580_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 579 (all B_29 all A_29 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_29)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_29),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(B_29),A_29)),zero_zero_int))))) # label(fact_581_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 580 (all B_28 all A_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_28),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_28)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_28),B_28)),zero_zero_nat))))) # label(fact_582_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 581 (all B_28 all A_28 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_28),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_28)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_28),B_28)),zero_zero_real))))) # label(fact_583_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 582 (all B_28 all A_28 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_28),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_28)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_28),B_28)),zero_zero_int))))) # label(fact_584_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 583 (all B_27 all A_27 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_27),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_27),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_27),B_27)))))) # label(fact_585_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 584 (all B_27 all A_27 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_27),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_27),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_27),B_27)))))) # label(fact_586_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 585 (all C_15 all A_26 all B_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_26)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_26),C_15)),hAPP_nat_nat(times_times_nat(B_26),C_15)))))) # label(fact_587_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 586 (all C_15 all A_26 all B_26 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_26),B_26)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_15)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_26),C_15)),hAPP_real_real(times_times_real(B_26),C_15)))))) # label(fact_588_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 587 (all C_15 all A_26 all B_26 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_26),B_26)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_15)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_26),C_15)),hAPP_int_int(times_times_int(B_26),C_15)))))) # label(fact_589_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 588 (all C_14 all A_25 all B_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),B_25)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_14)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(C_14),A_25)),hAPP_nat_nat(times_times_nat(C_14),B_25)))))) # label(fact_590_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 589 (all C_14 all A_25 all B_25 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_25),B_25)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_14)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_14),A_25)),hAPP_real_real(times_times_real(C_14),B_25)))))) # label(fact_591_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 590 (all C_14 all A_25 all B_25 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_25),B_25)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_14)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_14),A_25)),hAPP_int_int(times_times_int(C_14),B_25)))))) # label(fact_592_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 591 (all C_13 all A_24 all B_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_24),B_24)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_13)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(C_13),A_24)),hAPP_nat_nat(times_times_nat(C_13),B_24)))))) # label(fact_593_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 592 (all C_13 all A_24 all B_24 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_24),B_24)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_13)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_13),A_24)),hAPP_real_real(times_times_real(C_13),B_24)))))) # label(fact_594_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 593 (all C_13 all A_24 all B_24 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_24),B_24)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_13),A_24)),hAPP_int_int(times_times_int(C_13),B_24)))))) # label(fact_595_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 594 (all C_12 all B_23 all A_23 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_23),A_23)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_12),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_23),C_12)),hAPP_real_real(times_times_real(B_23),C_12)))))) # label(fact_596_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 595 (all C_12 all B_23 all A_23 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_23),A_23)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_23),C_12)),hAPP_int_int(times_times_int(B_23),C_12)))))) # label(fact_597_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 596 (all C_11 all B_22 all A_22 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_22),A_22)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_11),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_11),A_22)),hAPP_real_real(times_times_real(C_11),B_22)))))) # label(fact_598_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 597 (all C_11 all B_22 all A_22 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_22),A_22)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_11),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_11),A_22)),hAPP_int_int(times_times_int(C_11),B_22)))))) # label(fact_599_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 598 (all C_10 all D_4 all A_21 all B_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_21)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_10),D_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_21)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_10)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_21),C_10)),hAPP_nat_nat(times_times_nat(B_21),D_4)))))))) # label(fact_600_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 599 (all C_10 all D_4 all A_21 all B_21 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_21),B_21)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_10),D_4)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_21)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_10)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_21),C_10)),hAPP_real_real(times_times_real(B_21),D_4)))))))) # label(fact_601_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 600 (all C_10 all D_4 all A_21 all B_21 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_21),B_21)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_10),D_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_21)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_21),C_10)),hAPP_int_int(times_times_int(B_21),D_4)))))))) # label(fact_602_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 601 (all C_9 all D_3 all A_20 all B_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_20)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_9),D_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_20)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_20),C_9)),hAPP_nat_nat(times_times_nat(B_20),D_3)))))))) # label(fact_603_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 602 (all C_9 all D_3 all A_20 all B_20 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_20),B_20)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_9),D_3)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_20)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_9)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_20),C_9)),hAPP_real_real(times_times_real(B_20),D_3)))))))) # label(fact_604_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 603 (all C_9 all D_3 all A_20 all B_20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_20),B_20)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_9),D_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_20)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_9)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_20),C_9)),hAPP_int_int(times_times_int(B_20),D_3)))))))) # label(fact_605_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 604 (all B_19 all A_19 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_19)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_19)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_19),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_19),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_19),B_19))))) # label(fact_606_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 605 (all B_19 all A_19 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_19)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_19)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_19),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_19),B_19))))) # label(fact_607_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 606 (all B_18 all A_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_18)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_18),zero_zero_nat)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_18),zero_zero_nat)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_18),B_18)),zero_zero_nat)))) # label(fact_608_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 607 (all B_18 all A_18 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_18)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_18),zero_zero_real)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_18),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_18)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_18),B_18)),zero_zero_real)))) # label(fact_609_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 608 (all B_18 all A_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_18)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_18),zero_zero_int)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_18),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_18)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_18),B_18)),zero_zero_int)))) # label(fact_610_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 609 (all A_17 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_17),A_17)),zero_zero_real))) # label(fact_611_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 610 (all A_17 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_17),A_17)),zero_zero_int))) # label(fact_612_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 611 (all Aa all C_1 all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(Aa),C_1)),hAPP_real_real(times_times_real(Ba),C_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_1),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),Aa)))) # label(fact_613_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 612 (all Aa all C_1 all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(Aa),C_1)),hAPP_int_int(times_times_int(Ba),C_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_1),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa)))) # label(fact_614_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 613 (all C_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_1),Aa)),hAPP_real_real(times_times_real(C_1),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_1),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),Aa)))) # label(fact_615_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 614 (all C_1 all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_1),Aa)),hAPP_int_int(times_times_int(C_1),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_1),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa)))) # label(fact_616_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 615 (all Aa all Ba all C_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_1),Aa)),hAPP_real_real(times_times_real(C_1),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba))))) # label(fact_617_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 616 (all Aa all Ba all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_1),Aa)),hAPP_int_int(times_times_int(C_1),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba))))) # label(fact_618_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 617 (all B_17 all A_16 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_16)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_16),B_17)))))) # label(fact_619_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 618 (all B_17 all A_16 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_16)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_17)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_16),B_17)))))) # label(fact_620_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 619 (all B_17 all A_16 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_16)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_17)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_16),B_17)))))) # label(fact_621_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 620 (all B_16 all A_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_15)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_16),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_15),B_16)),zero_zero_nat))))) # label(fact_622_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 621 (all B_16 all A_15 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_15)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_16),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_15),B_16)),zero_zero_real))))) # label(fact_623_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 622 (all B_16 all A_15 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_15)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_16),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_15),B_16)),zero_zero_int))))) # label(fact_624_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 623 (all B_15 all A_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_14)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_15),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(B_15),A_14)),zero_zero_nat))))) # label(fact_625_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 624 (all B_15 all A_14 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_14)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_15),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(B_15),A_14)),zero_zero_real))))) # label(fact_626_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 625 (all B_15 all A_14 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_14)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_15),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(B_15),A_14)),zero_zero_int))))) # label(fact_627_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 626 (all A_13 all B_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_13),B_14))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_13)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_14))))) # label(fact_628_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 627 (all A_13 all B_14 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_13),B_14))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_13)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_14))))) # label(fact_629_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 628 (all A_13 all B_14 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_13),B_14))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_14))))) # label(fact_630_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 629 (all B_13 all A_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(B_13),A_12))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_12)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_13))))) # label(fact_631_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 630 (all B_13 all A_12 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(B_13),A_12))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_12)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_13))))) # label(fact_632_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 631 (all B_13 all A_12 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(B_13),A_12))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_13))))) # label(fact_633_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 632 (all Aa all Ba all C_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_1),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_1),Aa)),hAPP_real_real(times_times_real(C_1),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),Aa))))) # label(fact_634_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 