TSTP Solution File: NUM923+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM923+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 13:33:08 EDT 2022
% Result : Timeout 300.02s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM923+2 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 20:21:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.10/1.43 ============================== Prover9 ===============================
% 1.10/1.43 Prover9 (32) version 2009-11A, November 2009.
% 1.10/1.43 Process 11400 was started by sandbox on n004.cluster.edu,
% 1.10/1.43 Wed Jul 6 20:21:53 2022
% 1.10/1.43 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11247_n004.cluster.edu".
% 1.10/1.43 ============================== end of head ===========================
% 1.10/1.43
% 1.10/1.43 ============================== INPUT =================================
% 1.10/1.43
% 1.10/1.43 % Reading from file /tmp/Prover9_11247_n004.cluster.edu
% 1.10/1.43
% 1.10/1.43 set(prolog_style_variables).
% 1.10/1.43 set(auto2).
% 1.10/1.43 % set(auto2) -> set(auto).
% 1.10/1.43 % set(auto) -> set(auto_inference).
% 1.10/1.43 % set(auto) -> set(auto_setup).
% 1.10/1.43 % set(auto_setup) -> set(predicate_elim).
% 1.10/1.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.10/1.43 % set(auto) -> set(auto_limits).
% 1.10/1.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.10/1.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.10/1.43 % set(auto) -> set(auto_denials).
% 1.10/1.43 % set(auto) -> set(auto_process).
% 1.10/1.43 % set(auto2) -> assign(new_constants, 1).
% 1.10/1.43 % set(auto2) -> assign(fold_denial_max, 3).
% 1.10/1.43 % set(auto2) -> assign(max_weight, "200.000").
% 1.10/1.43 % set(auto2) -> assign(max_hours, 1).
% 1.10/1.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.10/1.43 % set(auto2) -> assign(max_seconds, 0).
% 1.10/1.43 % set(auto2) -> assign(max_minutes, 5).
% 1.10/1.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.10/1.43 % set(auto2) -> set(sort_initial_sos).
% 1.10/1.43 % set(auto2) -> assign(sos_limit, -1).
% 1.10/1.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.10/1.43 % set(auto2) -> assign(max_megs, 400).
% 1.10/1.43 % set(auto2) -> assign(stats, some).
% 1.10/1.43 % set(auto2) -> clear(echo_input).
% 1.10/1.43 % set(auto2) -> set(quiet).
% 1.10/1.43 % set(auto2) -> clear(print_initial_clauses).
% 1.10/1.43 % set(auto2) -> clear(print_given).
% 1.10/1.43 assign(lrs_ticks,-1).
% 1.10/1.43 assign(sos_limit,10000).
% 1.10/1.43 assign(order,kbo).
% 1.10/1.43 set(lex_order_vars).
% 1.10/1.43 clear(print_given).
% 1.10/1.43
% 1.10/1.43 % formulas(sos). % not echoed (651 formulas)
% 1.10/1.43
% 1.10/1.43 ============================== end of input ==========================
% 1.10/1.43
% 1.10/1.43 % From the command line: assign(max_seconds, 300).
% 1.10/1.43
% 1.10/1.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.10/1.43
% 1.10/1.43 % Formulas that are not ordinary clauses:
% 1.10/1.43 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].
% 1.10/1.43 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].
% 1.10/1.43 3 (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].
% 1.10/1.43 4 (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].
% 1.10/1.43 5 (all A_19 all R_1 all B all M all C_31 all D all N plus_plus_int(times_times_int(minus_minus_int(A_19,times_times_int(R_1,B)),M),times_times_int(minus_minus_int(C_31,times_times_int(R_1,D)),N)) = minus_minus_int(plus_plus_int(times_times_int(A_19,M),times_times_int(C_31,N)),times_times_int(R_1,plus_plus_int(times_times_int(B,M),times_times_int(D,N))))) # label(fact_0_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 6 (all X_44 all Y_43 all A_146 all B_112 minus_minus_int(times_times_int(X_44,Y_43),times_times_int(A_146,B_112)) = plus_plus_int(times_times_int(X_44,minus_minus_int(Y_43,B_112)),times_times_int(minus_minus_int(X_44,A_146),B_112))) # label(fact_1_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 7 (all Aa all E all C_4 all Ba all D_3 (plus_plus_int(times_times_int(Aa,E),C_4) = plus_plus_int(times_times_int(Ba,E),D_3) <-> C_4 = plus_plus_int(times_times_int(minus_minus_int(Ba,Aa),E),D_3))) # label(fact_2_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 8 (all Aa all E all C_4 all Ba all D_3 (plus_plus_int(times_times_int(Aa,E),C_4) = plus_plus_int(times_times_int(Ba,E),D_3) <-> plus_plus_int(times_times_int(minus_minus_int(Aa,Ba),E),C_4) = D_3)) # label(fact_3_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 9 (all X_1 (hBOOL(hAPP_int_bool(twoSqu142715416sum2sq,X_1)) <-> (exists A_88 exists B_92 twoSqu140629262sum2sq(product_Pair_int_int(A_88,B_92)) = X_1))) # label(fact_4_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 10 (all A_19 all B all C_31 (minus_minus_int(A_19,B) = C_31 -> A_19 = plus_plus_int(C_31,B))) # label(fact_5_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 11 (all W all Z1 all Z2 times_times_int(W,minus_minus_int(Z1,Z2)) = minus_minus_int(times_times_int(W,Z1),times_times_int(W,Z2))) # label(fact_6_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 12 (all Z1 all Z2 all W times_times_int(minus_minus_int(Z1,Z2),W) = minus_minus_int(times_times_int(Z1,W),times_times_int(Z2,W))) # label(fact_7_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 13 (all W all Z1 all Z2 times_times_int(W,plus_plus_int(Z1,Z2)) = plus_plus_int(times_times_int(W,Z1),times_times_int(W,Z2))) # label(fact_8_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 14 (all Z1 all Z2 all W times_times_int(plus_plus_int(Z1,Z2),W) = plus_plus_int(times_times_int(Z1,W),times_times_int(Z2,W))) # label(fact_9_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 15 (all A_145 all B_111 plus_plus_int(minus_minus_int(A_145,B_111),B_111) = A_145) # label(fact_10_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 16 (all A_144 all B_110 all C_67 times_times_int(times_times_int(A_144,B_110),C_67) = times_times_int(A_144,times_times_int(B_110,C_67))) # label(fact_11_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 17 (all A_144 all B_110 all C_67 times_times_nat(times_times_nat(A_144,B_110),C_67) = times_times_nat(A_144,times_times_nat(B_110,C_67))) # label(fact_12_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 18 (all B_109 all A_143 all C_66 (plus_plus_int(B_109,A_143) = plus_plus_int(C_66,A_143) -> B_109 = C_66)) # label(fact_13_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 19 (all B_109 all A_143 all C_66 (plus_plus_nat(B_109,A_143) = plus_plus_nat(C_66,A_143) -> B_109 = C_66)) # label(fact_14_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 20 (all A_142 all B_108 all C_65 (plus_plus_int(A_142,B_108) = plus_plus_int(A_142,C_65) -> B_108 = C_65)) # label(fact_15_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 21 (all A_142 all B_108 all C_65 (plus_plus_nat(A_142,B_108) = plus_plus_nat(A_142,C_65) -> B_108 = C_65)) # label(fact_16_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 22 (all A_141 all B_107 all C_64 (plus_plus_int(A_141,B_107) = plus_plus_int(A_141,C_64) -> B_107 = C_64)) # label(fact_17_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 23 (all A_141 all B_107 all C_64 (plus_plus_nat(A_141,B_107) = plus_plus_nat(A_141,C_64) -> B_107 = C_64)) # label(fact_18_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 24 (all Ba all Aa all C_4 (plus_plus_int(Ba,Aa) = plus_plus_int(C_4,Aa) <-> Ba = C_4)) # label(fact_19_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 25 (all Ba all Aa all C_4 (plus_plus_nat(Ba,Aa) = plus_plus_nat(C_4,Aa) <-> Ba = C_4)) # label(fact_20_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 26 (all Aa all Ba all C_4 (plus_plus_int(Aa,Ba) = plus_plus_int(Aa,C_4) <-> Ba = C_4)) # label(fact_21_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 27 (all Aa all Ba all C_4 (plus_plus_nat(Aa,Ba) = plus_plus_nat(Aa,C_4) <-> Ba = C_4)) # label(fact_22_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 28 (all A_140 all B_106 all C_63 plus_plus_int(plus_plus_int(A_140,B_106),C_63) = plus_plus_int(A_140,plus_plus_int(B_106,C_63))) # label(fact_23_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 29 (all A_140 all B_106 all C_63 plus_plus_nat(plus_plus_nat(A_140,B_106),C_63) = plus_plus_nat(A_140,plus_plus_nat(B_106,C_63))) # label(fact_24_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 30 (all Aa all Ba all C_4 all D_3 (minus_minus_int(Aa,Ba) = minus_minus_int(C_4,D_3) -> (Aa = Ba <-> C_4 = D_3))) # label(fact_25_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 31 (all Z1 all Z2 all Z3 times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3))) # label(fact_26_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 32 (all Z all W times_times_int(Z,W) = times_times_int(W,Z)) # label(fact_27_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 33 (all Z1 all Z2 all Z3 plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3))) # label(fact_28_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 34 (all X all Y all Z plus_plus_int(X,plus_plus_int(Y,Z)) = plus_plus_int(Y,plus_plus_int(X,Z))) # label(fact_29_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 35 (all Z all W plus_plus_int(Z,W) = plus_plus_int(W,Z)) # label(fact_30_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 36 (all A_139 all E_1 all B_105 all C_62 plus_plus_int(times_times_int(A_139,E_1),plus_plus_int(times_times_int(B_105,E_1),C_62)) = plus_plus_int(times_times_int(plus_plus_int(A_139,B_105),E_1),C_62)) # label(fact_31_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 37 (all A_139 all E_1 all B_105 all C_62 plus_plus_nat(times_times_nat(A_139,E_1),plus_plus_nat(times_times_nat(B_105,E_1),C_62)) = plus_plus_nat(times_times_nat(plus_plus_nat(A_139,B_105),E_1),C_62)) # label(fact_32_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 38 (all A_138 all B_104 all C_61 times_times_int(plus_plus_int(A_138,B_104),C_61) = plus_plus_int(times_times_int(A_138,C_61),times_times_int(B_104,C_61))) # label(fact_33_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 39 (all A_138 all B_104 all C_61 times_times_nat(plus_plus_nat(A_138,B_104),C_61) = plus_plus_nat(times_times_nat(A_138,C_61),times_times_nat(B_104,C_61))) # label(fact_34_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 40 (all A_137 all C_60 all B_103 all D_18 minus_minus_int(plus_plus_int(A_137,C_60),plus_plus_int(B_103,D_18)) = plus_plus_int(minus_minus_int(A_137,B_103),minus_minus_int(C_60,D_18))) # label(fact_35_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 41 (all A_136 all B_102 minus_minus_int(plus_plus_int(A_136,B_102),B_102) = A_136) # label(fact_36_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 42 (all W_1 all Y_3 all X_1 all Z_1 (plus_plus_int(times_times_int(W_1,Y_3),times_times_int(X_1,Z_1)) = plus_plus_int(times_times_int(W_1,Z_1),times_times_int(X_1,Y_3)) <-> W_1 = X_1 | Y_3 = Z_1)) # label(fact_37_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 43 (all W_1 all Y_3 all X_1 all Z_1 (plus_plus_nat(times_times_nat(W_1,Y_3),times_times_nat(X_1,Z_1)) = plus_plus_nat(times_times_nat(W_1,Z_1),times_times_nat(X_1,Y_3)) <-> W_1 = X_1 | Y_3 = Z_1)) # label(fact_38_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 44 (all A_135 all M_6 all B_101 plus_plus_int(times_times_int(A_135,M_6),times_times_int(B_101,M_6)) = times_times_int(plus_plus_int(A_135,B_101),M_6)) # label(fact_39_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 45 (all A_135 all M_6 all B_101 plus_plus_nat(times_times_nat(A_135,M_6),times_times_nat(B_101,M_6)) = times_times_nat(plus_plus_nat(A_135,B_101),M_6)) # label(fact_40_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 46 (all A_134 all B_100 all C_59 times_times_int(plus_plus_int(A_134,B_100),C_59) = plus_plus_int(times_times_int(A_134,C_59),times_times_int(B_100,C_59))) # label(fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 47 (all A_134 all B_100 all C_59 times_times_nat(plus_plus_nat(A_134,B_100),C_59) = plus_plus_nat(times_times_nat(A_134,C_59),times_times_nat(B_100,C_59))) # label(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 48 (all C_4 all D_3 all Aa all Ba (Aa != Ba & C_4 != D_3 <-> plus_plus_int(times_times_int(Aa,C_4),times_times_int(Ba,D_3)) != plus_plus_int(times_times_int(Aa,D_3),times_times_int(Ba,C_4)))) # label(fact_43_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 49 (all C_4 all D_3 all Aa all Ba (Aa != Ba & C_4 != D_3 <-> plus_plus_nat(times_times_nat(Aa,C_4),times_times_nat(Ba,D_3)) != plus_plus_nat(times_times_nat(Aa,D_3),times_times_nat(Ba,C_4)))) # label(fact_44_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 50 (all X_43 all Y_42 all Z_12 times_times_int(X_43,plus_plus_int(Y_42,Z_12)) = plus_plus_int(times_times_int(X_43,Y_42),times_times_int(X_43,Z_12))) # label(fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 51 (all X_43 all Y_42 all Z_12 times_times_nat(X_43,plus_plus_nat(Y_42,Z_12)) = plus_plus_nat(times_times_nat(X_43,Y_42),times_times_nat(X_43,Z_12))) # label(fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 52 (all A_133 all B_99 all A_132 all B_98 (product_Pair_int_int(A_133,B_99) = product_Pair_int_int(A_132,B_98) -> -(A_133 = A_132 -> B_99 != B_98))) # label(fact_47_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 53 (all A_133 all B_99 all A_132 all B_98 (produc282740534nt_int(A_133,B_99) = produc282740534nt_int(A_132,B_98) -> -(A_133 = A_132 -> B_99 != B_98))) # label(fact_48_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 54 (all Aa all Ba all A_131 all B_97 (product_Pair_int_int(Aa,Ba) = product_Pair_int_int(A_131,B_97) <-> Aa = A_131 & Ba = B_97)) # label(fact_49_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 55 (all Aa all Ba all A_131 all B_97 (produc282740534nt_int(Aa,Ba) = produc282740534nt_int(A_131,B_97) <-> Aa = A_131 & Ba = B_97)) # label(fact_50_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 56 (all P ((all X1 hBOOL(hAPP_P603027463t_bool(P,X1))) <-> (all A_88 all B_92 hBOOL(hAPP_P603027463t_bool(P,product_Pair_int_int(A_88,B_92)))))) # label(fact_51_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 57 (all P ((all X1 hBOOL(hAPP_P178748804t_bool(P,X1))) <-> (all A_88 all B_92 hBOOL(hAPP_P178748804t_bool(P,produc282740534nt_int(A_88,B_92)))))) # label(fact_52_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 58 (all A_130 all B_96 all C_58 all D_17 plus_plus_int(plus_plus_int(A_130,B_96),plus_plus_int(C_58,D_17)) = plus_plus_int(plus_plus_int(A_130,C_58),plus_plus_int(B_96,D_17))) # label(fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 59 (all A_130 all B_96 all C_58 all D_17 plus_plus_nat(plus_plus_nat(A_130,B_96),plus_plus_nat(C_58,D_17)) = plus_plus_nat(plus_plus_nat(A_130,C_58),plus_plus_nat(B_96,D_17))) # label(fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 60 (all A_129 all B_95 times_times_int(A_129,B_95) = times_times_int(B_95,A_129)) # label(fact_55_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 61 (all A_129 all B_95 times_times_nat(A_129,B_95) = times_times_nat(B_95,A_129)) # label(fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 62 (all Lx_6 all Rx_6 all Ry_4 times_times_int(Lx_6,times_times_int(Rx_6,Ry_4)) = times_times_int(Rx_6,times_times_int(Lx_6,Ry_4))) # label(fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 63 (all Lx_6 all Rx_6 all Ry_4 times_times_nat(Lx_6,times_times_nat(Rx_6,Ry_4)) = times_times_nat(Rx_6,times_times_nat(Lx_6,Ry_4))) # label(fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 64 (all Lx_5 all Rx_5 all Ry_3 times_times_int(Lx_5,times_times_int(Rx_5,Ry_3)) = times_times_int(times_times_int(Lx_5,Rx_5),Ry_3)) # label(fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 65 (all Lx_5 all Rx_5 all Ry_3 times_times_nat(Lx_5,times_times_nat(Rx_5,Ry_3)) = times_times_nat(times_times_nat(Lx_5,Rx_5),Ry_3)) # label(fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 66 (all Lx_4 all Ly_4 all Rx_4 times_times_int(times_times_int(Lx_4,Ly_4),Rx_4) = times_times_int(Lx_4,times_times_int(Ly_4,Rx_4))) # label(fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 67 (all Lx_4 all Ly_4 all Rx_4 times_times_nat(times_times_nat(Lx_4,Ly_4),Rx_4) = times_times_nat(Lx_4,times_times_nat(Ly_4,Rx_4))) # label(fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 68 (all Lx_3 all Ly_3 all Rx_3 times_times_int(times_times_int(Lx_3,Ly_3),Rx_3) = times_times_int(times_times_int(Lx_3,Rx_3),Ly_3)) # label(fact_63_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 69 (all Lx_3 all Ly_3 all Rx_3 times_times_nat(times_times_nat(Lx_3,Ly_3),Rx_3) = times_times_nat(times_times_nat(Lx_3,Rx_3),Ly_3)) # label(fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 70 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 times_times_int(times_times_int(Lx_2,Ly_2),times_times_int(Rx_2,Ry_2)) = times_times_int(Lx_2,times_times_int(Ly_2,times_times_int(Rx_2,Ry_2)))) # label(fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 71 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 times_times_nat(times_times_nat(Lx_2,Ly_2),times_times_nat(Rx_2,Ry_2)) = times_times_nat(Lx_2,times_times_nat(Ly_2,times_times_nat(Rx_2,Ry_2)))) # label(fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 72 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 times_times_int(times_times_int(Lx_1,Ly_1),times_times_int(Rx_1,Ry_1)) = times_times_int(Rx_1,times_times_int(times_times_int(Lx_1,Ly_1),Ry_1))) # label(fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 73 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 times_times_nat(times_times_nat(Lx_1,Ly_1),times_times_nat(Rx_1,Ry_1)) = times_times_nat(Rx_1,times_times_nat(times_times_nat(Lx_1,Ly_1),Ry_1))) # label(fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 74 (all Lx all Ly all Rx all Ry times_times_int(times_times_int(Lx,Ly),times_times_int(Rx,Ry)) = times_times_int(times_times_int(Lx,Rx),times_times_int(Ly,Ry))) # label(fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 75 (all Lx all Ly all