TSTP Solution File: NUM923+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM923+4 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 13:33:10 EDT 2022
% Result : Unknown 32.88s 32.92s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM923+4 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 19:29:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.57/4.66 ============================== Prover9 ===============================
% 4.57/4.66 Prover9 (32) version 2009-11A, November 2009.
% 4.57/4.66 Process 20959 was started by sandbox on n012.cluster.edu,
% 4.57/4.66 Tue Jul 5 19:29:34 2022
% 4.57/4.66 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20806_n012.cluster.edu".
% 4.57/4.66 ============================== end of head ===========================
% 4.57/4.66
% 4.57/4.66 ============================== INPUT =================================
% 4.57/4.66
% 4.57/4.66 % Reading from file /tmp/Prover9_20806_n012.cluster.edu
% 4.57/4.66
% 4.57/4.66 set(prolog_style_variables).
% 4.57/4.66 set(auto2).
% 4.57/4.66 % set(auto2) -> set(auto).
% 4.57/4.66 % set(auto) -> set(auto_inference).
% 4.57/4.66 % set(auto) -> set(auto_setup).
% 4.57/4.66 % set(auto_setup) -> set(predicate_elim).
% 4.57/4.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.57/4.66 % set(auto) -> set(auto_limits).
% 4.57/4.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.57/4.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.57/4.66 % set(auto) -> set(auto_denials).
% 4.57/4.66 % set(auto) -> set(auto_process).
% 4.57/4.66 % set(auto2) -> assign(new_constants, 1).
% 4.57/4.66 % set(auto2) -> assign(fold_denial_max, 3).
% 4.57/4.66 % set(auto2) -> assign(max_weight, "200.000").
% 4.57/4.66 % set(auto2) -> assign(max_hours, 1).
% 4.57/4.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.57/4.66 % set(auto2) -> assign(max_seconds, 0).
% 4.57/4.66 % set(auto2) -> assign(max_minutes, 5).
% 4.57/4.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.57/4.66 % set(auto2) -> set(sort_initial_sos).
% 4.57/4.66 % set(auto2) -> assign(sos_limit, -1).
% 4.57/4.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.57/4.66 % set(auto2) -> assign(max_megs, 400).
% 4.57/4.66 % set(auto2) -> assign(stats, some).
% 4.57/4.66 % set(auto2) -> clear(echo_input).
% 4.57/4.66 % set(auto2) -> set(quiet).
% 4.57/4.66 % set(auto2) -> clear(print_initial_clauses).
% 4.57/4.66 % set(auto2) -> clear(print_given).
% 4.57/4.66 assign(lrs_ticks,-1).
% 4.57/4.66 assign(sos_limit,10000).
% 4.57/4.66 assign(order,kbo).
% 4.57/4.66 set(lex_order_vars).
% 4.57/4.66 clear(print_given).
% 4.57/4.66
% 4.57/4.66 % formulas(sos). % not echoed (5469 formulas)
% 4.57/4.66
% 4.57/4.66 ============================== end of input ==========================
% 4.57/4.66
% 4.57/4.66 % From the command line: assign(max_seconds, 300).