633 (all Aa all Ba all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_1),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_1),Aa)),hAPP_int_int(times_times_int(C_1),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa))))) # label(fact_635_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 634 (all B_12 all A_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_11),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_12)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_11),B_12)),zero_zero_nat))))) # label(fact_636_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 635 (all B_12 all A_11 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_11),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_12)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_11),B_12)),zero_zero_real))))) # label(fact_637_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 636 (all B_12 all A_11 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_11),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_11),B_12)),zero_zero_int))))) # label(fact_638_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 637 (all B_11 all A_10 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_10),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_11),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_10),B_11)))))) # label(fact_639_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 638 (all B_11 all A_10 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_10),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_11),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_10),B_11)))))) # label(fact_640_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 639 (all C_8 all A_9 all B_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_9),B_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_9),C_8)),hAPP_nat_nat(times_times_nat(B_10),C_8)))))) # label(fact_641_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 640 (all C_8 all A_9 all B_10 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_9),B_10)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_8)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_9),C_8)),hAPP_real_real(times_times_real(B_10),C_8)))))) # label(fact_642_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 641 (all C_8 all A_9 all B_10 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_9),B_10)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_9),C_8)),hAPP_int_int(times_times_int(B_10),C_8)))))) # label(fact_643_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 642 (all C_7 all A_8 all B_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_8),B_9)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(C_7),A_8)),hAPP_nat_nat(times_times_nat(C_7),B_9)))))) # label(fact_644_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 643 (all C_7 all A_8 all B_9 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_8),B_9)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_7)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_7),A_8)),hAPP_real_real(times_times_real(C_7),B_9)))))) # label(fact_645_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 644 (all C_7 all A_8 all B_9 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_8),B_9)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_7)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_7),A_8)),hAPP_int_int(times_times_int(C_7),B_9)))))) # label(fact_646_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 645 (all C_6 all A_7 all B_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_7),B_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(C_6),A_7)),hAPP_nat_nat(times_times_nat(C_6),B_8)))))) # label(fact_647_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 646 (all C_6 all A_7 all B_8 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_7),B_8)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_6)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_6),A_7)),hAPP_real_real(times_times_real(C_6),B_8)))))) # label(fact_648_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 647 (all C_6 all A_7 all B_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_7),B_8)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_6),A_7)),hAPP_int_int(times_times_int(C_6),B_8)))))) # label(fact_649_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 648 (all C_5 all B_7 all A_6 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_7),A_6)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_5),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_6),C_5)),hAPP_real_real(times_times_real(B_7),C_5)))))) # label(fact_650_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 649 (all C_5 all B_7 all A_6 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_7),A_6)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_5),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_6),C_5)),hAPP_int_int(times_times_int(B_7),C_5)))))) # label(fact_651_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 650 (all C_4 all B_6 all A_5 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_6),A_5)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_4),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_4),A_5)),hAPP_real_real(times_times_real(C_4),B_6)))))) # label(fact_652_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 651 (all C_4 all B_6 all A_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_6),A_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_4),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_4),A_5)),hAPP_int_int(times_times_int(C_4),B_6)))))) # label(fact_653_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 652 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(Aa),Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)))) # label(fact_654_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 653 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(Aa),Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)))) # label(fact_655_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 654 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(Aa),Aa)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)))) # label(fact_656_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 655 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(Aa),Aa)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int)))) # label(fact_657_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 656 (all B_5 all A_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(A_4),B_5)))))) # label(fact_658_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 657 (all B_5 all A_4 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_4)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_5)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(A_4),B_5)))))) # label(fact_659_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.91 658 (all B_5 all A_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(A_4),B_5)))))) # label(fact_660_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 659 (all Y_1 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_1)) -> (hAPP_nat_nat(plus_plus_nat(X_1),Y_1) = zero_zero_nat <-> X_1 = zero_zero_nat & Y_1 = zero_zero_nat)))) # label(fact_661_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 660 (all Y_1 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_1)) -> (hAPP_real_real(plus_plus_real(X_1),Y_1) = zero_zero_real <-> X_1 = zero_zero_real & Y_1 = zero_zero_real)))) # label(fact_662_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 661 (all Y_1 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1)) -> (hAPP_int_int(plus_plus_int(X_1),Y_1) = zero_zero_int <-> X_1 = zero_zero_int & Y_1 = zero_zero_int)))) # label(fact_663_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 662 (all B_4 all C_3 all A_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_4),C_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_4),hAPP_nat_nat(plus_plus_nat(A_3),C_3)))))) # label(fact_664_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 663 (all B_4 all C_3 all A_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_3)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_4),C_3)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_4),hAPP_real_real(plus_plus_real(A_3),C_3)))))) # label(fact_665_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 664 (all B_4 all C_3 all A_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_4),C_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_4),hAPP_int_int(plus_plus_int(A_3),C_3)))))) # label(fact_666_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 665 (all B_3 all A_2 all C_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_3),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_3),hAPP_nat_nat(plus_plus_nat(A_2),C_2)))))) # label(fact_667_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 666 (all B_3 all A_2 all C_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_3),A_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_3),hAPP_real_real(plus_plus_real(A_2),C_2)))))) # label(fact_668_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 667 (all B_3 all A_2 all C_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_3),A_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_3),hAPP_int_int(plus_plus_int(A_2),C_2)))))) # label(fact_669_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 668 (all B_2 all A_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_1),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(A_1),B_2)),zero_zero_nat))))) # label(fact_670_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 669 (all B_2 all A_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_2),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(A_1),B_2)),zero_zero_real))))) # label(fact_671_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 670 (all B_2 all A_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_1),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(A_1),B_2)),zero_zero_int))))) # label(fact_672_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 671 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(Aa),Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Aa)))) # label(fact_673_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 672 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(Aa),Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa)))) # label(fact_674_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 673 (all A all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),A)) -> (X != hAPP_int_int(minus_minus_int(A),one_one_int) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),hAPP_int_int(minus_minus_int(A),one_one_int))))))) # label(fact_675_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 674 (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(times_times_int(K),I)),hAPP_int_int(times_times_int(K),J)))))) # label(fact_677_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 675 (all Z_1 hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),Z_1)),Z_1) != zero_zero_int) # label(fact_678_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 676 (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(minus_minus_int(K_1),L)),zero_zero_int)))) # label(fact_679_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 677 (all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z)))) # label(fact_680_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 678 (all N_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (hAPP_int_int(times_times_int(M_1),N_2) = one_one_int <-> M_1 = one_one_int & N_2 = one_one_int))) # label(fact_681_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 679 (all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),Z)),Z)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),zero_zero_int)))) # label(fact_682_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 680 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),Z_1))))) # label(fact_683_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 681 (all R all Q all A (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) -> (A = hAPP_int_int(plus_plus_int(R),hAPP_int_int(times_times_int(A),Q)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q),one_one_int)))))) # label(fact_684_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 682 (all R all Q all A (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) -> (A = hAPP_int_int(plus_plus_int(R),hAPP_int_int(times_times_int(A),Q)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R),A)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q)))))) # label(fact_685_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 683 (all B all Q all R all B_1 all Q_1 all R_1 (hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q)),R) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_1)),R_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_1)),R_1)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q))))))))) # label(fact_686_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 684 (all B all Q_1 all R_1 all Q all R (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q)),R))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q),Q_1))))))) # label(fact_687_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 685 (all B all Q all R all B_1 all Q_1 all R_1 (hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q)),R) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_1)),R_1) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_1)),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q),Q_1))))))))) # label(fact_688_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 686 (all B all Q_1 all R_1 all Q all R (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q)),R))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q))))))) # label(fact_689_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 687 (all B_1 all Q_1 all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_1)),R_1)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),zero_zero_int)))))) # label(fact_690_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 688 (all B_1 all Q_1 all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_1)),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_1)))))) # label(fact_691_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 689 (all M all R all S all T all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> (xzgcd(M,N_1) = produc282740534nt_int(R,product_Pair_int_int(S,T)) -> R = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(S),M)),hAPP_int_int(times_times_int(T),N_1))))) # label(fact_692_xzgcd__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 690 (all M all N_1 all R_1 all S_1 all S all T_1 all T all Rn all Sn all Tn all R (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),R)) -> (xzgcda(M,N_1,R_1,R,S_1,S,T_1,T) = produc282740534nt_int(Rn,product_Pair_int_int(Sn,Tn)) -> (R_1 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(S_1),M)),hAPP_int_int(times_times_int(T_1),N_1)) -> (R = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(S),M)),hAPP_int_int(times_times_int(T),N_1)) -> Rn = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Sn),M)),hAPP_int_int(times_times_int(Tn),N_1))))))) # label(fact_693_xzgcda__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 691 (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(plus_plus_int(X),Y)))))) # label(fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 692 (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(times_times_int(X),Y)))))) # label(fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 693 (all B all A (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A),B))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))))) # label(fact_696_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 694 (all M all N_1 xzgcd(M,N_1) = xzgcda(M,N_1,M,N_1,one_one_int,zero_zero_int,zero_zero_int,one_one_int)) # label(fact_699_xzgcd__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 695 (all K_1 all P_1 all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_2)) -> ((all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(minus_minus_int(X_2),D_2))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> (all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(minus_minus_int(X_2),hAPP_int_int(times_times_int(K_1),D_2)))))))))) # label(fact_700_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 696 (all K_1 all P_1 all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_2)) -> ((all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(plus_plus_int(X_2),D_2))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> (all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(plus_plus_int(X_2),hAPP_int_int(times_times_int(K_1),D_2)))))))))) # label(fact_701_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 697 (all A all B all Q all R (A = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q)),R) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R),B))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R),zero_zero_int))) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,B),product_Pair_int_int(Q,R)))))) # label(fact_702_divmod__int__relI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 698 (all Y all X ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> nat_tsub(X,Y) = hAPP_int_int(minus_minus_int(X),Y)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> nat_tsub(X,Y) = zero_zero_int))) # label(fact_703_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 699 (all B (B != zero_zero_int -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(zero_zero_int,B),product_Pair_int_int(zero_zero_int,zero_zero_int))))) # label(fact_704_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 700 (all A all Q all R (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,A),product_Pair_int_int(Q,R))) -> (A != zero_zero_int -> R = zero_zero_int))) # label(fact_705_self__remainder) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 701 (all Q_1 all R_1 all A all B all Q all R (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,B),product_Pair_int_int(Q,R))) -> (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,B),product_Pair_int_int(Q_1,R_1))) -> (B != zero_zero_int -> Q = Q_1)))) # label(fact_706_unique__quotient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 702 (all Q_1 all R_1 all A all B all Q all R (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,B),product_Pair_int_int(Q,R))) -> (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,B),product_Pair_int_int(Q_1,R_1))) -> (B != zero_zero_int -> R = R_1)))) # label(fact_707_unique__remainder) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 703 (all A all Q all R (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,A),product_Pair_int_int(Q,R))) -> (A != zero_zero_int -> Q = one_one_int))) # label(fact_708_self__quotient) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 704 (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),nat_tsub(X,Y)))))) # label(fact_709_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 705 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> nat_tsub(X,Y) = hAPP_int_int(minus_minus_int(X),Y))) # label(fact_710_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 706 (all P_2 all P_1 all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P_1) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P_2)))) # label(fact_711_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 707 (all P_2 all P_1 all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P_1)) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P_2))))) # label(fact_712_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 708 (all P_1 all P1 all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_2)) -> ((all X_2 all K_2 (hBOOL(hAPP_int_bool(P1,X_2)) <-> hBOOL(hAPP_int_bool(P1,hAPP_int_int(minus_minus_int(X_2),hAPP_int_int(times_times_int(K_2),D_2)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z_3)) -> (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P1,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(P_1,X1)))))))) # label(fact_713_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 709 (all P_1 all P_2 all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_2)) -> ((all X_2 all K_2 (hBOOL(hAPP_int_bool(P_2,X_2)) <-> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(X_2),hAPP_int_int(times_times_int(K_2),D_2)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),X_2)) -> (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_2,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_2,X1))) -> (exists X1 hBOOL(hAPP_int_bool(P_1,X1)))))))) # label(fact_714_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 710 (all N_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int)) -> zfact(N_1) = one_one_int) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int)) -> zfact(N_1) = hAPP_int_int(times_times_int(N_1),zfact(hAPP_int_int(minus_minus_int(N_1),one_one_int)))))) # label(fact_715_zfact_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 711 (all B all A (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(archim1246769320r_real(A)),archim1246769320r_real(B))),archim1246769320r_real(hAPP_real_real(times_times_real(A),B))))))) # label(fact_716_le__mult__floor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 712 (all B all A (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A,B),posDivAlg(A,B)))))) # label(fact_717_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 713 (all Z_1 all X all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),hAPP_int_int(plus_plus_int(X),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(abs_abs_int(hAPP_int_int(minus_minus_int(X),Z_1))),one_one_int)),D_1)))))) # label(fact_718_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 714 (all X all Z_1 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(X),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(abs_abs_int(hAPP_int_int(minus_minus_int(X),Z_1))),one_one_int)),D_1))),Z_1)))) # label(fact_719_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 715 (all W_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W_1),W_1))) # label(fact_720_real__le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 716 (all Z_1 all W_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_1),W_1)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W_1),Z_1)))) # label(fact_721_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 717 (all Z_1 all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(Z_1),X)),hAPP_real_real(plus_plus_real(Z_1),Y))))) # label(fact_722_real__add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 718 (all K all I all J (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I),J)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,J),K)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I),K))))) # label(fact_723_real__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 719 (all Z_1 all W_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_1),W_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W_1),Z_1)) -> Z_1 = W_1))) # label(fact_724_real__le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 720 (all Z1 all Z2 all W_1 hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(Z1),Z2)),W_1) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Z1),W_1)),hAPP_real_real(times_times_real(Z2),W_1))) # label(fact_725_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 721 (all Z1 all Z2 all Z3 hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Z1),Z2)),Z3) = hAPP_real_real(times_times_real(Z1),hAPP_real_real(times_times_real(Z2),Z3))) # label(fact_726_real__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 722 (all Z_1 all W_1 hAPP_real_real(times_times_real(Z_1),W_1) = hAPP_real_real(times_times_real(W_1),Z_1)) # label(fact_727_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 723 (all Z_1 hAPP_real_real(times_times_real(one_one_real),Z_1) = Z_1) # label(fact_728_real__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 724 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) | X_1 = Y_1)) # label(fact_729_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 725 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) & X_1 != Y_1)) # label(fact_730_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 726 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X_1),Y_1)),zero_zero_real)))) # label(fact_731_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 727 (all Aa all Ba all C_1 (C_1 != zero_zero_real -> (hAPP_real_real(times_times_real(C_1),Aa) = hAPP_real_real(times_times_real(C_1),Ba) <-> Aa = Ba))) # label(fact_732_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 728 (all Aa all Ba all C_1 (C_1 != zero_zero_real -> (hAPP_real_real(times_times_real(Aa),C_1) = hAPP_real_real(times_times_real(Ba),C_1) <-> Aa = Ba))) # label(fact_733_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 729 (all X_1 all Y_1 (hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_1),X_1)),hAPP_real_real(times_times_real(Y_1),Y_1)) = zero_zero_real <-> X_1 = zero_zero_real & Y_1 = zero_zero_real)) # label(fact_734_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 730 (all X_1 all Y_1 all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X_1),Z)),hAPP_real_real(times_times_real(Y_1),Z))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1))))) # label(fact_736_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 731 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X),Y)))))) # label(fact_737_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 732 (all X all Y all Z_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(Z_1),X)),hAPP_real_real(times_times_real(Z_1),Y)))))) # label(fact_738_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 733 (all X_1 all Y_1 all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(Z),X_1)),hAPP_real_real(times_times_real(Z),Y_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1))))) # label(fact_739_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 734 (all X_1 all Y_1 all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X_1),Z)),hAPP_real_real(times_times_real(Y_1),Z))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1))))) # label(fact_740_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 735 (all M all N_1 (abs_abs_int(hAPP_int_int(times_times_int(M),N_1)) = one_one_int -> abs_abs_int(M) = one_one_int)) # label(fact_741_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 736 (all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(Z)),one_one_int)) <-> Z = zero_zero_int)) # label(fact_742_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 737 (all B posDivAlg(zero_zero_int,B) = product_Pair_int_int(zero_zero_int,zero_zero_int)) # label(fact_743_posDivAlg__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 738 (all K all L_1 ((L_1 = zero_zero_int -> pdivmod(K,L_1) = product_Pair_int_int(zero_zero_int,abs_abs_int(K))) & (L_1 != zero_zero_int -> pdivmod(K,L_1) = posDivAlg(abs_abs_int(K),abs_abs_int(L_1))))) # label(fact_744_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 739 (all K_1 all F all N_2 all M_1 ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),I_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(F,hAPP_nat_nat(plus_plus_nat(I_2),one_one_nat))),hAPP_nat_int(F,I_2)))),one_one_int)))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,M_1)),K_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),hAPP_nat_int(F,N_2))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),I_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N_2)) & hAPP_nat_int(F,I_2) = K_1))))))) # label(fact_745_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 740 (all K_1 all F all N_2 ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(F,hAPP_nat_nat(plus_plus_nat(I_2),one_one_nat))),hAPP_nat_int(F,I_2)))),one_one_int)))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),hAPP_nat_int(F,N_2))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N_2)) & hAPP_nat_int(F,I_2) = K_1)))))) # label(fact_746_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 741 (all K_1 all F all N_2 ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(minus_minus_int(hAPP_nat_int(F,hAPP_nat_nat(plus_plus_nat(I_2),one_one_nat))),hAPP_nat_int(F,I_2)))),one_one_int)))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),hAPP_nat_int(F,N_2))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N_2)) & hAPP_nat_int(F,I_2) = K_1)))))) # label(fact_747_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 742 (all N_1 all M ((M = zero_zero_nat -> hAPP_nat_nat(times_times_nat(M),N_1) = zero_zero_nat) & (M != zero_zero_nat -> hAPP_nat_nat(times_times_nat(M),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N_1))))) # label(fact_748_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 743 (all X -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(abs_abs_real(X)),one_one_real)),X))) # label(fact_749_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 744 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),abs_abs_real(X))))) # label(fact_750_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 745 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_751_le0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 746 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_752_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 747 (all U_1 all V all X all Y (X = Y -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,abs_abs_real(U_1)),V)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,abs_abs_real(hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(X),U_1)),Y))),V))))) # label(fact_753_sin__bound__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 748 (all U all M_1 all N_2 all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U)),M_1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_1)),U)),N_2)))))) # label(fact_754_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 749 (all K all M all N_1 hAPP_nat_nat(times_times_nat(K),hAPP_nat_nat(minus_minus_nat(M),N_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(K),M)),hAPP_nat_nat(times_times_nat(K),N_1))) # label(fact_755_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 750 (all M all N_1 all K hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),K) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(M),K)),hAPP_nat_nat(times_times_nat(N_1),K))) # label(fact_756_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 751 (all I all J all K hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J)),K) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),K)),J)) # label(fact_757_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 752 (all M all N_1 hAPP_nat_nat(times_times_nat(M),N_1) = hAPP_nat_nat(times_times_nat(N_1),M)) # label(fact_758_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 753 (all M all N_1 all K hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(M),N_1)),K) = hAPP_nat_nat(times_times_nat(M),hAPP_nat_nat(times_times_nat(N_1),K))) # label(fact_759_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 754 (all N_1 hAPP_nat_nat(times_times_nat(zero_zero_nat),N_1) = zero_zero_nat) # label(fact_760_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 755 (all M hAPP_nat_nat(times_times_nat(M),zero_zero_nat) = zero_zero_nat) # label(fact_761_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 756 (all M_1 all N_2 (hAPP_nat_nat(times_times_nat(M_1),N_2) = zero_zero_nat <-> M_1 = zero_zero_nat | N_2 = zero_zero_nat)) # label(fact_762_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 757 (all K_1 all M_1 all N_2 (hAPP_nat_nat(times_times_nat(K_1),M_1) = hAPP_nat_nat(times_times_nat(K_1),N_2) <-> K_1 = zero_zero_nat | M_1 = N_2)) # label(fact_763_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 758 (all K_1 all M_1 all N_2 (hAPP_nat_nat(times_times_nat(K_1),M_1) = hAPP_nat_nat(times_times_nat(K_1),N_2) <-> M_1 = N_2 | K_1 = zero_zero_nat)) # label(fact_764_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 759 (all M_1 all K_1 all N_2 (hAPP_nat_nat(times_times_nat(M_1),K_1) = hAPP_nat_nat(times_times_nat(N_2),K_1) <-> M_1 = N_2 | K_1 = zero_zero_nat)) # label(fact_765_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 760 (all M all N_1 (hAPP_nat_nat(minus_minus_nat(M),N_1) = zero_zero_nat -> (hAPP_nat_nat(minus_minus_nat(N_1),M) = zero_zero_nat -> M = N_1))) # label(fact_766_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 761 (all M hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat) # label(fact_767_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 762 (all M hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M) # label(fact_768_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 763 (all N_1 hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N_1) = zero_zero_nat) # label(fact_769_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 764 (all P_1 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(P_1,N_2),M_1))) -> ((M_1 = N_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_2),M_1))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_2),M_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_2),M_1)))))) # label(fact_770_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 765 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_771_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 766 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)) -> M != N_1)) # label(fact_772_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 767 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_773_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 768 (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_774_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 769 (all M_1 all N_2 (M_1 != 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,N_2),M_1)))) # label(fact_775_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 