Rx all Ry times_times_nat(times_times_nat(Lx,Ly),times_times_nat(Rx,Ry)) = times_times_nat(times_times_nat(Lx,Rx),times_times_nat(Ly,Ry))) # label(fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 76 (all A_128 all C_57 plus_plus_int(A_128,C_57) = plus_plus_int(C_57,A_128)) # label(fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 77 (all A_128 all C_57 plus_plus_nat(A_128,C_57) = plus_plus_nat(C_57,A_128)) # label(fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 78 (all A_127 all C_56 all D_16 plus_plus_int(A_127,plus_plus_int(C_56,D_16)) = plus_plus_int(C_56,plus_plus_int(A_127,D_16))) # label(fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 79 (all A_127 all C_56 all D_16 plus_plus_nat(A_127,plus_plus_nat(C_56,D_16)) = plus_plus_nat(C_56,plus_plus_nat(A_127,D_16))) # label(fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 80 (all A_126 all C_55 all D_15 plus_plus_int(A_126,plus_plus_int(C_55,D_15)) = plus_plus_int(plus_plus_int(A_126,C_55),D_15)) # label(fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 81 (all A_126 all C_55 all D_15 plus_plus_nat(A_126,plus_plus_nat(C_55,D_15)) = plus_plus_nat(plus_plus_nat(A_126,C_55),D_15)) # label(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 82 (all A_125 all B_94 all C_54 plus_plus_int(plus_plus_int(A_125,B_94),C_54) = plus_plus_int(A_125,plus_plus_int(B_94,C_54))) # label(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 83 (all A_125 all B_94 all C_54 plus_plus_nat(plus_plus_nat(A_125,B_94),C_54) = plus_plus_nat(A_125,plus_plus_nat(B_94,C_54))) # label(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 84 (all A_124 all B_93 all C_53 plus_plus_int(plus_plus_int(A_124,B_93),C_53) = plus_plus_int(plus_plus_int(A_124,C_53),B_93)) # label(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 85 (all A_124 all B_93 all C_53 plus_plus_nat(plus_plus_nat(A_124,B_93),C_53) = plus_plus_nat(plus_plus_nat(A_124,C_53),B_93)) # label(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 86 (all P ((exists X1 hBOOL(hAPP_P603027463t_bool(P,X1))) <-> (exists A_88 exists B_92 hBOOL(hAPP_P603027463t_bool(P,product_Pair_int_int(A_88,B_92)))))) # label(fact_81_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 87 (all P ((exists X1 hBOOL(hAPP_P178748804t_bool(P,X1))) <-> (exists A_88 exists B_92 hBOOL(hAPP_P178748804t_bool(P,produc282740534nt_int(A_88,B_92)))))) # label(fact_82_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 88 (all X_1 all P ((all A_88 all B_92 all C_52 hBOOL(hAPP_P178748804t_bool(P,produc282740534nt_int(A_88,product_Pair_int_int(B_92,C_52))))) -> hBOOL(hAPP_P178748804t_bool(P,X_1)))) # label(fact_83_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 89 (all Y_41 -(all A_88 all B_92 all C_52 Y_41 != produc282740534nt_int(A_88,product_Pair_int_int(B_92,C_52)))) # label(fact_84_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 90 (all Y_40 -(all A_88 all B_92 Y_40 != product_Pair_int_int(A_88,B_92))) # label(fact_85_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 91 (all Y_40 -(all A_88 all B_92 Y_40 != produc282740534nt_int(A_88,B_92))) # label(fact_86_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 92 (all P_2 -(all X_3 all Y_39 P_2 != product_Pair_int_int(X_3,Y_39))) # label(fact_87_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 93 (all P_2 -(all X_3 all Y_39 P_2 != produc282740534nt_int(X_3,Y_39))) # label(fact_88_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 94 (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_89_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.43 95 (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_90_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 96 (all Aa all E all C_4 all Ba all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(times_times_int(Aa,E),C_4)),plus_plus_int(times_times_int(Ba,E),D_3))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(times_times_int(minus_minus_int(Aa,Ba),E),C_4)),D_3)))) # label(fact_91_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 97 (all Aa all E all C_4 all Ba all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(times_times_int(Aa,E),C_4)),plus_plus_int(times_times_int(Ba,E),D_3))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_4),plus_plus_int(times_times_int(minus_minus_int(Ba,Aa),E),D_3))))) # label(fact_92_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 98 (all X_42 minus_minus_int(times_times_int(X_42,X_42),one_one_int) = times_times_int(plus_plus_int(X_42,one_one_int),minus_minus_int(X_42,one_one_int))) # label(fact_93_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 99 (all Aa all E all C_4 all Ba all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(times_times_int(Aa,E),C_4)),plus_plus_int(times_times_int(Ba,E),D_3))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(times_times_int(minus_minus_int(Aa,Ba),E),C_4)),D_3)))) # label(fact_94_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 100 (all Aa all E all C_4 all Ba all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(times_times_int(Aa,E),C_4)),plus_plus_int(times_times_int(Ba,E),D_3))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_4),plus_plus_int(times_times_int(minus_minus_int(Ba,Aa),E),D_3))))) # label(fact_95_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 101 (all X_1 (one_one_int = X_1 <-> X_1 = one_one_int)) # label(fact_96_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 102 (all X_1 (one_one_nat = X_1 <-> X_1 = one_one_nat)) # label(fact_97_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 103 (all W_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),plus_plus_int(Z_1,one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_1)))) # label(fact_98_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 104 (all W_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(W_1,one_one_int)),Z_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)))) # label(fact_99_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 105 (all X_41 all Y_38 (X_41 != Y_38 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_41),Y_38)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_38),X_41))))) # label(fact_100_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 106 (all W all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(W,one_one_int)),Z)))) # label(fact_101_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 107 (all X_40 all Y_37 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_40),Y_37)) -> (X_40 != Y_37 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_40),Y_37))))) # label(fact_102_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 108 (all X_40 all Y_37 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_40),Y_37)) -> (X_40 != Y_37 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_40),Y_37))))) # label(fact_103_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 109 (all W_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),plus_plus_int(Z_1,one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) | W_1 = Z_1)) # label(fact_104_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 110 (all Z_11 all Z all W_2 all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_2),W)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_11),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(W_2,Z_11)),plus_plus_int(W,Z)))))) # label(fact_105_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 111 (all C_51 all D_14 all A_123 all B_91 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_123),B_91)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_51),D_14)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(A_123,C_51)),plus_plus_int(B_91,D_14)))))) # label(fact_106_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 112 (all C_51 all D_14 all A_123 all B_91 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_123),B_91)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_51),D_14)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(A_123,C_51)),plus_plus_nat(B_91,D_14)))))) # label(fact_107_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 113 (all C_50 all D_13 all A_122 all B_90 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_122),B_90)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_50),D_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(A_122,C_50)),plus_plus_int(B_90,D_13)))))) # label(fact_108_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 114 (all C_50 all D_13 all A_122 all B_90 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_122),B_90)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_50),D_13)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(A_122,C_50)),plus_plus_nat(B_90,D_13)))))) # label(fact_109_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 115 (all A_121 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_121),plus_plus_int(A_121,one_one_int)))) # label(fact_110_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 116 (all A_121 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_121),plus_plus_nat(A_121,one_one_nat)))) # label(fact_111_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 117 (all N_2 all M_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),N_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),times_times_int(M_5,N_2)))))) # label(fact_112_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 118 (all N_2 all M_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),M_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),times_times_nat(M_5,N_2)))))) # label(fact_113_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 119 (all W_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),minus_minus_int(Z_1,one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)))) # label(fact_114_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 120 (all Aa all C_4 all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(Aa,C_4)),plus_plus_int(Ba,C_4))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)))) # label(fact_115_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 121 (all Aa all C_4 all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(Aa,C_4)),plus_plus_nat(Ba,C_4))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_116_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 122 (all C_4 all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(C_4,Aa)),plus_plus_int(C_4,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)))) # label(fact_117_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 123 (all C_4 all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(C_4,Aa)),plus_plus_nat(C_4,Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_118_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 124 (all C_49 all A_120 all B_89 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_120),B_89)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(A_120,C_49)),plus_plus_int(B_89,C_49))))) # label(fact_119_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 125 (all C_49 all A_120 all B_89 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_120),B_89)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(A_120,C_49)),plus_plus_nat(B_89,C_49))))) # label(fact_120_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 126 (all C_48 all A_119 all B_88 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_119),B_88)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(C_48,A_119)),plus_plus_int(C_48,B_88))))) # label(fact_121_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 127 (all C_48 all A_119 all B_88 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_119),B_88)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(C_48,A_119)),plus_plus_nat(C_48,B_88))))) # label(fact_122_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 128 (all C_47 all D_12 all A_118 all B_87 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_118),B_87)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_47),D_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(A_118,C_47)),plus_plus_int(B_87,D_12)))))) # label(fact_123_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 129 (all C_47 all D_12 all A_118 all B_87 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_118),B_87)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_47),D_12)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(A_118,C_47)),plus_plus_nat(B_87,D_12)))))) # label(fact_124_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 130 (all A_117 all C_46 all B_86 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(A_117,C_46)),plus_plus_int(B_86,C_46))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_117),B_86)))) # label(fact_125_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 131 (all A_117 all C_46 all B_86 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(A_117,C_46)),plus_plus_nat(B_86,C_46))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_117),B_86)))) # label(fact_126_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 132 (all C_45 all A_116 all B_85 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(C_45,A_116)),plus_plus_int(C_45,B_85))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_116),B_85)))) # label(fact_127_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 133 (all C_45 all A_116 all B_85 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(C_45,A_116)),plus_plus_nat(C_45,B_85))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_116),B_85)))) # label(fact_128_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 134 (all A_115 times_times_int(one_one_int,A_115) = A_115) # label(fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 135 (all A_115 times_times_nat(one_one_nat,A_115) = A_115) # label(fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 136 (all A_114 times_times_int(A_114,one_one_int) = A_114) # label(fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 137 (all A_114 times_times_nat(A_114,one_one_nat) = A_114) # label(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 138 (all A_113 times_times_int(one_one_int,A_113) = A_113) # label(fact_133_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 139 (all A_113 times_times_nat(one_one_nat,A_113) = A_113) # label(fact_134_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 140 (all A_112 times_times_int(one_one_int,A_112) = A_112) # label(fact_135_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 141 (all A_112 times_times_nat(one_one_nat,A_112) = A_112) # label(fact_136_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 142 (all A_111 times_times_int(A_111,one_one_int) = A_111) # label(fact_137_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 143 (all A_111 times_times_nat(A_111,one_one_nat) = A_111) # label(fact_138_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 144 (all A_110 times_times_int(A_110,one_one_int) = A_110) # label(fact_139_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 145 (all A_110 times_times_nat(A_110,one_one_nat) = A_110) # label(fact_140_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 146 (all Aa all Ba all C_4 all D_3 (minus_minus_int(Aa,Ba) = minus_minus_int(C_4,D_3) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_4),D_3))))) # label(fact_141_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 147 (all Aa all C_4 all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(Aa,C_4)),plus_plus_int(Ba,C_4))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)))) # label(fact_142_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 148 (all Aa all C_4 all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(Aa,C_4)),plus_plus_nat(Ba,C_4))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_143_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 149 (all C_4 all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(C_4,Aa)),plus_plus_int(C_4,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)))) # label(fact_144_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 150 (all C_4 all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(C_4,Aa)),plus_plus_nat(C_4,Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_145_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 151 (all C_44 all A_109 all B_84 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_109),B_84)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(A_109,C_44)),plus_plus_int(B_84,C_44))))) # label(fact_146_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 152 (all C_44 all A_109 all B_84 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_109),B_84)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(A_109,C_44)),plus_plus_nat(B_84,C_44))))) # label(fact_147_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 153 (all C_43 all A_108 all B_83 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_108),B_83)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(C_43,A_108)),plus_plus_int(C_43,B_83))))) # label(fact_148_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 154 (all C_43 all A_108 all B_83 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_108),B_83)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(C_43,A_108)),plus_plus_nat(C_43,B_83))))) # label(fact_149_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 155 (all C_42 all D_11 all A_107 all B_82 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_107),B_82)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_42),D_11)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(A_107,C_42)),plus_plus_int(B_82,D_11)))))) # label(fact_150_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 156 (all C_42 all D_11 all A_107 all B_82 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_107),B_82)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_42),D_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(A_107,C_42)),plus_plus_nat(B_82,D_11)))))) # label(fact_151_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 157 (all A_106 all C_41 all B_81 