% 4.57/4.66
% 4.57/4.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.57/4.66
% 4.57/4.66 % Formulas that are not ordinary clauses:
% 4.57/4.66 1 (all B_1_1 all B_2_1 all B_3_1 is_bool(tendst1507391555omplex(B_1_1,B_2_1,B_3_1))) # label(gsy_c_Limits_Otendsto_000tc__Complex__Ocomplex_000tc__Complex__Ocomplex) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 2 (all B_1_1 all B_2_1 all B_3_1 is_bool(tendsto_complex_real(B_1_1,B_2_1,B_3_1))) # label(gsy_c_Limits_Otendsto_000tc__Complex__Ocomplex_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 3 (all B_1_1 all B_2_1 all B_3_1 is_bool(tendsto_nat_complex(B_1_1,B_2_1,B_3_1))) # label(gsy_c_Limits_Otendsto_000tc__Nat__Onat_000tc__Complex__Ocomplex) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 4 (all B_1_1 all B_2_1 all B_3_1 is_bool(tendsto_nat_real(B_1_1,B_2_1,B_3_1))) # label(gsy_c_Limits_Otendsto_000tc__Nat__Onat_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 5 (all B_1_1 all B_2_1 all B_3_1 is_bool(tendsto_real_real(B_1_1,B_2_1,B_3_1))) # label(gsy_c_Limits_Otendsto_000tc__RealDef__Oreal_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 6 (all B_1_1 is_bool(trivial_limit_nat(B_1_1))) # label(gsy_c_Limits_Otrivial__limit_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 7 (all B_1_1 is_bool(vanishes(B_1_1))) # label(gsy_c_RealDef_Ovanishes) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 8 (all B_1_1 is_bool(bseq_real(B_1_1))) # label(gsy_c_SEQ_OBseq_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 9 (all B_1_1 is_bool(cauchy_complex(B_1_1))) # label(gsy_c_SEQ_OCauchy_000tc__Complex__Ocomplex) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 10 (all B_1_1 is_bool(cauchy_real(B_1_1))) # label(gsy_c_SEQ_OCauchy_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 11 (all B_1_1 is_bool(monoseq_real(B_1_1))) # label(gsy_c_SEQ_Omonoseq_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 12 (all B_1_1 is_bool(summable_complex(B_1_1))) # label(gsy_c_Series_Osummable_000tc__Complex__Ocomplex) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 13 (all B_1_1 is_bool(summable_real(B_1_1))) # label(gsy_c_Series_Osummable_000tc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 14 (all B_1_1 all B_2_1 (is_bool(B_1_1) & is_bool(B_2_1) -> is_bool(fdisj(B_1_1,B_2_1)))) # label(gsy_c_fdisj) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 15 (all B_1_1 all B_2_1 is_bool(hAPP_C24501650l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Code____Numeral__Ocode____numeral_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 16 (all B_1_1 all B_2_1 is_bool(hAPP_complex_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Complex__Ocomplex_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 17 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 18 (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].
% 4.57/4.66 19 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 20 (all B_1_1 all B_2_1 is_bool(hAPP_Q2096512830t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Quickcheck____Narrowing__Ocode____int_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 21 (all B_1_1 all B_2_1 is_bool(hAPP_rat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Rat__Orat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 22 (all B_1_1 all B_2_1 is_bool(hAPP_real_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 23 (all B_1_1 all B_2_1 is_bool(hAPP_f1734966846l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Complex__Ocomplex_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 24 (all B_1_1 all B_2_1 is_bool(hAPP_f448129468l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 25 (all B_1_1 all B_2_1 is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 26 (all B_1_1 all B_2_1 is_bool(hAPP_f311463272l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Rat__Orat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 27 (all B_1_1 all B_2_1 is_bool(hAPP_f1501066425l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__RealDef__Oreal_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 28 (all B_1_1 all B_2_1 is_bool(hAPP_f215623910l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 29 (all B_1_1 all B_2_1 is_bool(hAPP_f251496625l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Code____Numeral__Ocode____numeral_Mtc__Code) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 30 (all B_1_1 all B_2_1 is_bool(hAPP_f851219889l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 31 (all B_1_1 all B_2_1 is_bool(hAPP_f928428050l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__prod_Itc__Int__Oint_Mtc__Int) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 32 (all B_1_1 all B_2_1 is_bool(hAPP_f879361201l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 33 (all B_1_1 all B_2_1 is_bool(hAPP_f222989233l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Quickcheck____Narrowing__Ocode____int_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 34 (all B_1_1 all B_2_1 is_bool(hAPP_f46817975l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 35 (all B_1_1 all B_2_1 is_bool(hAPP_f1469637905l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__f) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 36 (all B_1_1 all B_2_1 is_bool(hAPP_f526364711l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_Mtc__p) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 37 (all B_1_1 all B_2_1 is_bool(hAPP_f115998247l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__p) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 38 (all B_1_1 all B_2_1 is_bool(hAPP_P1164677895l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Code____Numeral__Ocode____numeral_Mtc__Code____Numer) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 39 (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].