770 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_776_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 771 (all L_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> (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(minus_minus_nat(L_1),N_1)),hAPP_nat_nat(minus_minus_nat(L_1),M)))))) # label(fact_777_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 772 (all N_1 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(minus_minus_nat(J),N_1)),K)))) # label(fact_778_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 773 (all M all N_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),N_1) = M) # label(fact_779_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 774 (all N_1 all M hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N_1),M)),N_1) = M) # label(fact_780_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 775 (all I all J all K hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J)),K) = hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(plus_plus_nat(J),K))) # label(fact_781_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 776 (all K all M all N_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K),M)),hAPP_nat_nat(plus_plus_nat(K),N_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1)) # label(fact_782_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 777 (all M all K all N_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(plus_plus_nat(N_1),K)) = hAPP_nat_nat(minus_minus_nat(M),N_1)) # label(fact_783_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 778 (all M_1 all K_1 all N_2 (hAPP_nat_nat(plus_plus_nat(M_1),K_1) = hAPP_nat_nat(plus_plus_nat(N_2),K_1) <-> M_1 = N_2)) # label(fact_784_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 779 (all K_1 all M_1 all N_2 (hAPP_nat_nat(plus_plus_nat(K_1),M_1) = hAPP_nat_nat(plus_plus_nat(K_1),N_2) <-> M_1 = N_2)) # label(fact_785_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 780 (all M all N_1 all K hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),K) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N_1),K))) # label(fact_786_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 781 (all X all Y all Z_1 hAPP_nat_nat(plus_plus_nat(X),hAPP_nat_nat(plus_plus_nat(Y),Z_1)) = hAPP_nat_nat(plus_plus_nat(Y),hAPP_nat_nat(plus_plus_nat(X),Z_1))) # label(fact_787_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 782 (all M all N_1 hAPP_nat_nat(plus_plus_nat(M),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),M)) # label(fact_788_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 783 (all K all M all N_1 hAPP_nat_nat(times_times_nat(K),hAPP_nat_nat(plus_plus_nat(M),N_1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K),M)),hAPP_nat_nat(times_times_nat(K),N_1))) # label(fact_789_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 784 (all M all N_1 all K hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),K) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(M),K)),hAPP_nat_nat(times_times_nat(N_1),K))) # label(fact_790_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 785 (all I all U_1 all J all K hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I),U_1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J),U_1)),K)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(I),J)),U_1)),K)) # label(fact_791_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 786 (all M all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)),M))) # label(fact_792_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 787 (all L_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L_1),N_1)),hAPP_nat_nat(minus_minus_nat(L_1),M))))) # label(fact_793_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 788 (all L_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L_1)),hAPP_nat_nat(minus_minus_nat(N_1),L_1))))) # label(fact_794_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 789 (all I all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N_1)) -> hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(minus_minus_nat(N_1),I)) = I)) # label(fact_795_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 790 (all N_2 all K_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_2)) -> (hAPP_nat_nat(minus_minus_nat(M_1),K_1) = hAPP_nat_nat(minus_minus_nat(N_2),K_1) <-> M_1 = N_2)))) # label(fact_796_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 791 (all N_1 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_1)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K)),hAPP_nat_nat(minus_minus_nat(N_1),K)) = hAPP_nat_nat(minus_minus_nat(M),N_1)))) # label(fact_797_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 792 (all N_2 all K_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_1)),hAPP_nat_nat(minus_minus_nat(N_2),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)))))) # label(fact_798_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 793 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1))) # label(fact_799_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 794 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)))) # label(fact_800_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 795 (all M all N_1 (M = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_801_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 796 (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_802_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 797 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) -> M = N_1))) # label(fact_803_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 798 (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(times_times_nat(I),K)),hAPP_nat_nat(times_times_nat(J),L_1)))))) # label(fact_804_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 799 (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(times_times_nat(K),I)),hAPP_nat_nat(times_times_nat(K),J))))) # label(fact_805_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 800 (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(times_times_nat(I),K)),hAPP_nat_nat(times_times_nat(J),K))))) # label(fact_806_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 801 (all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(times_times_nat(M),hAPP_nat_nat(times_times_nat(M),M))))) # label(fact_807_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 802 (all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(times_times_nat(M),M)))) # label(fact_808_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 803 (all N_1 hAPP_nat_nat(times_times_nat(one_one_nat),N_1) = N_1) # label(fact_809_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 804 (all M_1 all N_2 (one_one_nat = hAPP_nat_nat(times_times_nat(M_1),N_2) <-> M_1 = one_one_nat & N_2 = one_one_nat)) # label(fact_810_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 805 (all N_1 hAPP_nat_nat(times_times_nat(N_1),one_one_nat) = N_1) # label(fact_811_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 806 (all M_1 all N_2 (hAPP_nat_nat(times_times_nat(M_1),N_2) = one_one_nat <-> M_1 = one_one_nat & N_2 = one_one_nat)) # label(fact_812_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 807 (all N_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(N_2),M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_813_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 808 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)),M))))) # label(fact_814_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 809 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_815_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 810 (all N_2 (N_2 != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)))) # label(fact_816_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 811 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_817_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 812 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> N_1 != zero_zero_nat)) # label(fact_818_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 813 (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_819_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 814 (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,zero_zero_nat),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),I)),hAPP_nat_nat(times_times_nat(K),J)))))) # label(fact_820_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 815 (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,zero_zero_nat),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(I),K)),hAPP_nat_nat(times_times_nat(J),K)))))) # label(fact_821_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 816 (all M_1 all N_2 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K_1),M_1)),hAPP_nat_nat(times_times_nat(K_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2))))) # label(fact_822_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 817 (all M_1 all N_2 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hAPP_nat_nat(times_times_nat(K_1),M_1) = hAPP_nat_nat(times_times_nat(K_1),N_2) <-> M_1 = N_2))) # label(fact_823_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 818 (all M_1 all K_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(M_1),K_1)),hAPP_nat_nat(times_times_nat(N_2),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_824_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 819 (all K_1 all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K_1),M_1)),hAPP_nat_nat(times_times_nat(K_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_825_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 820 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(M_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)))) # label(fact_826_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 821 (all N_1 hAPP_nat_nat(plus_plus_nat(zero_zero_nat),N_1) = N_1) # label(fact_827_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 822 (all M hAPP_nat_nat(plus_plus_nat(M),zero_zero_nat) = M) # label(fact_828_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 823 (all M_1 all N_2 (hAPP_nat_nat(plus_plus_nat(M_1),N_2) = zero_zero_nat <-> M_1 = zero_zero_nat & N_2 = zero_zero_nat)) # label(fact_829_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 824 (all M all N_1 (hAPP_nat_nat(plus_plus_nat(M),N_1) = M -> N_1 = zero_zero_nat)) # label(fact_830_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 825 (all N_1 all M hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(plus_plus_nat(N_1),M)) = zero_zero_nat) # label(fact_831_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 826 (all M_1 all N_2 (hAPP_nat_nat(minus_minus_nat(M_1),N_2) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)))) # label(fact_832_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 827 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> hAPP_nat_nat(minus_minus_nat(M),N_1) = zero_zero_nat)) # label(fact_833_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 828 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_834_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 829 (all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),zero_zero_nat)) <-> N_2 = zero_zero_nat)) # label(fact_835_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 830 (all I all J -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J)),I))) # label(fact_836_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 831 (all J all I -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J),I)),I))) # label(fact_837_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 832 (all K_1 all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K_1),M_1)),hAPP_nat_nat(plus_plus_nat(K_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_838_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 833 (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(plus_plus_nat(J),M))))) # label(fact_839_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 834 (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(plus_plus_nat(M),J))))) # label(fact_840_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 835 (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(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J),K))))) # label(fact_841_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 836 (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(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J),L_1)))))) # label(fact_842_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 837 (all M all N_1 all K all L_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L_1)) -> (hAPP_nat_nat(plus_plus_nat(M),L_1) = hAPP_nat_nat(plus_plus_nat(K),N_1) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))))) # label(fact_843_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 838 (all I all J all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J)),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)))) # label(fact_844_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 839 (all M all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = M)) # label(fact_845_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 840 (all I_1 all J_2 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_2),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),J_2)))) # label(fact_846_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 841 (all M all N_1 (M = hAPP_nat_nat(times_times_nat(M),N_1) -> N_1 = one_one_nat | M = zero_zero_nat)) # label(fact_847_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 842 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) | M = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_848_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 843 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> (M != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))))) # label(fact_849_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 844 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_850_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 845 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)) | M_1 = N_2)) # label(fact_851_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 846 (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_eq_nat,M_1),N_2)) & M_1 != N_2)) # label(fact_852_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 847 (all N_2 all K_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_1)),hAPP_nat_nat(minus_minus_nat(N_2),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))))) # label(fact_853_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 848 (all C all A all B (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C)))))) # label(fact_854_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 849 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(minus_minus_nat(J),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),K)),J))) # label(fact_855_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 850 (all J_2 all K_1 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_2),K_1)),I_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(plus_plus_nat(I_1),K_1))))) # label(fact_856_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 851 (all M all K all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N_1),M)),K))))) # label(fact_857_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 852 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) -> hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = M)) # label(fact_858_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 853 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J)),K))) # label(fact_859_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 854 (all I_1 all K_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_2),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),J_2))))) # label(fact_860_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 855 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) -> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1) = M)) # label(fact_861_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 856 (all K_1 all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hAPP_nat_nat(minus_minus_nat(J_2),I_1) = K_1 <-> J_2 = hAPP_nat_nat(plus_plus_nat(K_1),I_1)))) # label(fact_862_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 857 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J)),K) = hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J),K)))) # label(fact_863_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 858 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J),K)),I) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J),I)),K))) # label(fact_864_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 859 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J),I)),K) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J),K)),I))) # label(fact_865_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 860 (all U all M_1 all N_2 