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(A_106,C_41)),plus_plus_int(B_81,C_41))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_106),B_81)))) # label(fact_152_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 158 (all A_106 all C_41 all B_81 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(A_106,C_41)),plus_plus_nat(B_81,C_41))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_106),B_81)))) # label(fact_153_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 159 (all C_40 all A_105 all B_80 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(C_40,A_105)),plus_plus_int(C_40,B_80))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_105),B_80)))) # label(fact_154_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 160 (all C_40 all A_105 all B_80 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(C_40,A_105)),plus_plus_nat(C_40,B_80))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_105),B_80)))) # label(fact_155_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 161 (all Aa all Ba all C_4 all D_3 (minus_minus_int(Aa,Ba) = minus_minus_int(C_4,D_3) -> (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_4),D_3))))) # label(fact_156_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 162 (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,plus_plus_int(I,K)),plus_plus_int(J,K))))) # label(fact_157_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 163 (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,plus_plus_int(K,I)),plus_plus_int(K,J))))) # label(fact_158_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 164 (all Z times_times_int(one_one_int,Z) = Z) # label(fact_159_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 165 (all Z times_times_int(Z,one_one_int) = Z) # label(fact_160_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 166 (all M_4 plus_plus_int(M_4,M_4) = times_times_int(plus_plus_int(one_one_int,one_one_int),M_4)) # label(fact_161_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 167 (all M_4 plus_plus_nat(M_4,M_4) = times_times_nat(plus_plus_nat(one_one_nat,one_one_nat),M_4)) # label(fact_162_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 168 (all M_3 all A_104 plus_plus_nat(M_3,times_times_nat(A_104,M_3)) = times_times_nat(plus_plus_nat(A_104,one_one_nat),M_3)) # label(fact_163_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 169 (all M_3 all A_104 plus_plus_int(M_3,times_times_int(A_104,M_3)) = times_times_int(plus_plus_int(A_104,one_one_int),M_3)) # label(fact_164_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 170 (all A_103 all M_2 plus_plus_nat(times_times_nat(A_103,M_2),M_2) = times_times_nat(plus_plus_nat(A_103,one_one_nat),M_2)) # label(fact_165_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 171 (all A_103 all M_2 plus_plus_int(times_times_int(A_103,M_2),M_2) = times_times_int(plus_plus_int(A_103,one_one_int),M_2)) # label(fact_166_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 172 (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_167_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 173 (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_168_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 174 (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_169_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 175 (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_170_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 176 (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_171_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 177 (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_172_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 178 (all X_39 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_39),X_39))) # label(fact_173_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 179 (all X_39 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_39),X_39))) # label(fact_174_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 180 (all Z_10 all Y_36 all X_38 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_36),X_38)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_10),Y_36)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_10),X_38))))) # label(fact_175_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 181 (all Z_10 all Y_36 all X_38 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_36),X_38)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_10),Y_36)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_10),X_38))))) # label(fact_176_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 182 (all Z_9 all X_37 all Y_35 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_37),Y_35)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_35),Z_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_37),Z_9))))) # label(fact_177_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 183 (all Z_9 all X_37 all Y_35 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_37),Y_35)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_35),Z_9)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_37),Z_9))))) # label(fact_178_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 184 (all Z_8 all Y_34 all X_36 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_34),X_36)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_8),Y_34)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_8),X_36))))) # label(fact_179_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 185 (all Z_8 all Y_34 all X_36 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_34),X_36)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_8),Y_34)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_8),X_36))))) # label(fact_180_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 186 (all Z_7 all X_35 all Y_33 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_35),Y_33)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_33),Z_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_35),Z_7))))) # label(fact_181_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 187 (all Z_7 all X_35 all Y_33 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_35),Y_33)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_33),Z_7)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_35),Z_7))))) # label(fact_182_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 188 (all B_79 all A_102 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_79),A_102)) -> (A_102 != B_79 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_79),A_102))))) # label(fact_183_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 189 (all B_79 all A_102 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_79),A_102)) -> (A_102 != B_79 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_79),A_102))))) # label(fact_184_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 190 (all A_101 all B_78 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_101),B_78)) -> (A_101 != B_78 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_101),B_78))))) # label(fact_185_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 191 (all A_101 all B_78 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_101),B_78)) -> (A_101 != B_78 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_101),B_78))))) # label(fact_186_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 192 (all X_34 all Y_32 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_34),Y_32)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_34),Y_32)) | X_34 = Y_32)) # label(fact_187_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 193 (all X_34 all Y_32 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_34),Y_32)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_34),Y_32)) | X_34 = Y_32)) # label(fact_188_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 194 (all W hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),W))) # label(fact_189_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 195 (all Z all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z)))) # label(fact_190_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 196 (all Z_1 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) & Z_1 != W_1)) # label(fact_191_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 197 (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_192_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 198 (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_193_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 199 (all Z all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z)) -> Z = W))) # label(fact_194_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 200 (all X_33 all Y_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_33),Y_31)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_31),X_33)))) # label(fact_195_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 201 (all X_33 all Y_31 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_33),Y_31)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_31),X_33)))) # label(fact_196_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 202 (all X_1 all Y_3 (X_1 = Y_3 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_1)))) # label(fact_197_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 203 (all X_1 all Y_3 (X_1 = Y_3 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_3),X_1)))) # label(fact_198_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 204 (all X_32 all Y_30 (X_32 = Y_30 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_32),Y_30)))) # label(fact_199_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 205 (all X_32 all Y_30 (X_32 = Y_30 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_32),Y_30)))) # label(fact_200_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 206 (all Y_3 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_201_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 207 (all Y_3 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_3),X_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_202_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 208 (all C_39 all A_100 all B_77 (A_100 = B_77 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_77),C_39)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_100),C_39))))) # label(fact_203_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 209 (all C_39 all A_100 all B_77 (A_100 = B_77 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_77),C_39)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_100),C_39))))) # label(fact_204_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 210 (all C_38 all A_99 all B_76 (A_99 = B_76 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_38),B_76)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_38),A_99))))) # label(fact_205_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 211 (all C_38 all A_99 all B_76 (A_99 = B_76 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_38),B_76)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_38),A_99))))) # label(fact_206_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 212 (all C_37 all A_98 all B_75 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_98),B_75)) -> (B_75 = C_37 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_98),C_37))))) # label(fact_207_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 213 (all C_37 all A_98 all B_75 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_98),B_75)) -> (B_75 = C_37 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_98),C_37))))) # label(fact_208_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 214 (all C_36 all B_74 all A_97 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_74),A_97)) -> (B_74 = C_36 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_36),A_97))))) # label(fact_209_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 215 (all C_36 all B_74 all A_97 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_74),A_97)) -> (B_74 = C_36 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_36),A_97))))) # label(fact_210_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 216 (all X_31 all Y_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_31),Y_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_29),X_31)) -> X_31 = Y_29))) # label(fact_211_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 217 (all X_31 all Y_29 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_31),Y_29)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_29),X_31)) -> X_31 = Y_29))) # label(fact_212_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 218 (all Z_6 all X_30 all Y_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_30),Y_28)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_28),Z_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_30),Z_6))))) # label(fact_213_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 219 (all Z_6 all X_30 all Y_28 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_30),Y_28)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_28),Z_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_30),Z_6))))) # label(fact_214_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 220 (all Y_27 all X_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_27),X_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_29),Y_27)) -> X_29 = Y_27))) # label(fact_215_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 221 (all Y_27 all X_29 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_27),X_29)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_29),Y_27)) -> X_29 = Y_27))) # label(fact_216_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 222 (all Z_5 all Y_26 all X_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_26),X_28)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),Y_26)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),X_28))))) # label(fact_217_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 223 (all Z_5 all Y_26 all X_28 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_26),X_28)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),Y_26)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),X_28))))) # label(fact_218_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 224 (all X_27 all Y_25 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_27),Y_25)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_25),X_27)))) # label(fact_219_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 225 (all X_27 all Y_25 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_27),Y_25)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_25),X_27)))) # label(fact_220_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 226 (all X_26 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),X_26))) # label(fact_221_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 227 (all X_26 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_26),X_26))) # label(fact_222_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 228 (all X_1 all Y_3 (X_1 != Y_3 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_1)))) # label(fact_223_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 229 (all X_1 all Y_3 (X_1 != Y_3 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_3),X_1)))) # label(fact_224_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 230 (all X_1 all Y_3 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_1)) | X_1 = Y_3)) # label(fact_225_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 231 (all X_1 all Y_3 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_3),X_1)) | X_1 = Y_3)) # label(fact_226_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 232 (all X_25 all Y_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_24)) | X_25 = Y_24 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_24),X_25)))) # label(fact_227_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 233 (all X_25 all Y_24 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_25),Y_24)) | X_25 = Y_24 | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_24),X_25)))) # label(fact_228_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 234 (all Y_3 all X_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_229_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 235 (all Y_3 all X_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_3),X_1)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_230_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 236 (all X_24 all Y_23 (X_24 != Y_23 -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_23)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_24))))) # label(fact_231_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 237 (all X_24 all Y_23 (X_24 != Y_23 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_24),Y_23)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_23),X_24))))) # label(fact_232_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 238 (all X_23 all Y_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_22)) -> X_23 != Y_22)) # label(fact_233_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 239 (all X_23 all Y_22 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_23),Y_22)) -> X_23 != Y_22)) # label(fact_234_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 240 (all X_22 all Y_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_21)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_22)))) # label(fact_235_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 241 (all X_22 all Y_21 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_22),Y_21)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_21),X_22)))) # label(fact_236_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 242 (all X_21 all Y_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),Y_20)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_21)))) # label(fact_237_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 243 (all X_21 all Y_20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_21),Y_20)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_20),X_21)))) # label(fact_238_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 244 (all