% 4.57/4.66 40 (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].
% 4.57/4.66 41 (all B_1_1 all B_2_1 is_bool(hAPP_P1555980039t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 42 (all B_1_1 all B_2_1 is_bool(hAPP_P1709355527t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Quickcheck____Narrowing__Ocode____int_Mtc__Quickchec) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 43 (all B_1_1 all B_2_1 is_bool(hAPP_P1333854989l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 44 (all B_1_1 all B_2_1 is_bool(hAPP_P880235623l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__fun_Itc__I) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 45 (all B_1_1 all B_2_1 is_bool(hAPP_P62333565t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_Mtc__prod_Itc__) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 46 (all B_1_1 all B_2_1 is_bool(hAPP_P1463840893t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__prod_Itc__) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 47 (all A_2 all R_3 all B_1 all M_1 all C_1 all D_3 all N_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,R_3),B_1))),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,R_3),D_3))),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_1),N_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,R_3),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,D_3),N_1))))) # label(fact_0_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 48 (all X_4 all Y_4 all A_12 all B_10 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_4),Y_4)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_12),B_10)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_4),hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Y_4),B_10))),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_4),A_12)),B_10))) # label(fact_1_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 49 (all X_4 all Y_4 all A_12 all B_10 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_4),Y_4)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_12),B_10)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_4),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Y_4),B_10))),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_4),A_12)),B_10))) # label(fact_2_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 50 (all X_4 all Y_4 all A_12 all B_10 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_4),Y_4)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_12),B_10)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_4),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Y_4),B_10))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_4),A_12)),B_10))) # label(fact_3_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 51 (all X_4 all Y_4 all A_12 all B_10 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_4),Y_4)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_12),B_10)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_4),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Y_4),B_10))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_4),A_12)),B_10))) # label(fact_4_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 52 (all X_1 all Y_2 all A_249 all B_194 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_1),Y_2)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_249),B_194)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_1),A_249)),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Y_2),B_194))),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_1),A_249)),B_194))),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_249),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Y_2),B_194)))) # label(fact_5_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 53 (all X_1 all Y_2 all A_249 all B_194 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),Y_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_249),B_194)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),A_249)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Y_2),B_194))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),A_249)),B_194))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_249),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Y_2),B_194)))) # label(fact_6_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 54 (all Aa all E_2 all C all Ba all D (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),E_2)),C) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),E_2)),D) <-> C = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Ba),Aa)),E_2)),D))) # label(fact_7_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 55 (all Aa all E_2 all C all Ba all D (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Aa),E_2)),C) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ba),E_2)),D) <-> C = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Ba),Aa)),E_2)),D))) # label(fact_8_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 56 (all Aa all E_2 all C all Ba all D (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),E_2)),C) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),E_2)),D) <-> C = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa)),E_2)),D))) # label(fact_9_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 57 (all Aa all E_2 all C all Ba all D (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),E_2)),C) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),E_2)),D) <-> C = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ba),Aa)),E_2)),D))) # label(fact_10_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 58 (all Aa all E_2 all C all Ba all D (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),E_2)),C) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),E_2)),D) <-> hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba)),E_2)),C) = D)) # label(fact_11_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 59 (all Aa all E_2 all C all Ba all D (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Aa),E_2)),C) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ba),E_2)),D) <-> hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Aa),Ba)),E_2)),C) = D)) # label(fact_12_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 60 (all Aa all E_2 all C all Ba all D (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),E_2)),C) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),E_2)),D) <-> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba)),E_2)),C) = D)) # label(fact_13_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 61 (all Aa all E_2 all C all Ba all D (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),E_2)),C) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),E_2)),D) <-> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),E_2)),C) = D)) # label(fact_14_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 62 (all X_1 (hBOOL(hAPP_int_bool(twoSqu1770640450sum2sq,X_1)) <-> (exists A_1 exists B_3 hAPP_P1175774780nt_int(twoSqu1907779896sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_1),B_3)) = X_1))) # label(fact_15_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 63 (all A_2 all B_1 all C_1 (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_1) = C_1 -> A_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),B_1))) # label(fact_16_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 64 (all W all Z1 all Z2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2))) # label(fact_17_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 65 (all Z1 all Z2 all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W))) # label(fact_18_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 66 (all W all Z1 all Z2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2))) # label(fact_19_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 67 (all Z1 all Z2 