all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U)),M_1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N_2) <-> M_1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_1)),U)),N_2)))) # label(fact_866_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 861 (all U_1 all M all N_1 all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I),U_1)),M)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J),U_1)),N_1)) = hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J),I)),U_1)),N_1)))) # label(fact_867_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 862 (all U all M_1 all N_2 all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U)),M_1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_1)),U)),N_2)))))) # label(fact_868_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 863 (all U all M_1 all N_2 all J_2 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_1)) -> (hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U)),M_1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N_2) <-> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_2)),U)),M_1) = N_2))) # label(fact_869_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 864 (all U_1 all M all N_1 all J all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I),U_1)),M)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J),U_1)),N_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I),J)),U_1)),M)),N_1))) # label(fact_870_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 865 (all U all M_1 all N_2 all J_2 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U)),M_1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_2)),U)),M_1)),N_2))))) # label(fact_871_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 866 (all M all K all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N_1)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_1))))) # label(fact_872_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 867 (all M all K all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_873_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 868 (all M all K all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_1)))) # label(fact_874_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 869 (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(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J),L_1)))))) # label(fact_875_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.92 870 (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(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J),K))))) # label(fact_876_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 871 (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(plus_plus_nat(M),J))))) # label(fact_877_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 872 (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(plus_plus_nat(J),M))))) # label(fact_878_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 873 (all K_1 all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K_1),M_1)),hAPP_nat_nat(plus_plus_nat(K_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)))) # label(fact_879_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 874 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)) <-> (exists K_2 N_2 = hAPP_nat_nat(plus_plus_nat(M_1),K_2)))) # label(fact_880_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 875 (all N_1 all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(N_1),M)))) # label(fact_881_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 876 (all N_1 all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(M),N_1)))) # label(fact_882_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 877 (all X_1 all Y_1 all Z (X_1 = hAPP_real_real(minus_minus_real(Y_1),Z) <-> Y_1 = hAPP_real_real(plus_plus_real(X_1),Z))) # label(fact_883_eq__diff__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 878 (all P_1 all Aa all Ba (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(minus_minus_nat(Aa),Ba))) <-> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) & -hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) | (exists D (Aa = hAPP_nat_nat(plus_plus_nat(Ba),D) & -hBOOL(hAPP_nat_bool(P_1,D))))))) # label(fact_884_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 879 (all P_1 all Aa all Ba (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(minus_minus_nat(Aa),Ba))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))) & (all D (Aa = hAPP_nat_nat(plus_plus_nat(Ba),D) -> hBOOL(hAPP_nat_bool(P_1,D)))))) # label(fact_885_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 880 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(M_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)))) # label(fact_886_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 881 (all K_1 all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_1),M_1)),hAPP_nat_nat(times_times_nat(K_1),N_2))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2))))) # label(fact_887_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 882 (all M_1 all K_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(M_1),K_1)),hAPP_nat_nat(times_times_nat(N_2),K_1))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2))))) # label(fact_888_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 883 (all M_1 all N_2 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_1),M_1)),hAPP_nat_nat(times_times_nat(K_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2))))) # label(fact_889_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 884 (all U all M_1 all N_2 all J_2 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U)),M_1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_2)),U)),M_1)),N_2))))) # label(fact_890_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 885 (all N_2 all P_1 (-hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(P_1,N_2)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),N_2)) & (all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2)) -> -hBOOL(hAPP_nat_bool(P_1,I_2)))) & hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(plus_plus_nat(K_2),one_one_nat)))))))) # label(fact_891_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 886 (all X all Y all C (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,abs_abs_real(X)),hAPP_real_real(times_times_real(C),abs_abs_real(Y)))) -> X = zero_zero_real))) # label(fact_892_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 887 (all M_1 all K_1 all F ((all M_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F,M_1)),K_1)),hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(M_1),K_1)))))) # label(fact_893_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 888 (all N_2 all P_1 (-hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(P_1,N_2)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2)) & (all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) -> -hBOOL(hAPP_nat_bool(P_1,I_2)))) & hBOOL(hAPP_nat_bool(P_1,K_2))))))) # label(fact_894_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 889 (all K_1 all L (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L)) <-> (exists N L = hAPP_nat_nat(plus_plus_nat(K_1),N)))) # label(fact_895_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 890 (all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) & hAPP_nat_nat(plus_plus_nat(I),K_2) = J)))) # label(fact_896_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 891 (all X_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X_1),X_1))) <-> X_1 = zero_zero_real)) # label(fact_897_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 892 (all N_1 all M all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hAPP_nat_nat(times_times_nat(K),N_1) = hAPP_nat_nat(times_times_nat(K),M) -> N_1 = M))) # label(fact_898_mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 893 (all B all A all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),B)) -> (exists D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) & (all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,abs_abs_real(hAPP_real_real(minus_minus_real(X),Y_2))),D)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A),Y_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),B))))))))) # label(fact_899_lemma__interval) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 894 (all K all L_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),L_1)) -> (exists N L_1 = hAPP_nat_nat(plus_plus_nat(K),N)))) # label(fact_900_le__Suc__ex) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 895 (all I_1 all J_2 all F ((all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_2)))))) # label(fact_901_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 896 (all B all A all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),B)) -> (exists D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) & (all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,abs_abs_real(hAPP_real_real(minus_minus_real(X),Y_2))),D)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A),Y_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),B))))))))) # label(fact_902_lemma__interval__lt) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 897 (all D2 all D1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D2)) -> (exists E (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),E)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,E),D1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,E),D2))))))) # label(fact_903_real__lbound__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 898 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natceiling(hAPP_real_real(plus_plus_real(X),one_one_real)) = hAPP_nat_nat(plus_plus_nat(natceiling(X)),one_one_nat))) # label(fact_904_natceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 899 (all N_1 natceiling(number267125858f_real(N_1)) = number_number_of_nat(N_1)) # label(fact_905_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 900 (all X hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),natceiling(X)))) # label(fact_907_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 901 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X)),natceiling(Y))))) # label(fact_908_natceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 902 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> natceiling(X) = zero_zero_nat)) # label(fact_910_natceiling__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 903 (all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X_1)),one_one_nat)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),one_one_real)))) # label(fact_911_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 904 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natfloor(hAPP_real_real(plus_plus_real(X),one_one_real)) = hAPP_nat_nat(plus_plus_nat(natfloor(X)),one_one_nat))) # label(fact_912_natfloor__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 905 (all N_2 all M_1 (hAPP_nat_nat(times_times_nat(N_2),M_1) = one_one_nat <-> N_2 = one_one_nat & M_1 = one_one_nat)) # label(fact_913_nat__mult__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 906 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(plus_plus_real(hAPP_nat_real(real_nat,N_1)),one_one_real))) -> natceiling(X) = hAPP_nat_nat(plus_plus_nat(N_1),one_one_nat)))) # label(fact_914_natceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 907 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(real_nat,N_1)))) # label(fact_915_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 908 (all N_1 natceiling(hAPP_nat_real(real_nat,N_1)) = N_1) # label(fact_916_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 909 (all N_2 all M_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_2)),hAPP_nat_real(real_nat,M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_1)))) # label(fact_917_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 910 (all N_2 (hAPP_nat_real(real_nat,N_2) = zero_zero_real <-> N_2 = zero_zero_nat)) # label(fact_919_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 911 (all X abs_abs_real(hAPP_nat_real(real_nat,X)) = hAPP_nat_real(real_nat,X)) # label(fact_920_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 912 (all N_1 natfloor(hAPP_nat_real(real_nat,N_1)) = N_1) # label(fact_921_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 913 (all N_2 hBOOL(member_real(hAPP_nat_real(real_nat,N_2),ring_1_Ints_real))) # label(fact_922_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 914 (all N_1 natfloor(number267125858f_real(N_1)) = number_number_of_nat(N_1)) # label(fact_923_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 915 (all N_2 all M_1 (hAPP_nat_real(real_nat,N_2) = hAPP_nat_real(real_nat,M_1) <-> N_2 = M_1)) # label(fact_924_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 916 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,natfloor(X))),X)))) # label(fact_925_real__natfloor__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 917 (all X all A (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,X)),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),natfloor(A))))) # label(fact_926_le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 918 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(minus_minus_real(X),one_one_real)),hAPP_nat_real(real_nat,natfloor(X))))) # label(fact_927_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 919 (all A all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,A)),X)) -> natfloor(hAPP_real_real(minus_minus_real(X),hAPP_nat_real(real_nat,A))) = hAPP_nat_nat(minus_minus_nat(natfloor(X)),A))) # label(fact_928_natfloor__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 920 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(plus_plus_real(hAPP_nat_real(real_nat,natfloor(X))),one_one_real)))) # label(fact_929_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 921 (all Aa all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),natfloor(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,Aa)),X_1))))) # label(fact_930_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 922 (all N_1 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_1)),zero_zero_real))) # label(fact_931_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 923 (all N_2 all M_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N_2)),hAPP_nat_real(real_nat,M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_1)))) # label(fact_932_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 924 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_nat_real(real_nat,N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,natfloor(X)),N_1))))) # label(fact_933_less__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 925 (all M all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(times_times_nat(M),N_1)) = hAPP_real_real(times_times_real(hAPP_nat_real(real_nat,M)),hAPP_nat_real(real_nat,N_1))) # label(fact_934_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 926 (all A all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natfloor(hAPP_real_real(plus_plus_real(X),hAPP_nat_real(real_nat,A))) = hAPP_nat_nat(plus_plus_nat(natfloor(X)),A))) # label(fact_935_natfloor__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 927 (all M all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(plus_plus_nat(M),N_1)) = hAPP_real_real(plus_plus_real(hAPP_nat_real(real_nat,M)),hAPP_nat_real(real_nat,N_1))) # label(fact_936_real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 928 (all Z_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(natfloor(Z_1)),one_one_nat)),N_1)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_1),hAPP_nat_real(real_nat,N_1))))) # label(fact_937_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 929 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(plus_plus_real(hAPP_nat_real(real_nat,N_1)),one_one_real))) -> natfloor(X) = N_1))) # label(fact_938_natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 930 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_nat_real(real_nat,natceiling(X))))) # label(fact_940_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 931 (all X hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),natfloor(X)))) # label(fact_942_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 932 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natfloor(X)),natfloor(Y))))) # label(fact_943_natfloor__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 933 (all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N_2)),zero_zero_real)) <-> N_2 = zero_zero_nat)) # label(fact_945_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 934 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) -> hAPP_nat_real(real_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)) = hAPP_real_real(minus_minus_real(hAPP_nat_real(real_nat,M)),hAPP_nat_real(real_nat,N_1)))) # label(fact_946_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 935 (all X all A (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_nat_real(real_nat,A))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X)),A)))) # label(fact_947_natceiling__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 