X_20 all Y_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_20),Y_19)) -> X_20 != Y_19)) # label(fact_239_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 245 (all X_20 all Y_19 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_19)) -> X_20 != Y_19)) # label(fact_240_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.44 246 (all X_19 all Y_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_19),Y_18)) -> Y_18 != X_19)) # label(fact_241_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 247 (all X_19 all Y_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_19),Y_18)) -> Y_18 != X_19)) # label(fact_242_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 248 (all P all X_1 all Y_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_1)) -> hBOOL(P)))) # label(fact_243_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 249 (all P all X_1 all Y_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_3),X_1)) -> hBOOL(P)))) # label(fact_244_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 250 (all A_96 all B_73 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_96),B_73)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_73),A_96)))) # label(fact_245_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 251 (all A_96 all B_73 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_96),B_73)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_73),A_96)))) # label(fact_246_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 252 (all B_72 all A_95 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_72),A_95)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_95),B_72)))) # label(fact_247_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 253 (all B_72 all A_95 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_72),A_95)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_95),B_72)))) # label(fact_248_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 254 (all C_35 all A_94 all B_71 (A_94 = B_71 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_71),C_35)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_94),C_35))))) # label(fact_249_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 255 (all C_35 all A_94 all B_71 (A_94 = B_71 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_71),C_35)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_94),C_35))))) # label(fact_250_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 256 (all C_34 all A_93 all B_70 (A_93 = B_70 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_34),B_70)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_34),A_93))))) # label(fact_251_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 257 (all C_34 all A_93 all B_70 (A_93 = B_70 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_34),B_70)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_34),A_93))))) # label(fact_252_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 258 (all C_33 all A_92 all B_69 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_92),B_69)) -> (B_69 = C_33 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_92),C_33))))) # label(fact_253_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 259 (all C_33 all A_92 all B_69 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_92),B_69)) -> (B_69 = C_33 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_92),C_33))))) # label(fact_254_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 260 (all C_32 all B_68 all A_91 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_68),A_91)) -> (B_68 = C_32 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_32),A_91))))) # label(fact_255_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 261 (all C_32 all B_68 all A_91 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_68),A_91)) -> (B_68 = C_32 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_32),A_91))))) # label(fact_256_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 262 (all Z_4 all X_18 all Y_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_18),Y_17)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_17),Z_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_18),Z_4))))) # label(fact_257_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 263 (all Z_4 all X_18 all Y_17 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_18),Y_17)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_17),Z_4)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_18),Z_4))))) # label(fact_258_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 264 (all Z_3 all Y_16 all X_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_16),X_17)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_3),Y_16)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_3),X_17))))) # label(fact_259_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 265 (all Z_3 all Y_16 all X_17 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_16),X_17)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),Y_16)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),X_17))))) # label(fact_260_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 266 (all X_16 all Y_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_16),Y_15)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_15),X_16)))) # label(fact_261_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 267 (all X_16 all Y_15 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_16),Y_15)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_15),X_16)))) # label(fact_262_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 268 (all X_15 all Y_14 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_15),Y_14)) -> (X_15 != Y_14 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_14),X_15))))) # label(fact_263_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 269 (all X_15 all Y_14 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_15),Y_14)) -> (X_15 != Y_14 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_14),X_15))))) # label(fact_264_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 270 (all X_1 all Y_3 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_1)))) # label(fact_265_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 271 (all X_1 all Y_3 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_3),X_1)))) # label(fact_266_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 272 (all X_1 all Y_3 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_1)))) # label(fact_267_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 273 (all X_1 all Y_3 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_3),X_1)))) # label(fact_268_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 274 (all X_14 all Y_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_13)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_13),X_14)))) # label(fact_269_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 275 (all X_14 all Y_13 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_14),Y_13)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_13),X_14)))) # label(fact_270_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 276 (all X_1 all Y_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) & X_1 != Y_3)) # label(fact_271_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 277 (all X_1 all Y_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) & X_1 != Y_3)) # label(fact_272_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 278 (all X_1 all Y_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_1)))) # label(fact_273_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 279 (all X_1 all Y_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) & -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_3),X_1)))) # label(fact_274_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 280 (all X_1 all Y_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) | X_1 = Y_3)) # label(fact_275_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 281 (all X_1 all Y_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) | X_1 = Y_3)) # label(fact_276_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 282 (all X_13 all Y_12 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_12)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_12),X_13)))) # label(fact_277_leI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 283 (all X_13 all Y_12 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_13),Y_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_12),X_13)))) # label(fact_278_leI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 284 (all Y_11 all X_12 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_12)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_12),Y_11)))) # label(fact_279_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 285 (all Y_11 all X_12 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_11),X_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_12),Y_11)))) # label(fact_280_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 286 (all X_1 all Y_3 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_281_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 287 (all X_1 all Y_3 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_282_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 288 (all A_90 all B_67 (A_90 != B_67 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_90),B_67)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_90),B_67))))) # label(fact_283_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 289 (all A_90 all B_67 (A_90 != B_67 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_90),B_67)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_90),B_67))))) # label(fact_284_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 290 (all A_89 all B_66 (A_89 != B_66 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_66),A_89)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_66),A_89))))) # label(fact_285_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 291 (all A_89 all B_66 (A_89 != B_66 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_66),A_89)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_66),A_89))))) # label(fact_286_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 292 (all Y_10 all X_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_11)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_10)))) # label(fact_287_leD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 293 (all Y_10 all X_11 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_10),X_11)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_11),Y_10)))) # label(fact_288_leD) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 294 (all X_10 all Y_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_9)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),Y_9)))) # label(fact_289_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 295 (all X_10 all Y_9 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_10),Y_9)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_10),Y_9)))) # label(fact_290_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 296 (all X_1 all Y_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_3)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_291_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 297 (all X_1 all Y_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_3)) <-> X_1 = Y_3))) # label(fact_292_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 298 (all A_19 all B (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),minus_minus_int(B,one_one_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_19),B)))) # label(fact_293_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 299 (all P 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,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,I_2)) -> hBOOL(hAPP_int_bool(P,minus_minus_int(I_2,one_one_int)))))) -> hBOOL(hAPP_int_bool(P,I_1)))))) # label(fact_294_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 300 (all P 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,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,I_2)) -> hBOOL(hAPP_int_bool(P,minus_minus_int(I_2,one_one_int)))))) -> hBOOL(hAPP_int_bool(P,I_1)))))) # label(fact_295_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 301 (all P 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,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,I_2)) -> hBOOL(hAPP_int_bool(P,plus_plus_int(I_2,one_one_int)))))) -> hBOOL(hAPP_int_bool(P,I_1)))))) # label(fact_296_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 302 (all P 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,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,I_2)) -> hBOOL(hAPP_int_bool(P,plus_plus_int(I_2,one_one_int)))))) -> hBOOL(hAPP_int_bool(P,I_1)))))) # label(fact_297_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 303 (all I_1 all P all K_1 (hBOOL(hAPP_int_bool(P,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,I_2)) -> hBOOL(hAPP_int_bool(P,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,I_2)) -> hBOOL(hAPP_int_bool(P,minus_minus_int(I_2,one_one_int)))))) -> hBOOL(hAPP_int_bool(P,I_1)))))) # label(fact_298_int__induct) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 304 (all B all A_19 all C_31 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_19),C_31)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),C_31)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),B)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),A_19))))) # label(fact_299_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 305 (all X_1 all P ((all A_88 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_88)) -> hBOOL(hAPP_int_bool(P,minus_minus_int(A_88,one_one_int)))) -> hBOOL(hAPP_int_bool(P,A_88)))) -> hBOOL(hAPP_int_bool(P,X_1)))) # label(fact_300_d22set__induct__old) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 306 (all V_1 all U_1 all Y_8 all X_9 all A_87 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),A_87)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_8),A_87)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_1)) -> (plus_plus_int(U_1,V_1) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(times_times_int(U_1,X_9),times_times_int(V_1,Y_8))),A_87)))))))) # label(fact_301_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 307 (all A_86 times_times_nat(zero_zero_nat,A_86) = zero_zero_nat) # label(fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 308 (all A_86 times_times_int(zero_zero_int,A_86) = zero_zero_int) # label(fact_303_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 309 (all A_85 times_times_nat(A_85,zero_zero_nat) = zero_zero_nat) # label(fact_304_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 310 (all A_85 times_times_int(A_85,zero_zero_int) = zero_zero_int) # label(fact_305_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 311 (all A_84 times_times_nat(zero_zero_nat,A_84) = zero_zero_nat) # label(fact_306_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 312 (all A_84 times_times_int(zero_zero_int,A_84) = zero_zero_int) # label(fact_307_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 313 (all A_83 times_times_nat(A_83,zero_zero_nat) = zero_zero_nat) # label(fact_308_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 314 (all A_83 times_times_int(A_83,zero_zero_int) = zero_zero_int) # label(fact_309_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 315 (all Aa all Ba (times_times_int(Aa,Ba) = zero_zero_int <-> Aa = zero_zero_int | Ba = zero_zero_int)) # label(fact_310_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 316 (all B_65 all A_82 (A_82 != zero_zero_nat -> (B_65 != zero_zero_nat -> times_times_nat(A_82,B_65) != zero_zero_nat))) # label(fact_311_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 317 (all B_65 all A_82 (A_82 != zero_zero_int -> (B_65 != zero_zero_int -> times_times_int(A_82,B_65) != zero_zero_int))) # label(fact_312_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 318 (all A_81 all B_64 (times_times_nat(A_81,B_64) = zero_zero_nat -> A_81 = zero_zero_nat | B_64 = zero_zero_nat)) # label(fact_313_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 319 (all A_81 all B_64 (times_times_int(A_81,B_64) = zero_zero_int -> A_81 = zero_zero_int | B_64 = zero_zero_int)) # label(fact_314_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 320 (all A_80 plus_plus_nat(zero_zero_nat,A_80) = A_80) # label(fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 321 (all A_80 plus_plus_int(zero_zero_int,A_80) = A_80) # label(fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 322 (all A_79 plus_plus_nat(A_79,zero_zero_nat) = A_79) # label(fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 323 (all A_79 plus_plus_int(A_79,zero_zero_int) = A_79) # label(fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 324 (all Ba all Aa (Ba = plus_plus_nat(Ba,Aa) <-> Aa = zero_zero_nat)) # label(fact_319_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 325 (all Ba all Aa (Ba = plus_plus_int(Ba,Aa) <-> Aa = zero_zero_int)) # label(fact_320_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 326 (all A_78 plus_plus_nat(zero_zero_nat,A_78) = A_78) # label(fact_321_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 327 (all A_78 plus_plus_int(zero_zero_int,A_78) = A_78) # label(fact_322_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 328 (all A_77 plus_plus_nat(zero_zero_nat,A_77) = A_77) # label(fact_323_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 329 (all A_77 plus_plus_int(zero_zero_int,A_77) = A_77) # label(fact_324_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 330 (all Aa (zero_zero_int = plus_plus_int(Aa,Aa) <-> Aa = zero_zero_int)) # label(fact_325_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 331 (all A_76 plus_plus_nat(A_76,zero_zero_nat) = A_76) # label(fact_326_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 332 (all A_76 plus_plus_int(A_76,zero_zero_int) = A_76) # label(fact_327_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 