all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W))) # label(fact_20_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 68 (all A_248 all B_193 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_248),B_193)),B_193) = A_248) # label(fact_21_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 69 (all A_248 all B_193 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_248),B_193)),B_193) = A_248) # label(fact_22_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 70 (all A_248 all B_193 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_248),B_193)),B_193) = A_248) # label(fact_23_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 71 (all A_248 all B_193 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_248),B_193)),B_193) = A_248) # label(fact_24_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 72 (all A_247 all B_192 all C_101 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_247),B_192)),C_101) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_247),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_192),C_101))) # label(fact_25_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 73 (all A_247 all B_192 all C_101 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_247),B_192)),C_101) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_247),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_192),C_101))) # label(fact_26_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 74 (all A_247 all B_192 all C_101 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_247),B_192)),C_101) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_247),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_192),C_101))) # label(fact_27_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 75 (all A_247 all B_192 all C_101 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_247),B_192)),C_101) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_247),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_192),C_101))) # label(fact_28_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 76 (all A_247 all B_192 all C_101 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_247),B_192)),C_101) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_247),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_192),C_101))) # label(fact_29_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 77 (all A_247 all B_192 all C_101 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_247),B_192)),C_101) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_247),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_192),C_101))) # label(fact_30_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 78 (all B_191 all A_246 all C_100 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_191),A_246) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_100),A_246) -> B_191 = C_100)) # label(fact_31_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 79 (all B_191 all A_246 all C_100 (hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_191),A_246) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_100),A_246) -> B_191 = C_100)) # label(fact_32_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 80 (all B_191 all A_246 all C_100 (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_191),A_246) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,C_100),A_246) -> B_191 = C_100)) # label(fact_33_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 81 (all B_191 all A_246 all C_100 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_191),A_246) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_100),A_246) -> B_191 = C_100)) # label(fact_34_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 82 (all B_191 all A_246 all C_100 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_191),A_246) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_100),A_246) -> B_191 = C_100)) # label(fact_35_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 83 (all B_191 all A_246 all C_100 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_191),A_246) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_100),A_246) -> B_191 = C_100)) # label(fact_36_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 84 (all A_245 all B_190 all C_99 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_245),B_190) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_245),C_99) -> B_190 = C_99)) # label(fact_37_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 85 (all A_245 all B_190 all C_99 (hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_245),B_190) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_245),C_99) -> B_190 = C_99)) # label(fact_38_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.57/4.66 86 (all A_245 all B_190 all C_99 (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_245),B_190) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_245),C_99) -> B_190 = C_99)) # label(fact_39_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 87 (all A_245 all B_190 all C_99 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_245),B_190) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_245),C_99) -> B_190 = C_99)) # label(fact_40_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 88 (all A_245 all B_190 all C_99 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_245),B_190) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_245),C_99) -> B_190 = C_99)) # label(fact_41_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 89 (all A_245 all B_190 all C_99 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_245),B_190) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_245),C_99) -> B_190 = C_99)) # label(fact_42_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 90 (all A_244 all B_189 all C_98 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_244),B_189) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_244),C_98) -> B_189 = C_98)) # label(fact_43_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 91 (all A_244 all B_189 all C_98 (hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_244),B_189) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_244),C_98) -> B_189 = C_98)) # label(fact_44_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 92 (all A_244 all B_189 all C_98 (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_244),B_189) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_244),C_98) -> B_189 = C_98)) # label(fact_45_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 93 (all A_244 all B_189 all C_98 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_244),B_189) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_244),C_98) -> B_189 = C_98)) # label(fact_46_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 94 (all A_244 all B_189 all C_98 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_244),B_189) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_244),C_98) -> B_189 = C_98)) # label(fact_47_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 95 (all A_244 all B_189 all C_98 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_244),B_189) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_244),C_98) -> B_189 = C_98)) # label(fact_48_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 96 (all Ba all Aa all C (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Ba),Aa) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C),Aa) <-> Ba = C)) # label(fact_49_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 97 (all Ba all Aa all C (hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Ba),Aa) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C),Aa) <-> Ba = C)) # label(fact_50_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 98 (all Ba all Aa all C (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Ba),Aa) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,C),Aa) <-> Ba = C)) # label(fact_51_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 