936 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> natfloor(X) = zero_zero_nat)) # label(fact_948_natfloor__neg) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 937 (all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(real_nat,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)))) # label(fact_949_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 938 (all N_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(real_nat,N_2)),one_one_real)),hAPP_nat_real(real_nat,M_1))))) # label(fact_950_nat__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 939 (all N_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_2)),hAPP_real_real(plus_plus_real(hAPP_nat_real(real_nat,M_1)),one_one_real))))) # label(fact_951_nat__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 940 (all Aa all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_nat_real(real_nat,Aa)))))) # label(fact_952_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 941 (all A all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,A)),X)) -> natceiling(hAPP_real_real(minus_minus_real(X),hAPP_nat_real(real_nat,A))) = hAPP_nat_nat(minus_minus_nat(natceiling(X)),A))) # label(fact_953_natceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 942 (all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),natfloor(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X_1)))) # label(fact_954_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 943 (all A all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natceiling(hAPP_real_real(plus_plus_real(X),hAPP_nat_real(real_nat,A))) = hAPP_nat_nat(plus_plus_nat(natceiling(X)),A))) # label(fact_955_natceiling__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 944 (all B all A (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(natfloor(A)),natfloor(B))),natfloor(hAPP_real_real(times_times_real(A),B))))))) # label(fact_956_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 945 (all R (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),R)) -> (exists N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,hAPP_nat_nat(minus_minus_nat(N),one_one_nat))),R)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),hAPP_nat_real(real_nat,N))))))) # label(fact_957_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 946 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (all Y_2 exists N hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),hAPP_real_real(times_times_real(hAPP_nat_real(real_nat,N)),X)))))) # label(fact_958_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 947 (all X all N_1 (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(N_1))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natceiling(hAPP_real_real(plus_plus_real(X),number267125858f_real(N_1))) = hAPP_nat_nat(plus_plus_nat(natceiling(X)),number_number_of_nat(N_1))))) # label(fact_959_natceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 948 (all Z_2 (hBOOL(hAPP_int_bool(nat_neg,Z_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),zero_zero_int)))) # label(fact_962_neg__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 949 (all X_1 (-hBOOL(hAPP_int_bool(nat_neg,X_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)))) # label(fact_963_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 950 (all V (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> number_number_of_nat(V) = zero_zero_nat)) # label(fact_964_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 951 (all V_1 all V_3 (number_number_of_nat(V_1) = number_number_of_nat(V_3) <-> (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_3)),zero_zero_int))) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1))) -> (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) -> number_number_of_int(V_1) = zero_zero_int) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) -> V_1 = V_3)))) # label(fact_965_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 952 (all V_2 all K all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V_2)),K)) = hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V_2)),K)) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V_2)),K)) = hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),K)) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V_2)),K)) = hAPP_nat_nat(plus_plus_nat(number_number_of_nat(hAPP_int_int(plus_plus_int(V),V_2))),K))))) # label(fact_966_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 953 (all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_real(real_nat,number_number_of_nat(V)) = zero_zero_real) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_real(real_nat,number_number_of_nat(V)) = number267125858f_real(V)))) # label(fact_967_real__of__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 954 (all X_1 all N_2 (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(N_2))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(N_2)),natfloor(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(N_2)),X_1)))))) # label(fact_968_le__natfloor__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 955 (all X_1 all N_2 (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(N_2))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X_1)),number_number_of_nat(N_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),number267125858f_real(N_2))))))) # label(fact_969_natceiling__le__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 956 (all X all N_1 (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(N_1))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natfloor(hAPP_real_real(plus_plus_real(X),number267125858f_real(N_1))) = hAPP_nat_nat(plus_plus_nat(natfloor(X)),number_number_of_nat(N_1))))) # label(fact_970_natfloor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 957 (all X exists N hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_nat_real(real_nat,N)))) # label(fact_971_reals__Archimedean2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 958 (all Y all X all Z_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z_1))))) # label(fact_972_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 959 (all Z_1 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(plus_plus_nat(Y),Z_1))))) # label(fact_973_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 960 (all Y all X all Z_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(plus_plus_nat(Y),Z_1))))) # label(fact_974_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 961 (all Z_1 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(plus_plus_nat(Y),Z_1))))) # label(fact_975_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 962 (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_976_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 963 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,N_1)),one_one_real))) -> archim856651990g_real(X) = hAPP_int_int(plus_plus_int(N_1),one_one_int)))) # label(fact_977_ceiling__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 964 (all X all Y hAPP_int_real(real_int,hAPP_int_int(plus_plus_int(X),Y)) = hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,X)),hAPP_int_real(real_int,Y))) # label(fact_978_real__of__int__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 965 (all X all A archim856651990g_real(hAPP_real_real(plus_plus_real(X),hAPP_int_real(real_int,A))) = hAPP_int_int(plus_plus_int(archim856651990g_real(X)),A)) # label(fact_979_ceiling__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 966 (all X_1 (hAPP_int_real(real_int,archim1246769320r_real(X_1)) = X_1 <-> (exists N X_1 = hAPP_int_real(real_int,N)))) # label(fact_980_real__of__int__floor__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 967 (all N_1 archim1246769320r_real(hAPP_int_real(real_int,N_1)) = N_1) # label(fact_981_floor__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 968 (all X_1 (hAPP_int_real(real_int,archim856651990g_real(X_1)) = X_1 <-> (exists N X_1 = hAPP_int_real(real_int,N)))) # label(fact_982_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 969 (all N_1 archim856651990g_real(hAPP_int_real(real_int,N_1)) = N_1) # label(fact_983_ceiling__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 970 (all V hAPP_int_real(real_int,number_number_of_int(V)) = number267125858f_real(V)) # label(fact_984_real__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 971 (all X_1 all Y_1 (hAPP_int_real(real_int,X_1) = hAPP_int_real(real_int,Y_1) <-> X_1 = Y_1)) # label(fact_985_real__of__int__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 972 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,R),hAPP_int_real(real_int,archim856651990g_real(R))))) # label(fact_986_real__of__int__ceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 973 (all X all Y hAPP_int_real(real_int,hAPP_int_int(times_times_int(X),Y)) = hAPP_real_real(times_times_real(hAPP_int_real(real_int,X)),hAPP_int_real(real_int,Y))) # label(fact_988_real__of__int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 974 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_int_real(real_int,Aa))))) # label(fact_989_ceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 975 (all X all A (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_int_real(real_int,A))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X)),A)))) # label(fact_990_ceiling__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 976 (all X all A (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X)),A)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_int_real(real_int,A))))) # label(fact_991_ceiling__le__real) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 977 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,X_1)),hAPP_int_real(real_int,Y_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)))) # label(fact_992_real__of__int__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 978 (all X_1 all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,X_1)),hAPP_int_real(real_int,Y_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)))) # label(fact_993_real__of__int__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 979 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,Aa)),X_1)))) # label(fact_994_less__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 980 (all X_1 (hAPP_int_real(real_int,X_1) = zero_zero_real <-> X_1 = zero_zero_int)) # label(fact_995_real__of__int__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 981 (all X all A archim856651990g_real(hAPP_real_real(minus_minus_real(X),hAPP_int_real(real_int,A))) = hAPP_int_int(minus_minus_int(archim856651990g_real(X)),A)) # label(fact_997_ceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 982 (all X all Y hAPP_int_real(real_int,hAPP_int_int(minus_minus_int(X),Y)) = hAPP_real_real(minus_minus_real(hAPP_int_real(real_int,X)),hAPP_int_real(real_int,Y))) # label(fact_998_real__of__int__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 983 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,archim1246769320r_real(R))),R))) # label(fact_999_real__of__int__floor__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 984 (all X hAPP_int_real(real_int,abs_abs_int(X)) = abs_abs_real(hAPP_int_real(real_int,X))) # label(fact_1000_real__of__int__abs) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 985 (all X_1 hBOOL(member_real(hAPP_int_real(real_int,X_1),ring_1_Ints_real))) # label(fact_1001_Ints__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 986 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,archim856651990g_real(R))),hAPP_real_real(plus_plus_real(R),one_one_real)))) # label(fact_1002_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 987 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(hAPP_int_real(real_int,archim856651990g_real(R))),one_one_real)),R))) # label(fact_1003_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 988 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1246769320r_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_int_real(real_int,Aa))))) # label(fact_1004_floor__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 989 (all A all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,A)),X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),archim1246769320r_real(X))))) # label(fact_1005_le__floor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 990 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,Aa)),X_1)))) # label(fact_1006_le__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 991 (all A all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),archim1246769320r_real(X))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,A)),X)))) # label(fact_1007_real__le__floor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 992 (all X all A archim1246769320r_real(hAPP_real_real(plus_plus_real(X),hAPP_int_real(real_int,A))) = hAPP_int_int(plus_plus_int(archim1246769320r_real(X)),A)) # label(fact_1008_floor__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 993 (all X all A archim1246769320r_real(hAPP_real_real(minus_minus_real(X),hAPP_int_real(real_int,A))) = hAPP_int_int(minus_minus_int(archim1246769320r_real(X)),A)) # label(fact_1009_floor__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 994 (all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_2)))) # label(fact_1010_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 995 (all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_2)),zero_zero_real)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,N_2),zero_zero_int)))) # label(fact_1011_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 996 (all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_int_real(real_int,N_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_2)))) # label(fact_1012_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 997 (all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N_2)),zero_zero_real)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_2),zero_zero_int)))) # label(fact_1013_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 998 (all N_2 all M_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(N_2)),hAPP_int_real(real_int,M_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(N_2)),M_1)))) # label(fact_1014_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 999 (all M_1 all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,M_1)),number267125858f_real(N_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,M_1),number_number_of_int(N_2))))) # label(fact_1015_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1000 (all N_2 all M_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(N_2)),hAPP_int_real(real_int,M_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(N_2)),M_1)))) # label(fact_1016_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1001 (all M_1 all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,M_1)),number267125858f_real(N_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M_1),number_number_of_int(N_2))))) # label(fact_1017_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1002 (all N_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,N_2),M_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,N_2)),one_one_real)),hAPP_int_real(real_int,M_1))))) # label(fact_1018_int__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1003 (all N_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_2),M_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_2)),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,M_1)),one_one_real))))) # label(fact_1019_int__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1004 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,X)),one_one_real))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),X)))) # label(fact_1020_lemma__floor2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1005 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(minus_minus_real(hAPP_int_real(real_int,N_1)),one_one_real)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_int_real(real_int,N_1))) -> archim856651990g_real(X) = N_1))) # label(fact_1021_ceiling__eq3) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1006 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_real_real(minus_minus_real(hAPP_int_real(real_int,Aa)),one_one_real))))) # label(fact_1022_ceiling__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1007 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(minus_minus_real(hAPP_int_real(real_int,Aa)),one_one_real)),X_1)))) # label(fact_1023_le__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1008 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,R),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,archim1246769320r_real(R))),one_one_real)))) # label(fact_1024_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1009 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,archim1246769320r_real(R))),one_one_real)))) # label(fact_1025_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1010 