333 (all A_75 plus_plus_nat(A_75,zero_zero_nat) = A_75) # label(fact_328_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 334 (all A_75 plus_plus_int(A_75,zero_zero_int) = A_75) # label(fact_329_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 335 (all Aa (plus_plus_int(Aa,Aa) = zero_zero_int <-> Aa = zero_zero_int)) # label(fact_330_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 336 (all X_1 (zero_zero_nat = X_1 <-> X_1 = zero_zero_nat)) # label(fact_331_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 337 (all X_1 (zero_zero_int = X_1 <-> X_1 = zero_zero_int)) # label(fact_332_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 338 (all A_74 minus_minus_int(A_74,zero_zero_int) = A_74) # label(fact_333_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 339 (all A_73 minus_minus_int(A_73,A_73) = zero_zero_int) # label(fact_334_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 340 (all Aa all Ba (Aa = Ba <-> minus_minus_int(Aa,Ba) = zero_zero_int)) # label(fact_335_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 341 (all Aa all Ba (minus_minus_int(Aa,Ba) = zero_zero_int <-> Aa = Ba)) # label(fact_336_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 342 (all Z plus_plus_int(Z,zero_zero_int) = Z) # label(fact_342_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 343 (all Z plus_plus_int(zero_zero_int,Z) = Z) # label(fact_343_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 344 (all B_63 all A_72 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_72)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_63),zero_zero_nat)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_72),zero_zero_nat)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_63)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(A_72,B_63)),zero_zero_nat)))) # label(fact_344_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 345 (all B_63 all A_72 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_72)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_63),zero_zero_int)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_72),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_63)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_72,B_63)),zero_zero_int)))) # label(fact_345_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 346 (all B_62 all A_71 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_71)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_62)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_71),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_62),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(A_71,B_62))))) # label(fact_346_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 347 (all C_30 all D_10 all A_70 all B_61 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_70),B_61)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_30),D_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_61)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_30)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(A_70,C_30)),times_times_nat(B_61,D_10)))))))) # label(fact_347_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 348 (all C_30 all D_10 all A_70 all B_61 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_70),B_61)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_30),D_10)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_61)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_30)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_70,C_30)),times_times_int(B_61,D_10)))))))) # label(fact_348_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 349 (all C_29 all D_9 all A_69 all B_60 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_69),B_60)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_29),D_9)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_69)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(A_69,C_29)),times_times_nat(B_60,D_9)))))))) # label(fact_349_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 350 (all C_29 all D_9 all A_69 all B_60 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_69),B_60)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_29),D_9)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_69)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_29)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_69,C_29)),times_times_int(B_60,D_9)))))))) # label(fact_350_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 351 (all C_28 all B_59 all A_68 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_59),A_68)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_28),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(C_28,A_68)),times_times_int(C_28,B_59)))))) # label(fact_351_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 352 (all C_27 all B_58 all A_67 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_58),A_67)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_27),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_67,C_27)),times_times_int(B_58,C_27)))))) # label(fact_352_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 353 (all C_26 all A_66 all B_57 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_66),B_57)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_26)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(C_26,A_66)),times_times_nat(C_26,B_57)))))) # label(fact_353_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 354 (all C_26 all A_66 all B_57 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_66),B_57)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_26)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(C_26,A_66)),times_times_int(C_26,B_57)))))) # label(fact_354_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 355 (all C_25 all A_65 all B_56 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_65),B_56)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_25)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(C_25,A_65)),times_times_nat(C_25,B_56)))))) # label(fact_355_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 356 (all C_25 all A_65 all B_56 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_65),B_56)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_25)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(C_25,A_65)),times_times_int(C_25,B_56)))))) # label(fact_356_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 357 (all C_24 all A_64 all B_55 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_64),B_55)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_24)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(A_64,C_24)),times_times_nat(B_55,C_24)))))) # label(fact_357_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 358 (all C_24 all A_64 all B_55 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_64),B_55)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_24)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_64,C_24)),times_times_int(B_55,C_24)))))) # label(fact_358_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 359 (all B_54 all A_63 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_63),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_54),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(A_63,B_54)))))) # label(fact_359_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 360 (all B_53 all A_62 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_62),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_53)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(A_62,B_53)),zero_zero_nat))))) # label(fact_360_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 361 (all B_53 all A_62 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_62),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_53)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_62,B_53)),zero_zero_int))))) # label(fact_361_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 362 (all B_52 all A_61 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_61)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_52),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(B_52,A_61)),zero_zero_nat))))) # label(fact_362_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 363 (all B_52 all A_61 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_61)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_52),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(B_52,A_61)),zero_zero_int))))) # label(fact_363_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 364 (all B_51 all A_60 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_60)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_51),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(A_60,B_51)),zero_zero_nat))))) # label(fact_364_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 365 (all B_51 all A_60 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_60)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_51),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_60,B_51)),zero_zero_int))))) # label(fact_365_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 366 (all B_50 all A_59 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_59)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_50)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),times_times_nat(A_59,B_50)))))) # label(fact_366_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 367 (all B_50 all A_59 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_59)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_50)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(A_59,B_50)))))) # label(fact_367_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 368 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_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_368_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 369 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_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_369_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 370 (all A_58 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(A_58,A_58)))) # label(fact_370_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 371 (all C_23 all B_49 all A_57 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_49),A_57)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_23),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(C_23,A_57)),times_times_int(C_23,B_49)))))) # label(fact_371_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 372 (all C_22 all B_48 all A_56 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_48),A_56)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_22),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_56,C_22)),times_times_int(B_48,C_22)))))) # label(fact_372_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 373 (all C_21 all A_55 all B_47 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_55),B_47)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_21)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(C_21,A_55)),times_times_nat(C_21,B_47)))))) # label(fact_373_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 374 (all C_21 all A_55 all B_47 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_55),B_47)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_21)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(C_21,A_55)),times_times_int(C_21,B_47)))))) # label(fact_374_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 375 (all C_20 all A_54 all B_46 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_54),B_46)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_20)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(C_20,A_54)),times_times_nat(C_20,B_46)))))) # label(fact_375_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 376 (all C_20 all A_54 all B_46 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_54),B_46)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_20)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(C_20,A_54)),times_times_int(C_20,B_46)))))) # label(fact_376_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 377 (all C_19 all A_53 all B_45 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_53),B_45)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_19)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_53,C_19)),times_times_nat(B_45,C_19)))))) # label(fact_377_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 378 (all C_19 all A_53 all B_45 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_53),B_45)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_19)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_53,C_19)),times_times_int(B_45,C_19)))))) # label(fact_378_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 379 (all B_44 all A_52 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_52),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_44),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),times_times_int(A_52,B_44)))))) # label(fact_379_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 380 (all B_43 all A_51 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_51),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_43)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_51,B_43)),zero_zero_nat))))) # label(fact_380_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 381 (all B_43 all A_51 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_51),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_43)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_51,B_43)),zero_zero_int))))) # label(fact_381_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 382 (all Aa all Ba all C_4 (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,times_times_int(C_4,Aa)),times_times_int(C_4,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa))))) # label(fact_382_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 383 (all B_42 all A_50 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),times_times_nat(B_42,A_50))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_50)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_42))))) # label(fact_383_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 384 (all B_42 all A_50 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),times_times_int(B_42,A_50))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_50)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_42))))) # label(fact_384_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 385 (all A_49 all B_41 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),times_times_nat(A_49,B_41))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_49)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_41))))) # label(fact_385_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 386 (all A_49 all B_41 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),times_times_int(A_49,B_41))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_49)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_41))))) # label(fact_386_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 387 (all B_40 all A_48 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_48)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_40),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(B_40,A_48)),zero_zero_nat))))) # label(fact_387_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 388 (all B_40 all A_48 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_48)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_40),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(B_40,A_48)),zero_zero_int))))) # label(fact_388_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 389 (all B_39 all A_47 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_47)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_39),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_47,B_39)),zero_zero_nat))))) # label(fact_389_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 390 (all B_39 all A_47 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_47)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_39),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_47,B_39)),zero_zero_int))))) # label(fact_390_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 391 (all B_38 all A_46 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_46)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_38)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),times_times_nat(A_46,B_38)))))) # label(fact_391_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 392 (all B_38 all A_46 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_46)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_38)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),times_times_int(A_46,B_38)))))) # label(fact_392_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 393 (all Aa all Ba all C_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(C_4,Aa)),times_times_int(C_4,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba))))) # label(fact_393_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 394 (all C_4 all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(C_4,Aa)),times_times_int(C_4,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_4)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | 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,Ba),Aa)))) # label(fact_394_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 395 (all Aa all C_4 all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(Aa,C_4)),times_times_int(Ba,C_4))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_4)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | 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,Ba),Aa)))) # label(fact_395_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 396 (all A_45 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_45,A_45)),zero_zero_int))) # label(fact_396_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 397 (all B_37 all A_44 