99 (all Ba all Aa all C (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C),Aa) <-> Ba = C)) # label(fact_52_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 100 (all Ba all Aa all C (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Ba),Aa) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C),Aa) <-> Ba = C)) # label(fact_53_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 101 (all Ba all Aa all C (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),Aa) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C),Aa) <-> Ba = C)) # label(fact_54_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 102 (all Aa all Ba all C (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Ba) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),C) <-> Ba = C)) # label(fact_55_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 103 (all Aa all Ba all C (hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Aa),Ba) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Aa),C) <-> Ba = C)) # label(fact_56_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 104 (all Aa all Ba all C (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Aa),Ba) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Aa),C) <-> Ba = C)) # label(fact_57_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 105 (all Aa all Ba all C (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C) <-> Ba = C)) # label(fact_58_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 106 (all Aa all Ba all C (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Ba) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),C) <-> Ba = C)) # label(fact_59_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 107 (all Aa all Ba all C (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),C) <-> Ba = C)) # label(fact_60_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 108 (all A_243 all B_188 all C_97 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_243),B_188)),C_97) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_243),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_188),C_97))) # label(fact_61_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 109 (all A_243 all B_188 all C_97 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_243),B_188)),C_97) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_243),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_188),C_97))) # label(fact_62_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 110 (all A_243 all B_188 all C_97 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_243),B_188)),C_97) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_243),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_188),C_97))) # label(fact_63_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 111 (all A_243 all B_188 all C_97 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_243),B_188)),C_97) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_243),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_188),C_97))) # label(fact_64_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 112 (all A_243 all B_188 all C_97 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_243),B_188)),C_97) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_243),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_188),C_97))) # label(fact_65_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 113 (all A_243 all B_188 all C_97 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_243),B_188)),C_97) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_243),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_188),C_97))) # label(fact_66_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 114 (all Aa all Ba all C all D (hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,C),D) -> (Aa = Ba <-> C = D))) # label(fact_67_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 115 (all Aa all Ba all C all D (hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Aa),Ba) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,C),D) -> (Aa = Ba <-> C = D))) # label(fact_68_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 116 (all Aa all Ba all C all D (hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C),D) -> (Aa = Ba <-> C = D))) # label(fact_69_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 117 (all Aa all Ba all C all D (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C),D) -> (Aa = Ba <-> C = D))) # label(fact_70_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 118 (all Z1 all Z2 all Z3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),Z3))) # label(fact_71_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 119 (all Z_1 all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),W) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z_1)) # label(fact_72_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 120 (all Z1 all Z2 all Z3 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z2),Z3))) # label(fact_73_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 121 (all X all Y all Z_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),Z_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Z_1))) # label(fact_74_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 122 (all Z_1 all W hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z_1)) # label(fact_75_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 123 (all A_242 all E_3 all B_187 all C_96 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_242),E_3)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_187),E_3)),C_96)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_242),B_187)),E_3)),C_96)) # label(fact_76_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 124 (all A_242 all E_3 all B_187 all C_96 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_242),E_3)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_187),E_3)),C_96)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_242),B_187)),E_3)),C_96)) # label(fact_77_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 125 (all A_242 all E_3 all B_187 all C_96 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_242),E_3)),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_187),E_3)),C_96)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_242),B_187)),E_3)),C_96)) # label(fact_78_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 126 (all A_242 all E_3 all B_187 all C_96 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_242),E_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_187),E_3)),C_96)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_242),B_187)),E_3)),C_96)) # label(fact_79_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 127 (all A_242 all E_3 all B_187 all C_96 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_242),E_3)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_187),E_3)),C_96)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_242),B_187)),E_3)),C_96)) # label(fact_80_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 128 (all A_242 all E_3 all B_187 all C_96 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_242),E_3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_187),E_3)),C_96)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_242),B_187)),E_3)),C_96)) # label(fact_81_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 129 (all X_76 all Y_63 all Ya_4 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X_76),Y_63)),Ya_4) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_76),Ya_4)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Y_63),Ya_4))) # label(fact_82_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 130 (all X_76 all Y_63 all Ya_4 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_76),Y_63)),Ya_4) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_76),Ya_4)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_63),Ya_4))) # label(fact_83_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 