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,N_1)),one_one_real))) -> archim1246769320r_real(X) = N_1))) # label(fact_1026_floor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1011 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(R),one_one_real)),hAPP_int_real(real_int,archim1246769320r_real(R))))) # label(fact_1027_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1012 (all R hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(minus_minus_real(R),one_one_real)),hAPP_int_real(real_int,archim1246769320r_real(R))))) # label(fact_1028_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1013 (all N_1 all M all R (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,M)),R)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,N_1)),one_one_real))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M),N_1))))) # label(fact_1029_lemma__floor) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1014 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,N_1)),one_one_real))) -> archim856651990g_real(X) = hAPP_int_int(plus_plus_int(N_1),one_one_int)))) # label(fact_1030_ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1015 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,N_1)),one_one_real))) -> archim1246769320r_real(X) = N_1))) # label(fact_1031_floor__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1016 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,Aa)),one_one_real)),X_1)))) # label(fact_1032_less__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1017 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1246769320r_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_real_real(plus_plus_real(hAPP_int_real(real_int,Aa)),one_one_real))))) # label(fact_1033_floor__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1018 (all R (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),R)) -> (exists N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N)),R)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),hAPP_int_real(real_int,hAPP_int_int(plus_plus_int(N),one_one_int)))))))) # label(fact_1034_reals__Archimedean__6b__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1019 (all R (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),zero_zero_real)) -> (exists N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N)),R)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),hAPP_int_real(real_int,hAPP_int_int(plus_plus_int(N),one_one_int)))))))) # label(fact_1035_reals__Archimedean__6c__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1020 (all R exists N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N)),R)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),hAPP_int_real(real_int,hAPP_int_int(plus_plus_int(N),one_one_int)))))) # label(fact_1036_real__lb__ub__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1021 (all N_1 archim856651990g_real(hAPP_nat_real(real_nat,N_1)) = hAPP_nat_int(semiri1621563631at_int,N_1)) # label(fact_1037_ceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1022 (all K -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K)),zero_zero_int))) # label(fact_1038_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1023 (all N_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_1039_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1024 (all P_1 ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> hBOOL(hAPP_int_bool(P_1,X_2)))) <-> (all X_2 hBOOL(hAPP_int_bool(P_1,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_1040_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1025 (all P_1 ((exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) & hBOOL(hAPP_int_bool(P_1,X_2)))) <-> (exists X_2 hBOOL(hAPP_int_bool(P_1,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_1041_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1026 (all Z_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))) # label(fact_1042_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1027 (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_1043_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1028 (all M_1 all N_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_1044_zless__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1029 (all M abs_abs_int(hAPP_nat_int(semiri1621563631at_int,M)) = hAPP_nat_int(semiri1621563631at_int,M)) # label(fact_1045_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1030 (all N_2 (hAPP_nat_int(semiri1621563631at_int,N_2) = zero_zero_int <-> N_2 = zero_zero_nat)) # label(fact_1046_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1031 (all X all Y hAPP_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(plus_plus_nat(X),Y))) # label(fact_1051_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1032 (all M all N_1 hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(M),N_1))) # label(fact_1052_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1033 (all M all N_1 all Z_1 hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,M)),hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,N_1)),Z_1)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(M),N_1))),Z_1)) # label(fact_1053_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1034 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z)) <-> (exists N Z = hAPP_int_int(plus_plus_int(W),hAPP_nat_int(semiri1621563631at_int,N))))) # label(fact_1054_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1035 (all M all N_1 hAPP_int_int(times_times_int(hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(times_times_nat(M),N_1))) # label(fact_1055_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1036 (all M all N_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(times_times_nat(M),N_1)) = hAPP_int_int(times_times_int(hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N_1))) # label(fact_1056_int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1037 (all X all Y hAPP_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(times_times_nat(X),Y))) # label(fact_1057_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1038 (all M_1 all N_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)))) # label(fact_1058_zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1039 (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_1059_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1040 (all N_1 -hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_1060_not__neg__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1041 (all N_1 hAPP_int_real(real_int,hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_real(real_nat,N_1)) # label(fact_1062_real__of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1042 (all N_1 archim1246769320r_real(hAPP_nat_real(real_nat,N_1)) = hAPP_nat_int(semiri1621563631at_int,N_1)) # label(fact_1064_floor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1043 (all X all Y nat_tsub(hAPP_nat_int(semiri1621563631at_int,X),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(minus_minus_nat(X),Y))) # label(fact_1065_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1044 (all N_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,N_2)),zero_zero_int)) <-> N_2 = zero_zero_nat)) # label(fact_1066_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1045 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) -> hAPP_int_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(minus_minus_nat(M),N_1)))) # label(fact_1067_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1046 (all N_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)))) # label(fact_1068_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1047 (all K all I all J (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_nat_int(semiri1621563631at_int,K)),I)),hAPP_int_int(times_times_int(hAPP_nat_int(semiri1621563631at_int,K)),J)))))) # label(fact_1069_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1048 (all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = zero_zero_int) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = number_number_of_int(V)))) # label(fact_1070_int__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1049 (all P_1 all X_1 all Y_1 (hBOOL(hAPP_int_bool(P_1,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(minus_minus_nat(X_1),Y_1)))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))))) & (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) -> hBOOL(hAPP_int_bool(P_1,zero_zero_int))))) # label(fact_1071_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1050 (all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K)) -> (exists N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) & K = hAPP_nat_int(semiri1621563631at_int,N))))) # label(fact_1072_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1051 (all M_1 all N_2 (hAPP_nat_int(semiri1621563631at_int,M_1) = hAPP_nat_int(semiri1621563631at_int,N_2) <-> M_1 = N_2)) # label(fact_1073_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1052 (all X_1 all Y_1 all P_1 ((hBOOL(P_1) -> hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(P_1,X_1),Y_1))) & (-hBOOL(P_1) -> hAPP_nat_int(semiri1621563631at_int,Y_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(P_1,X_1),Y_1))))) # label(fact_1074_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1053 (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_1075_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1054 (all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K)) -> (exists N K = hAPP_nat_int(semiri1621563631at_int,N)))) # label(fact_1076_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1055 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> -(all M_2 Z_1 != hAPP_nat_int(semiri1621563631at_int,M_2)))) # label(fact_1077_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1056 (all K (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K)) -> -(all N K != hAPP_nat_int(semiri1621563631at_int,N)))) # label(fact_1078_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1057 (all Z_1 -(all M_2 all N Z_1 != hAPP_int_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,M_2)),hAPP_nat_int(semiri1621563631at_int,N)))) # label(fact_1079_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1058 (all V_2 all V ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),number_number_of_nat(V_2)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),number_number_of_nat(V_2)) = number_number_of_nat(hAPP_int_int(times_times_int(V),V_2))))) # label(fact_1080_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1059 (all V_2 all K all V ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_2)),K)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_2)),K)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(V),V_2))),K)))) # label(fact_1081_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1060 (all K hAPP_int_int(minus_minus_int(K),pls) = K) # label(fact_1082_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1061 (all W_1 hAPP_int_int(times_times_int(pls),W_1) = pls) # label(fact_1083_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1062 (all K hAPP_int_int(plus_plus_int(pls),K) = K) # label(fact_1085_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1063 (all K hAPP_int_int(plus_plus_int(K),pls) = K) # label(fact_1086_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1064 (all V_1 (zero_zero_nat = number_number_of_nat(V_1) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_1),pls)))) # label(fact_1094_eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1065 (all V_1 (number_number_of_nat(V_1) = zero_zero_nat <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_1),pls)))) # label(fact_1095_eq__number__of__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1066 (all V_1 all V_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(V_1)),number_number_of_nat(V_3))) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_1),V_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_3))) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_1),V_3)))) # label(fact_1096_less__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1067 (all V_1 all V_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_1)),number_number_of_nat(V_3))) <-> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_1),V_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_1),pls))))) # label(fact_1098_le__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1068 (all V_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_1)))) # label(fact_1099_less__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1069 (all V_2 all V ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_2)) = number_number_of_nat(V_2)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_2)) = number_number_of_nat(V)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(V),V_2)))))) # label(fact_1100_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1070 (all V ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(V)) = one_one_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(V)) = number_number_of_nat(succ(V))))) # label(fact_1101_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1071 (all V ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),one_one_nat) = one_one_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) -> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),one_one_nat) = number_number_of_nat(succ(V))))) # label(fact_1102_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1072 (all K succ(K) = hAPP_int_int(plus_plus_int(K),one_one_int)) # label(fact_1103_succ__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1073 (all V ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V),pls)) -> hAPP_nat_nat(minus_minus_nat(number_number_of_nat(V)),one_one_nat) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V),pls)) -> hAPP_nat_nat(minus_minus_nat(number_number_of_nat(V)),one_one_nat) = number_number_of_nat(pred(V))))) # label(fact_1104_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1074 (all N_1 all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),N_1)) = hAPP_nat_nat(plus_plus_nat(one_one_nat),N_1)) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),N_1)) = hAPP_nat_nat(plus_plus_nat(number_number_of_nat(succ(V))),N_1)))) # label(fact_1105_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1075 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1)))) # label(fact_1106_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1076 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_1))))) # label(fact_1107_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1077 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1)))) # label(fact_1108_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1078 (all X succ(pred(X)) = X) # label(fact_1109_succ__pred) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1079 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_2))) <-> M_1 = zero_zero_nat | (exists J_1 (M_1 = hAPP_nat_nat(suc,J_1) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),N_2)))))) # label(fact_1110_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1080 (all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,zero_zero_nat))) <-> N_2 = zero_zero_nat)) # label(fact_1111_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1081 (all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) <-> (exists M_2 N_2 = hAPP_nat_nat(suc,M_2)))) # label(fact_1112_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1082 (all M_1 all N_2 (hAPP_nat_nat(plus_plus_nat(M_1),N_2) = hAPP_nat_nat(suc,zero_zero_nat) <-> M_1 = hAPP_nat_nat(suc,zero_zero_nat) & N_2 = zero_zero_nat | M_1 = zero_zero_nat & N_2 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1113_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1083 (all M_1 all N_2 (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(M_1),N_2) <-> M_1 = hAPP_nat_nat(suc,zero_zero_nat) & N_2 = zero_zero_nat | M_1 = zero_zero_nat & N_2 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1114_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1084 (all M_1 all N_2 (hAPP_nat_nat(times_times_nat(M_1),N_2) = hAPP_nat_nat(suc,zero_zero_nat) <-> M_1 = hAPP_nat_nat(suc,zero_zero_nat) & N_2 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1115_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1085 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)) <-> (exists K_2 N_2 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_1),K_2))))) # label(fact_1116_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1086 (all I all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),I))))) # label(fact_1117_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1087 (all I all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(I),M))))) # label(fact_1118_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1088 (all N_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_1)))) # label(fact_1120_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1089 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)))) # label(fact_1121_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1090 