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_44),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_37),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,plus_plus_nat(A_44,B_37)),zero_zero_nat))))) # label(fact_397_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 398 (all B_37 all A_44 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_44),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_37),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(A_44,B_37)),zero_zero_int))))) # label(fact_398_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 399 (all B_36 all A_43 all C_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_18)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_36),A_43)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_36),plus_plus_nat(A_43,C_18)))))) # label(fact_399_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 400 (all B_36 all A_43 all C_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_18)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_36),A_43)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_36),plus_plus_int(A_43,C_18)))))) # label(fact_400_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 401 (all B_35 all C_17 all A_42 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_42)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_35),C_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_35),plus_plus_nat(A_42,C_17)))))) # label(fact_401_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 402 (all B_35 all C_17 all A_42 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_42)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_35),C_17)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_35),plus_plus_int(A_42,C_17)))))) # label(fact_402_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 403 (all Y_3 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_3)) -> (plus_plus_nat(X_1,Y_3) = zero_zero_nat <-> X_1 = zero_zero_nat & Y_3 = zero_zero_nat)))) # label(fact_403_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 404 (all Y_3 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_3)) -> (plus_plus_int(X_1,Y_3) = zero_zero_int <-> X_1 = zero_zero_int & Y_3 = zero_zero_int)))) # label(fact_404_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 405 (all B_34 all A_41 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_41)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_34)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),plus_plus_nat(A_41,B_34)))))) # label(fact_405_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 406 (all B_34 all A_41 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_41)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_34)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(A_41,B_34)))))) # label(fact_406_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 407 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_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_407_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 408 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(Aa,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)))) # label(fact_408_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 409 (all B_33 all A_40 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_40),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_33),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(A_40,B_33)),zero_zero_nat))))) # label(fact_409_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 410 (all B_33 all A_40 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_40),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_33),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(A_40,B_33)),zero_zero_int))))) # label(fact_410_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 411 (all B_32 all C_16 all A_39 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_39)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_32),C_16)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_32),plus_plus_nat(A_39,C_16)))))) # label(fact_411_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 412 (all B_32 all C_16 all A_39 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_39)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_32),C_16)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_32),plus_plus_int(A_39,C_16)))))) # label(fact_412_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 413 (all B_31 all A_38 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_38)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_31)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(A_38,B_31)))))) # label(fact_413_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 414 (all B_31 all A_38 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_38)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_31)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(A_38,B_31)))))) # label(fact_414_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 415 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(Aa,Aa)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int)))) # label(fact_415_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 416 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(Aa,Aa)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int)))) # label(fact_416_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 417 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(Aa,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa)))) # label(fact_417_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 418 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,minus_minus_int(Aa,Ba)),zero_zero_int)))) # label(fact_426_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 419 (all C_15 all D_8 all A_37 all B_30 all R_3 (R_3 != zero_zero_nat -> (A_37 = B_30 & C_15 != D_8 -> plus_plus_nat(A_37,times_times_nat(R_3,C_15)) != plus_plus_nat(B_30,times_times_nat(R_3,D_8))))) # label(fact_427_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 420 (all C_15 all D_8 all A_37 all B_30 all R_3 (R_3 != zero_zero_int -> (A_37 = B_30 & C_15 != D_8 -> plus_plus_int(A_37,times_times_int(R_3,C_15)) != plus_plus_int(B_30,times_times_int(R_3,D_8))))) # label(fact_428_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 421 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,minus_minus_int(Aa,Ba)),zero_zero_int)))) # label(fact_429_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 422 (all A_19 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_19)) -> (X != minus_minus_int(A_19,one_one_int) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),minus_minus_int(A_19,one_one_int))))))) # label(fact_430_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 423 (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,times_times_int(K,I)),times_times_int(K,J)))))) # label(fact_432_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 424 (all Z plus_plus_int(plus_plus_int(one_one_int,Z),Z) != zero_zero_int) # label(fact_433_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 425 (all K_1 all L_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,minus_minus_int(K_1,L_1)),zero_zero_int)))) # label(fact_434_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 426 (all C_14 all A_36 all B_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(C_14,A_36)),times_times_nat(C_14,B_29))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_14)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_36),B_29))))) # label(fact_435_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 427 (all C_14 all A_36 all B_29 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(C_14,A_36)),times_times_int(C_14,B_29))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_14)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_36),B_29))))) # label(fact_436_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 428 (all A_35 all C_13 all B_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(A_35,C_13)),times_times_nat(B_28,C_13))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_13)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_35),B_28))))) # label(fact_437_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 429 (all A_35 all C_13 all B_28 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(A_35,C_13)),times_times_int(B_28,C_13))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_35),B_28))))) # label(fact_438_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 430 (all C_12 all A_34 all B_27 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(C_12,A_34)),times_times_nat(C_12,B_27))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_12)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_34),B_27))))) # label(fact_439_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 431 (all C_12 all A_34 all B_27 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(C_12,A_34)),times_times_int(C_12,B_27))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_34),B_27))))) # label(fact_440_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 432 (all C_11 all A_33 all B_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(C_11,A_33)),times_times_nat(C_11,B_26))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_33),B_26))))) # label(fact_441_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 433 (all C_11 all A_33 all B_26 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(C_11,A_33)),times_times_int(C_11,B_26))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_11)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_33),B_26))))) # label(fact_442_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 434 (all A_32 all C_10 all B_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_32,C_10)),times_times_nat(B_25,C_10))) -> (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_nat,A_32),B_25))))) # label(fact_443_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 435 (all A_32 all C_10 all B_25 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_32,C_10)),times_times_int(B_25,C_10))) -> (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_int,A_32),B_25))))) # label(fact_444_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 436 (all A_31 all C_9 all B_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_31,C_9)),times_times_nat(B_24,C_9))) -> (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_nat,A_31),B_24))))) # label(fact_445_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 437 (all A_31 all C_9 all B_24 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_31,C_9)),times_times_int(B_24,C_9))) -> (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_int,A_31),B_24))))) # label(fact_446_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 438 (all C_8 all D_7 all A_30 all B_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_30),B_23)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_8),D_7)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_30)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_30,C_8)),times_times_nat(B_23,D_7)))))))) # label(fact_447_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 439 (all C_8 all D_7 all A_30 all B_23 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_30),B_23)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_8),D_7)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_30)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_30,C_8)),times_times_int(B_23,D_7)))))))) # label(fact_448_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 440 (all C_7 all D_6 all A_29 all B_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_29),B_22)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_7),D_6)) -> (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_nat,zero_zero_nat),C_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_29,C_7)),times_times_nat(B_22,D_6)))))))) # label(fact_449_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 441 (all C_7 all D_6 all A_29 all B_22 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_29),B_22)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_7),D_6)) -> (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_int,zero_zero_int),C_7)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_29,C_7)),times_times_int(B_22,D_6)))))))) # label(fact_450_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 442 (all C_6 all D_5 all A_28 all B_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_21)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_6),D_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_28)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_28,C_6)),times_times_nat(B_21,D_5)))))))) # label(fact_451_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 443 (all C_6 all D_5 all A_28 all B_21 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_28),B_21)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_6),D_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_28)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_28,C_6)),times_times_int(B_21,D_5)))))))) # label(fact_452_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 444 (all C_5 all D_4 all A_27 all B_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_27),B_20)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_5),D_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_20)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(A_27,C_5)),times_times_nat(B_20,D_4)))))))) # label(fact_453_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 445 (all C_5 all D_4 all A_27 all B_20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_27),B_20)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_5),D_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_20)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(A_27,C_5)),times_times_int(B_20,D_4)))))))) # label(fact_454_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 446 (all Aa all Ba all C_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_4),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(C_4,Aa)),times_times_int(C_4,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa))))) # label(fact_455_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 447 (all Aa all Ba all C_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(C_4,Aa)),times_times_int(C_4,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba))))) # label(fact_456_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 448 (all B_19 all A_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(A_26,B_19)),zero_zero_nat))))) # label(fact_457_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 449 (all B_19 all A_26 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_26),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_19),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(A_26,B_19)),zero_zero_int))))) # label(fact_458_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 450 (all B_18 all A_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_25),zero_zero_nat)) -> (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_nat,plus_plus_nat(A_25,B_18)),zero_zero_nat))))) # label(fact_459_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 451 (all B_18 all A_25 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_25),zero_zero_int)) -> (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_int,plus_plus_int(A_25,B_18)),zero_zero_int))))) # label(fact_460_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 452 (all B_17 all C_3 all A_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_24)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),C_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),plus_plus_nat(A_24,C_3)))))) # label(fact_461_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 453 (all B_17 all C_3 all A_24 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_24)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),C_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_17),plus_plus_int(A_24,C_3)))))) # label(fact_462_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 454 (all B_16 all C_2 all A_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_23)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_16),C_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_16),plus_plus_nat(A_23,C_2)))))) # label(fact_463_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 455 (all B_16 all C_2 all A_23 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_23)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_16),C_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_16),plus_plus_int(A_23,C_2)))))) # label(fact_464_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 456 (all B_15 all A_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_22)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(A_22,B_15)))))) # label(fact_465_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 457 (all B_15 all A_22 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_22)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_15)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(A_22,B_15)))))) # label(fact_466_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 458 (all B_14 all A_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_21)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_14)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(A_21,B_14)))))) # label(fact_467_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 459 (all B_14 all A_21 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_21)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_14)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(A_21,B_14)))))) # label(fact_468_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 460 (all Y_7 all X_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_8)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_7)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_7),one_one_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(Y_7,X_8)),X_8)))))) # label(fact_469_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 461 (all Y_6 all X_7 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_7)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_6)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_6),one_one_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X_7,Y_6)),X_7)))))) # label(fact_470_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 462 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1)))) # label(fact_473_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 463 (all N_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (times_times_int(M_1,N_1) = one_one_int <-> M_1 = one_one_int & N_1 = one_one_int))) # label(fact_474_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 464 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(plus_plus_int(one_one_int,Z_1),Z_1)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)))) # label(fact_475_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 465 (all V all U all Y_5 all X_6 all A_20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_6),A_20)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),A_20)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V)) -> (plus_plus_int(U,V) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(times_times_int(U,X_6),times_times_int(V,Y_5))),A_20)))))))) # label(fact_476_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 466 (all Z (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,Z))))) # label(fact_477_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 467 (all R_1 all Q all A_19 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_19)) -> (A_19 = plus_plus_int(R_1,times_times_int(A_19,Q)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),A_19)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q)))))) # label(fact_478_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 468 (all R_1 all Q all A_19 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_19)) -> (A_19 = plus_plus_int(R_1,times_times_int(A_19,Q)) -> (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_eq_int,Q),one_one_int)))))) # label(fact_479_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 469 (all B_13 all Q_1 all R_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(times_times_int(B_13,Q_1),R_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_13)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_1)))))) # label(fact_480_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 470 (all B_13 all Q_1 all R_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(times_times_int(B_13,Q_1),R_2)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),zero_zero_int)))))) # label(fact_481_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 471 (all B all Q all R_1 all B_13 all Q_1 all R_2 (plus_plus_int(times_times_int(B,Q),R_1) = plus_plus_int(times_times_int(B_13,Q_1),R_2) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(times_times_int(B_13,Q_1),R_2)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_13)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_13),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q))))))))) # label(fact_482_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 472 (all B all Q_1 all R_2 all Q all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(times_times_int(B,Q_1),R_2)),plus_plus_int(times_times_int(B,Q),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q),Q_1))))))) # label(fact_483_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 473 (all B all Q all R_1 all B_13 all Q_1 all R_2 (plus_plus_int(times_times_int(B,Q),R_1) = plus_plus_int(times_times_int(B_13,Q_1),R_2) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(times_times_int(B_13,Q_1),R_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_13)) -> (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_13)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_13),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q),Q_1))))))))) # label(fact_484_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 474 (all B all Q_1 all R_2 all Q all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(times_times_int(B,Q_1),R_2)),plus_plus_int(times_times_int(B,Q),R_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q))))))) # label(fact_485_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 475 (all M all R_1 all S all T all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N)) -> (xzgcd(M,N) = produc282740534nt_int(R_1,product_Pair_int_int(S,T)) -> R_1 = plus_plus_int(times_times_int(S,M),times_times_int(T,N))))) # label(fact_486_xzgcd__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 476 (all X_5 all Y_4 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,plus_plus_int(times_times_int(X_5,X_5),times_times_int(Y_4,Y_4))),zero_zero_int))) # label(fact_487_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 477 (all X_1 all Y_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(times_times_int(X_1,X_1),times_times_int(Y_3,Y_3)))) <-> X_1 != zero_zero_int | Y_3 != zero_zero_int)) # label(fact_488_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 478 (all X_1 all Y_3 (plus_plus_int(times_times_int(X_1,X_1),times_times_int(Y_3,Y_3)) = zero_zero_int <-> X_1 = zero_zero_int & Y_3 = zero_zero_int)) # label(fact_489_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 479 (all X_1 all Y_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,plus_plus_int(times_times_int(X_1,X_1),times_times_int(Y_3,Y_3))),zero_zero_int)) <-> X_1 = zero_zero_int & Y_3 = zero_zero_int)) # label(fact_490_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 480 (all X_4 all Y_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(times_times_int(X_4,X_4),times_times_int(Y_2,Y_2))))) # label(fact_491_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 481 (all M all N all R_2 all S_1 all S all T_5 all T all Rn all Sn all Tn all R_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),R_1)) -> (xzgcda(M,N,R_2,R_1,S_1,S,T_5,T) = produc282740534nt_int(Rn,product_Pair_int_int(Sn,Tn)) -> (R_2 = plus_plus_int(times_times_int(S_1,M),times_times_int(T_5,N)) -> (R_1 = plus_plus_int(times_times_int(S,M),times_times_int(T,N)) -> Rn = plus_plus_int(times_times_int(Sn,M),times_times_int(Tn,N))))))) # label(fact_492_xzgcda__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 482 (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),plus_plus_int(X,Y)))))) # label(fact_493_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 483 (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),times_times_int(X,Y)))))) # label(fact_494_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 484 (all M all N xzgcd(M,N) = xzgcda(M,N,M,N,one_one_int,zero_zero_int,zero_zero_int,one_one_int)) # label(fact_496_xzgcd__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 485 (all B all A_19 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_19)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),times_times_int(A_19,B))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))))) # label(fact_498_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 486 (all K_1 all P all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_3)) -> ((all X_3 (hBOOL(hAPP_int_bool(P,X_3)) -> hBOOL(hAPP_int_bool(P,minus_minus_int(X_3,D_3))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> (all X_3 (hBOOL(hAPP_int_bool(P,X_3)) -> hBOOL(hAPP_int_bool(P,minus_minus_int(X_3,times_times_int(K_1,D_3)))))))))) # label(fact_499_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 487 (all K_1 all P all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_3)) -> ((all X_3 (hBOOL(hAPP_int_bool(P,X_3)) -> hBOOL(hAPP_int_bool(P,plus_plus_int(X_3,D_3))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> (all X_3 (hBOOL(hAPP_int_bool(P,X_3)) -> hBOOL(hAPP_int_bool(P,plus_plus_int(X_3,times_times_int(K_1,D_3)))))))))) # label(fact_500_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 488 (all P_1 all P all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(P) <-> hBOOL(P_1))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P)) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P_1))))) # label(fact_501_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 489 (all P_1 all P all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(P) <-> hBOOL(P_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P_1)))) # label(fact_502_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 490 (all T_4 exists Z_2 all X_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_3),Z_2)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,T_4),X_3)))) # label(fact_503_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 491 (all T_4 exists Z_2 all X_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_3),Z_2)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T_4),X_3)))) # label(fact_504_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 492 (all T_3 exists Z_2 all X_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,T_3),X_3)))) # label(fact_505_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 493 (all T_3 exists Z_2 all X_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),X_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T_3),X_3)))) # label(fact_506_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 494 (all T_2 exists Z_2 all X_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_3)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),T_2)))) # label(fact_507_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 495 (all T_2 exists Z_2 all X_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),X_3)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_3),T_2)))) # label(fact_508_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 496 (all T_1 exists Z_2 all X_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_3),Z_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),T_1)))) # label(fact_509_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 497 (all T_1 exists Z_2 all X_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_3),Z_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_3),T_1)))) # label(fact_510_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 498 (all A_19 all B all Q all R_1 (A_19 = plus_plus_int(times_times_int(B,Q),R_1) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,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,zero_zero_int),B)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),zero_zero_int))) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,B),product_Pair_int_int(Q,R_1)))))) # label(fact_511_divmod__int__relI) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 499 (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_512_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 500 (all A_19 all Q all R_1 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,A_19),product_Pair_int_int(Q,R_1))) -> (A_19 != zero_zero_int -> R_1 = zero_zero_int))) # label(fact_513_self__remainder) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 501 (all Q_1 all R_2 all A_19 all B all Q all R_1 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,B),product_Pair_int_int(Q,R_1))) -> (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,B),product_Pair_int_int(Q_1,R_2))) -> (B != zero_zero_int -> Q = Q_1)))) # label(fact_514_unique__quotient) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 502 (all Q_1 all R_2 all A_19 all B all Q all R_1 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,B),product_Pair_int_int(Q,R_1))) -> (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,B),product_Pair_int_int(Q_1,R_2))) -> (B != zero_zero_int -> R_1 = R_2)))) # label(fact_515_unique__remainder) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 503 (all A_19 all Q all R_1 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,A_19),product_Pair_int_int(Q,R_1))) -> (A_19 != zero_zero_int -> Q = one_one_int))) # label(fact_516_self__quotient) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 504 (all P all P1 all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_3)) -> ((all X_3 all K_2 (hBOOL(hAPP_int_bool(P1,X_3)) <-> hBOOL(hAPP_int_bool(P1,minus_minus_int(X_3,times_times_int(K_2,D_3)))))) -> ((exists Z_2 all X_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_3),Z_2)) -> (hBOOL(hAPP_int_bool(P,X_3)) <-> hBOOL(hAPP_int_bool(P1,X_3))))) -> ((exists X1 hBOOL(hAPP_int_bool(P1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(P,X1)))))))) # label(fact_517_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 505 (all P all P_1 all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_3)) -> ((all X_3 all K_2 (hBOOL(hAPP_int_bool(P_1,X_3)) <-> hBOOL(hAPP_int_bool(P_1,minus_minus_int(X_3,times_times_int(K_2,D_3)))))) -> ((exists Z_2 all X_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),X_3)) -> (hBOOL(hAPP_int_bool(P,X_3)) <-> hBOOL(hAPP_int_bool(P_1,X_3))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(P,X1)))))))) # label(fact_518_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 506 (all Y all X ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> nat_tsub(X,Y) = 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_519_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 507 (all N ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N),zero_zero_int)) -> zfact(N) = one_one_int) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N),zero_zero_int)) -> zfact(N) = times_times_int(N,zfact(minus_minus_int(N,one_one_int)))))) # label(fact_520_zfact_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 508 (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_521_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 509 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> nat_tsub(X,Y) = minus_minus_int(X,Y))) # label(fact_522_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 510 (all B 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_int,zero_zero_int),B)) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_19,B),posDivAlg(A_19,B)))))) # label(fact_523_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 511 (all X all Z all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,minus_minus_int(X,times_times_int(plus_plus_int(abs_abs_int(minus_minus_int(X,Z)),one_one_int),D))),Z)))) # label(fact_524_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 512 (all Aa (abs_abs_int(Aa) = zero_zero_int <-> Aa = zero_zero_int)) # label(fact_525_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 513 (all A_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_18)) -> abs_abs_int(A_18) = A_18)) # label(fact_527_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 514 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(Aa)),zero_zero_int)) <-> Aa = zero_zero_int)) # label(fact_528_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 515 (all A_17 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),abs_abs_int(A_17)))) # label(fact_529_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 516 (all A_16 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_16)) -> abs_abs_int(A_16) = A_16)) # label(fact_530_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 517 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),abs_abs_int(Aa))) <-> Aa != zero_zero_int)) # label(fact_531_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 518 (all A_15 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(A_15)),zero_zero_int))) # label(fact_532_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 519 (all B_12 all D_2 all A_14 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(A_14)),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(B_12)),D_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(abs_abs_int(A_14),abs_abs_int(B_12))),times_times_int(C_1,D_2)))))) # label(fact_533_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 520 (all A_13 all B_11 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(plus_plus_int(A_13,B_11))),plus_plus_int(abs_abs_int(A_13),abs_abs_int(B_11))))) # label(fact_534_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 521 (all A_12 all B_10 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(minus_minus_int(abs_abs_int(A_12),abs_abs_int(B_10)))),abs_abs_int(minus_minus_int(A_12,B_10))))) # label(fact_535_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 522 (all A_11 all B_9 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,minus_minus_int(abs_abs_int(A_11),abs_abs_int(B_9))),abs_abs_int(minus_minus_int(A_11,B_9))))) # label(fact_536_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 523 (all A_10 all B_8 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,minus_minus_int(abs_abs_int(A_10),abs_abs_int(B_8))),abs_abs_int(minus_minus_int(B_8,A_10))))) # label(fact_537_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 524 (all M all N (abs_abs_int(times_times_int(M,N)) = one_one_int -> abs_abs_int(M) = one_one_int)) # label(fact_538_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 525 (all A_9 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_9),abs_abs_int(A_9)))) # label(fact_539_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 526 (all A_8 all B_7 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(A_8)),B_7)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_8),B_7)))) # label(fact_540_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 527 (all A_7 all B_6 abs_abs_int(times_times_int(A_7,B_6)) = times_times_int(abs_abs_int(A_7),abs_abs_int(B_6))) # label(fact_541_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 528 (all A_6 times_times_int(abs_abs_int(A_6),abs_abs_int(A_6)) = times_times_int(A_6,A_6)) # label(fact_542_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 529 (all A_5 all B_5 abs_abs_int(plus_plus_int(abs_abs_int(A_5),abs_abs_int(B_5))) = plus_plus_int(abs_abs_int(A_5),abs_abs_int(B_5))) # label(fact_543_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 530 (all A_4 all B_4 abs_abs_int(minus_minus_int(A_4,B_4)) = abs_abs_int(minus_minus_int(B_4,A_4))) # label(fact_545_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 