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_1122_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1091 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1))))) # label(fact_1123_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1092 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N_1)))) # label(fact_1124_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1093 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_1))) <-> N_2 = M_1))) # label(fact_1125_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1094 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1126_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1095 (all K_1 all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K_1)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K_1)),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_1127_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1096 (all M all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)),hAPP_nat_nat(suc,M)))) # label(fact_1128_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1097 (all M all N_1 hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,M)),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(times_times_nat(M),N_1))) # label(fact_1129_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1098 (all M all N_1 hAPP_nat_nat(times_times_nat(M),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(times_times_nat(M),N_1))) # label(fact_1130_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1099 (all K_1 all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K_1)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K_1)),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)))) # label(fact_1131_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.93 1100 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(plus_plus_nat(one_one_nat),N_1)) # label(fact_1132_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1101 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(plus_plus_nat(N_1),one_one_nat)) # label(fact_1133_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1102 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M),N_1)))) # label(fact_1134_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1103 (all N_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,N_1)),one_one_nat) = N_1) # label(fact_1135_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1104 (all M all N_1 hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N_1)) # label(fact_1136_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1105 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_1137_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1106 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> M = hAPP_nat_nat(suc,N_1)))) # label(fact_1138_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1107 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N_1))))) # label(fact_1139_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1108 (all N_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),hAPP_nat_nat(suc,M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_1)))) # label(fact_1140_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1109 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)) | M_1 = hAPP_nat_nat(suc,N_2))) # label(fact_1141_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1110 (all M_1 all N_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_1)))) # label(fact_1142_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1111 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1))) # label(fact_1143_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1112 (all M zero_zero_nat != hAPP_nat_nat(suc,M)) # label(fact_1144_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1113 (all Nat_3 zero_zero_nat != hAPP_nat_nat(suc,Nat_3)) # label(fact_1145_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1114 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_1146_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1115 (all Nat_2 hAPP_nat_nat(suc,Nat_2) != zero_zero_nat) # label(fact_1147_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1116 (all M zero_zero_nat != hAPP_nat_nat(suc,M)) # label(fact_1148_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1117 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_1149_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1118 (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,N_2),hAPP_nat_nat(suc,M_1))))) # label(fact_1150_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1119 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)) | M_1 = N_2)) # label(fact_1151_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1120 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_2)))) # label(fact_1152_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1121 (all N_2 all M_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_1))) <-> N_2 = M_1))) # label(fact_1153_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1122 (all N_1 all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M))) -> M = N_1))) # label(fact_1154_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1123 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1))))) # label(fact_1155_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1124 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> (hAPP_nat_nat(suc,M) != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N_1))))) # label(fact_1156_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1125 (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,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K))))) # label(fact_1157_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1126 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> M = N_1))) # label(fact_1158_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1127 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1159_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1128 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1160_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1129 (all M all N_1 hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N_1))) # label(fact_1161_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1130 (all M all N_1 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N_1))) # label(fact_1162_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1131 (all M all N_1 hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N_1) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N_1))) # label(fact_1163_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1132 (all M all N_1 all K hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N_1)),hAPP_nat_nat(suc,K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),K)) # label(fact_1164_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1133 (all M all N_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1)) # label(fact_1165_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1134 (all N_1 N_1 != hAPP_nat_nat(suc,N_1)) # label(fact_1166_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1135 (all N_1 hAPP_nat_nat(suc,N_1) != N_1) # label(fact_1167_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1136 (all Nat_1 all Nat (hAPP_nat_nat(suc,Nat_1) = hAPP_nat_nat(suc,Nat) <-> Nat_1 = Nat)) # label(fact_1168_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1137 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_1169_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1138 (all K_1 all M_1 all N_2 (hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K_1)),M_1) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K_1)),N_2) <-> M_1 = N_2)) # label(fact_1170_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1139 (all K pred(K) = hAPP_int_int(minus_minus_int(K),one_one_int)) # label(fact_1171_pred__def) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1140 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pred(K_1)),L)))) # label(fact_1172_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1141 (all M all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),number_number_of_nat(V)) = hAPP_nat_nat(minus_minus_nat(M),number_number_of_nat(pred(V))))) # label(fact_1173_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1142 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M),N_1)))))) # label(fact_1174_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1143 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(times_times_nat(N_1),M)))))) # label(fact_1175_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1144 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(times_times_nat(M),N_1)))))) # label(fact_1176_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1145 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) -> (hAPP_nat_nat(times_times_nat(M),N_1) = M -> N_1 = hAPP_nat_nat(suc,zero_zero_nat)))) # label(fact_1177_mn__eq__m__one) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1146 (all M all K all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) -> (hAPP_nat_nat(times_times_nat(M),N_1) = K -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),K))))))) # label(fact_1178_prod__mn__less__k) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1147 (all M all K (M != hAPP_nat_nat(times_times_nat(M),K) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M),K))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),K))))) # label(fact_1179_one__less__k) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1148 (all M all K (M != hAPP_nat_nat(times_times_nat(M),K) -> (M != hAPP_nat_nat(suc,zero_zero_nat) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M))))) # label(fact_1180_one__less__m) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1149 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(suc,zero_zero_nat))) = N_1)) # label(fact_1181_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1150 (all I all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(suc,I))),N_1)))) # label(fact_1182_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1151 (all M_1 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_1),N_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_2)))) # label(fact_1183_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1152 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_1))))) # label(fact_1184_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1153 (all M all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J),K))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(suc,J)))) # label(fact_1187_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1154 (all M all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J),K))),M) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,J)),hAPP_nat_nat(plus_plus_nat(K),M)))) # label(fact_1188_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1155 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)) <-> (exists N Z = hAPP_int_int(plus_plus_int(W),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N)))))) # label(fact_1189_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1156 (all M hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,M))) # label(fact_1190_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1157 (all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_1)) = hAPP_real_real(plus_plus_real(hAPP_nat_real(real_nat,N_1)),one_one_real)) # label(fact_1191_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1158 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N_1),one_one_nat)))) # label(fact_1192_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1159 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(N_1),one_one_nat)) = N_1)) # label(fact_1193_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1160 (all N_1 all M ((M = zero_zero_nat -> hAPP_nat_nat(plus_plus_nat(M),N_1) = N_1) & (M != zero_zero_nat -> hAPP_nat_nat(plus_plus_nat(M),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N_1))))) # label(fact_1194_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1161 (all V (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V))) -> number_number_of_nat(V) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(number_number_of_nat(V)),one_one_nat)))) # label(fact_1195_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1162 (all V_1 (hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pred(V_1)))) <-> number_number_of_nat(V_1) = zero_zero_nat)) # label(fact_1196_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.94 1163 (all V ((hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,number_number_of_nat(V)) = one_one_nat) & (-hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) -> hAPP_nat_nat(suc,number_number_of_nat(V)) = number_number_of_nat(succ(V))))) # label(fact_1197_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 2.09/2.34 1164 (all R (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),R)) -> (exists N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N)),R)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R),hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N)))))))) # label(fact_1198_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption].
% 2.09/2.34 1165 (all X all Y hAPP_nat_nat(if_nat(fTrue,X),Y) = X) # label(help_If_1_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 2.09/2.34 1166 (all X all Y hAPP_nat_nat(if_nat(fFalse,X),Y) = Y) # label(help_If_2_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 2.09/2.34 1167 (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].
% 2.09/2.34
% 2.09/2.34 ============================== end of process non-clausal formulas ===
% 2.09/2.34
% 2.09/2.34 ============================== PROCESS INITIAL CLAUSES ===============
% 2.09/2.34
% 2.09/2.34 ============================== PREDICATE ELIMINATION =================
% 2.09/2.34 1168 -is_bool(A) | A = fTrue | A = fFalse # label(help_If_3_1_If_000tc__Nat__Onat_T) # label(axiom). [clausify(1167)].
% 2.09/2.34 1169 is_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 2.09/2.34 1170 is_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 2.09/2.34 1171 is_bool(hAPP_int_bool(A,B)) # label(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) # label(axiom). [clausify(1)].
% 2.09/2.34 1172 is_bool(hAPP_nat_bool(A,B)) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom). [clausify(2)].
% 2.09/2.34 1173 is_bool(hAPP_real_bool(A,B)) # label(gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool) # label(axiom). [clausify(3)].
% 2.09/2.34 1174 is_bool(hAPP_P603027463t_bool(A,B)) # label(gsy_c_hAPP_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__HOL__Obool) # label(axiom). [clausify(4)].
% 2.09/2.34 1175 is_bool(hAPP_P178748804t_bool(A,B)) # label(gsy_c_hAPP_000tc__prod_Itc__Int__Oint_Mtc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_) # label(axiom). [clausify(5)].
% 2.09/2.34 1176 is_bool(member_real(A,B)) # label(gsy_c_member_000tc__RealDef__Oreal) # label(axiom). [clausify(6)].
% 2.09/2.34 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(1168,a,1169,a)].
% 2.09/2.34 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(1168,a,1170,a)].
% 2.09/2.34 Derived: hAPP_int_bool(A,B) = fTrue | hAPP_int_bool(A,B) = fFalse. [resolve(1168,a,1171,a)].
% 2.09/2.34 Derived: hAPP_nat_bool(A,B) = fTrue | hAPP_nat_bool(A,B) = fFalse. [resolve(1168,a,1172,a)].
% 2.09/2.34 Derived: hAPP_real_bool(A,B) = fTrue | hAPP_real_bool(A,B) = fFalse. [resolve(1168,a,1173,a)].
% 2.09/2.34 Derived: hAPP_P603027463t_bool(A,B) = fTrue | hAPP_P603027463t_bool(A,B) = fFalse. [resolve(1168,a,1174,a)].
% 2.09/2.34 Derived: hAPP_P178748804t_bool(A,B) = fTrue | hAPP_P178748804t_bool(A,B) = fFalse. [resolve(1168,a,1175,a)].
% 2.09/2.34 Derived: member_real(A,B) = fTrue | member_real(A,B) = fFalse. [resolve(1168,a,1176,a)].
% 2.09/2.34
% 2.09/2.34 ============================== end predicate elimination =============
% 2.09/2.34
% 2.09/2.34 Auto_denials: (non-Horn, no changes).
% 2.09/2.34
% 2.09/2.34 Term ordering decisions:
% 2.09/2.34 Function symbol KB weights: ord_less_eq_int=1. ord_less_eq_nat=1. ord_less_int=1. ord_less_nat=1. ord_less_eq_real=1. zero_zero_int=1. zero_zero_nat=1. ord_less_real=1. zero_zero_real=1. suc=1. real_int=1. semiri1621563631at_int=1. one_one_int=1. real_nat=1. one_one_nat=1. one_one_real=1. nat_neg=1. pls=1. fFalse=1. fTrue=1. ring_1_Ints_real=1. semiri132038758t_real=1. twoSqu1154269391sum2sq=1. a=1. b=1. p=1. q=1. hAPP_nat_nat=1. hAPP_int_bool=1. hAPP_nat_bool=1. hAPP_i1948725293t_bool=1. hAPP_int_int=1. hAPP_n1699378549t_bool=1. hAPP_real_bool=1. hAPP_r1134773055l_bool=1. hAPP_real_real=1. hAPP_nat_int=1. hAPP_int_real=1. hAPP_nat_real=1. product_Pair_int_int=1. hAPP_P603027463t_bool=1. produc282740534nt_int=1. hAPP_P178748804t_bool=1. divmod_int_rel=1. member_real=1. nat_tsub=1. produc262399358t_bool=1. produc97574839t_bool=1. if_nat=1. posDivAlg=1. pdivmod=1. Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------