531 (all A_3 abs_abs_int(abs_abs_int(A_3)) = abs_abs_int(A_3)) # label(fact_546_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 532 (all Y_1 all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> times_times_int(abs_abs_int(Y_1),X_2) = abs_abs_int(times_times_int(Y_1,X_2)))) # label(fact_547_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 533 (all B_3 all A_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int))) & (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_3)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_3),zero_zero_int))) -> abs_abs_int(times_times_int(A_2,B_3)) = times_times_int(abs_abs_int(A_2),abs_abs_int(B_3)))) # label(fact_548_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 534 (all A_1 all B_2 all C all D_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(minus_minus_int(plus_plus_int(A_1,B_2),plus_plus_int(C,D_1)))),plus_plus_int(abs_abs_int(minus_minus_int(A_1,C)),abs_abs_int(minus_minus_int(B_2,D_1)))))) # label(fact_549_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 535 (all A all B_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(minus_minus_int(A,B_1))),plus_plus_int(abs_abs_int(A),abs_abs_int(B_1))))) # label(fact_550_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 536 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(Z_1)),one_one_int)) <-> Z_1 = zero_zero_int)) # label(fact_551_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 537 (all B posDivAlg(zero_zero_int,B) = product_Pair_int_int(zero_zero_int,zero_zero_int)) # label(fact_552_posDivAlg__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 538 (all Z all X all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),plus_plus_int(X,times_times_int(plus_plus_int(abs_abs_int(minus_minus_int(X,Z)),one_one_int),D)))))) # label(fact_553_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 539 (all X_1 all Aa all R (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(minus_minus_int(X_1,Aa))),R)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,minus_minus_int(Aa,R)),X_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),plus_plus_int(Aa,R))))) # label(fact_554_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 540 (all K all L ((L = zero_zero_int -> pdivmod(K,L) = product_Pair_int_int(zero_zero_int,abs_abs_int(K))) & (L != zero_zero_int -> pdivmod(K,L) = posDivAlg(abs_abs_int(K),abs_abs_int(L))))) # label(fact_555_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 541 (all K_1 all F all N_1 ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(minus_minus_int(hAPP_nat_int(F,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_1))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N_1)) & hAPP_nat_int(F,I_2) = K_1)))))) # label(fact_556_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 542 (all K_1 all F all N_1 ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(minus_minus_int(hAPP_nat_int(F,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_1))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N_1)) & hAPP_nat_int(F,I_2) = K_1)))))) # label(fact_557_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 543 (all N all M ((M = zero_zero_nat -> times_times_nat(M,N) = zero_zero_nat) & (M != zero_zero_nat -> times_times_nat(M,N) = plus_plus_nat(N,times_times_nat(minus_minus_nat(M,one_one_nat),N))))) # label(fact_558_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 544 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_559_le0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 545 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_560_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 546 (all M all N times_times_nat(M,N) = times_times_nat(N,M)) # label(fact_561_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 547 (all M all N all K times_times_nat(times_times_nat(M,N),K) = times_times_nat(M,times_times_nat(N,K))) # label(fact_562_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 548 (all M all N all K times_times_nat(minus_minus_nat(M,N),K) = minus_minus_nat(times_times_nat(M,K),times_times_nat(N,K))) # label(fact_563_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 549 (all I all J all K minus_minus_nat(minus_minus_nat(I,J),K) = minus_minus_nat(minus_minus_nat(I,K),J)) # label(fact_564_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 550 (all K all M all N times_times_nat(K,minus_minus_nat(M,N)) = minus_minus_nat(times_times_nat(K,M),times_times_nat(K,N))) # label(fact_565_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 551 (all N times_times_nat(zero_zero_nat,N) = zero_zero_nat) # label(fact_566_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 552 (all M times_times_nat(M,zero_zero_nat) = zero_zero_nat) # label(fact_567_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 553 (all M_1 all N_1 (times_times_nat(M_1,N_1) = zero_zero_nat <-> M_1 = zero_zero_nat | N_1 = zero_zero_nat)) # label(fact_568_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 554 (all K_1 all M_1 all N_1 (times_times_nat(K_1,M_1) = times_times_nat(K_1,N_1) <-> M_1 = N_1 | K_1 = zero_zero_nat)) # label(fact_569_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 555 (all M_1 all K_1 all N_1 (times_times_nat(M_1,K_1) = times_times_nat(N_1,K_1) <-> M_1 = N_1 | K_1 = zero_zero_nat)) # label(fact_570_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 556 (all M all N (minus_minus_nat(M,N) = zero_zero_nat -> (minus_minus_nat(N,M) = zero_zero_nat -> M = N))) # label(fact_571_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 557 (all M minus_minus_nat(M,M) = zero_zero_nat) # label(fact_572_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 558 (all M minus_minus_nat(M,zero_zero_nat) = M) # label(fact_573_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 559 (all N minus_minus_nat(zero_zero_nat,N) = zero_zero_nat) # label(fact_574_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 560 (all N all J all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,minus_minus_nat(J,N)),K)))) # label(fact_575_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.46 561 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,minus_minus_nat(L,N)),minus_minus_nat(L,M)))))) # label(fact_576_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 562 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_577_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 563 (all M_1 all N_1 (M_1 != N_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)))) # label(fact_578_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 564 (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_579_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 565 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_580_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 566 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> M != N)) # label(fact_581_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 567 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_582_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 568 (all P all M_1 all N_1 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P,N_1),M_1))) -> ((M_1 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P,N_1),M_1))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P,N_1),M_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P,N_1),M_1)))))) # label(fact_583_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 569 (all M all N plus_plus_nat(M,N) = plus_plus_nat(N,M)) # label(fact_584_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 570 (all X all Y all Z plus_plus_nat(X,plus_plus_nat(Y,Z)) = plus_plus_nat(Y,plus_plus_nat(X,Z))) # label(fact_585_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 571 (all K all M all N times_times_nat(K,plus_plus_nat(M,N)) = plus_plus_nat(times_times_nat(K,M),times_times_nat(K,N))) # label(fact_586_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 572 (all M all N all K plus_plus_nat(plus_plus_nat(M,N),K) = plus_plus_nat(M,plus_plus_nat(N,K))) # label(fact_587_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 573 (all M all N all K times_times_nat(plus_plus_nat(M,N),K) = plus_plus_nat(times_times_nat(M,K),times_times_nat(N,K))) # label(fact_588_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 574 (all K_1 all M_1 all N_1 (plus_plus_nat(K_1,M_1) = plus_plus_nat(K_1,N_1) <-> M_1 = N_1)) # label(fact_589_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 575 (all M_1 all K_1 all N_1 (plus_plus_nat(M_1,K_1) = plus_plus_nat(N_1,K_1) <-> M_1 = N_1)) # label(fact_590_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 576 (all M all K all N minus_minus_nat(plus_plus_nat(M,K),plus_plus_nat(N,K)) = minus_minus_nat(M,N)) # label(fact_591_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 577 (all K all M all N minus_minus_nat(plus_plus_nat(K,M),plus_plus_nat(K,N)) = minus_minus_nat(M,N)) # label(fact_592_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 578 (all I all J all K minus_minus_nat(minus_minus_nat(I,J),K) = minus_minus_nat(I,plus_plus_nat(J,K))) # label(fact_593_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 579 (all N all M minus_minus_nat(plus_plus_nat(N,M),N) = M) # label(fact_594_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 580 (all M all N minus_minus_nat(plus_plus_nat(M,N),N) = M) # label(fact_595_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 581 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(M,N)),M))) # label(fact_596_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 582 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(L,N)),minus_minus_nat(L,M))))) # label(fact_597_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 583 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(M,L)),minus_minus_nat(N,L))))) # label(fact_598_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 584 (all I all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) -> minus_minus_nat(N,minus_minus_nat(N,I)) = I)) # label(fact_599_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 585 (all N_1 all K_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (minus_minus_nat(M_1,K_1) = minus_minus_nat(N_1,K_1) <-> M_1 = N_1)))) # label(fact_600_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 586 (all N all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> minus_minus_nat(minus_minus_nat(M,K),minus_minus_nat(N,K)) = minus_minus_nat(M,N)))) # label(fact_601_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 587 (all N_1 all K_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(M_1,K_1)),minus_minus_nat(N_1,K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))))) # label(fact_602_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 588 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N))) # label(fact_603_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 589 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)))) # label(fact_604_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 590 (all M all N (M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_605_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 591 (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_606_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 592 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> M = N))) # label(fact_607_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 593 (all K all L 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)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,times_times_nat(I,K)),times_times_nat(J,L)))))) # label(fact_608_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 594 (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,times_times_nat(K,I)),times_times_nat(K,J))))) # label(fact_609_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 595 (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,times_times_nat(I,K)),times_times_nat(J,K))))) # label(fact_610_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 596 (all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),times_times_nat(M,times_times_nat(M,M))))) # label(fact_611_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 597 (all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),times_times_nat(M,M)))) # label(fact_612_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 598 (all N times_times_nat(one_one_nat,N) = N) # label(fact_613_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 599 (all M_1 all N_1 (one_one_nat = times_times_nat(M_1,N_1) <-> M_1 = one_one_nat & N_1 = one_one_nat)) # label(fact_614_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 600 (all N times_times_nat(N,one_one_nat) = N) # label(fact_615_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 601 (all M_1 all N_1 (times_times_nat(M_1,N_1) = one_one_nat <-> M_1 = one_one_nat & N_1 = one_one_nat)) # label(fact_616_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 602 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),minus_minus_nat(N_1,M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_617_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 603 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,minus_minus_nat(M,N)),M))))) # label(fact_618_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 604 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_619_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 605 (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_620_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 606 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_621_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 607 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> N != zero_zero_nat)) # label(fact_622_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 608 (all N (N != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_623_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 609 (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,times_times_nat(K,I)),times_times_nat(K,J)))))) # label(fact_624_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 610 (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,times_times_nat(I,K)),times_times_nat(J,K)))))) # label(fact_625_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 611 (all M_1 all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(M_1,K_1)),times_times_nat(N_1,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_1)))) # label(fact_626_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 612 (all K_1 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,times_times_nat(K_1,M_1)),times_times_nat(K_1,N_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_1)))) # label(fact_627_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 613 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),times_times_nat(M_1,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_628_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 614 (all N plus_plus_nat(zero_zero_nat,N) = N) # label(fact_629_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 615 (all M plus_plus_nat(M,zero_zero_nat) = M) # label(fact_630_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 616 (all M_1 all N_1 (plus_plus_nat(M_1,N_1) = zero_zero_nat <-> M_1 = zero_zero_nat & N_1 = zero_zero_nat)) # label(fact_631_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 617 (all M all N (plus_plus_nat(M,N) = M -> N = zero_zero_nat)) # label(fact_632_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 618 (all N all M minus_minus_nat(N,plus_plus_nat(N,M)) = zero_zero_nat) # label(fact_633_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 619 (all M_1 all N_1 (minus_minus_nat(M_1,N_1) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_634_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 620 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> minus_minus_nat(M,N) = zero_zero_nat)) # label(fact_635_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 621 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_636_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 622 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),zero_zero_nat)) <-> N_1 = zero_zero_nat)) # label(fact_637_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 623 (all I_1 all J_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),minus_minus_nat(J_1,K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(I_1,K_1)),J_1)))) # label(fact_638_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 624 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> plus_plus_nat(N,minus_minus_nat(M,N)) = M)) # label(fact_639_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 625 (all I all J all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(I,J)),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)))) # label(fact_640_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 626 (all M all N all K all L (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) -> (plus_plus_nat(M,L) = plus_plus_nat(K,N) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_641_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 627 (all K all L 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)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(I,K)),plus_plus_nat(J,L)))))) # label(fact_642_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 628 (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,plus_plus_nat(I,K)),plus_plus_nat(J,K))))) # label(fact_643_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 629 (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),plus_plus_nat(M,J))))) # label(fact_644_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47 630 (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),plus_plus_nat(J,M))))) # label(fact_645_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.47
% 1.10/1.47 ============================== end of process non-clausal formulas ===
% 1.10/1.47
% 1.10/1.47 ============================== PROCCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------