131 (all A_241 all A_240 all B_186 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_241),A_240)),B_186) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_241),B_186)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_240),B_186))) # label(fact_84_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 132 (all A_241 all A_240 all B_186 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_241),A_240)),B_186) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_241),B_186)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_240),B_186))) # label(fact_85_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 133 (all A_239 all B_185 all C_95 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_239),B_185)),C_95) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_239),C_95)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_185),C_95))) # label(fact_86_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 134 (all A_239 all B_185 all C_95 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_239),B_185)),C_95) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_239),C_95)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_185),C_95))) # label(fact_87_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 135 (all A_239 all B_185 all C_95 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_239),B_185)),C_95) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_239),C_95)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_185),C_95))) # label(fact_88_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 136 (all A_239 all B_185 all C_95 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_239),B_185)),C_95) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_239),C_95)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_185),C_95))) # label(fact_89_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 137 (all A_239 all B_185 all C_95 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_239),B_185)),C_95) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_239),C_95)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_185),C_95))) # label(fact_90_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 138 (all A_239 all B_185 all C_95 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_239),B_185)),C_95) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_239),C_95)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_185),C_95))) # label(fact_91_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 139 (all Xa_5 all X_75 all Y_62 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_5),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X_75),Y_62)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_5),X_75)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_5),Y_62))) # label(fact_92_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 140 (all Xa_5 all X_75 all Y_62 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_5),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_75),Y_62)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_5),X_75)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_5),Y_62))) # label(fact_93_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 141 (all A_238 all B_184 all B_183 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_238),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_184),B_183)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_238),B_184)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_238),B_183))) # label(fact_94_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 142 (all A_238 all B_184 all B_183 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_238),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_184),B_183)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_238),B_184)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_238),B_183))) # label(fact_95_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 143 (all X_74 all Y_61 all Ya_3 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_74),Y_61)),Ya_3) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_74),Ya_3)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Y_61),Ya_3))) # label(fact_96_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 144 (all X_74 all Y_61 all Ya_3 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_74),Y_61)),Ya_3) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_74),Ya_3)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_61),Ya_3))) # label(fact_97_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 145 (all A_237 all A_236 all B_182 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_237),A_236)),B_182) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_237),B_182)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_236),B_182))) # label(fact_98_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 146 (all A_237 all A_236 all B_182 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_237),A_236)),B_182) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_237),B_182)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_236),B_182))) # label(fact_99_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 147 (all Xa_4 all X_73 all Y_60 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_4),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_73),Y_60)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_4),X_73)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_4),Y_60))) # label(fact_100_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 148 (all Xa_4 all X_73 all Y_60 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_4),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_73),Y_60)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_4),X_73)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_4),Y_60))) # label(fact_101_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 149 (all A_235 all B_181 all B_180 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_235),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,B_181),B_180)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_235),B_181)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_235),B_180))) # label(fact_102_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 150 (all A_235 all B_181 all B_180 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_235),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_181),B_180)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_235),B_181)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_235),B_180))) # label(fact_103_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 151 (all A_234 all C_94 all B_179 all D_21 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_234),C_94)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_179),D_21)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_234),B_179)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,C_94),D_21))) # label(fact_104_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 152 (all A_234 all C_94 all B_179 all D_21 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_234),C_94)),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_179),D_21)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_234),B_179)),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,C_94),D_21))) # label(fact_105_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 153 (all A_234 all C_94 all B_179 all D_21 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_234),C_94)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_179),D_21)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_234),B_179)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C_94),D_21))) # label(fact_106_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 154 (all A_234 all C_94 all B_179 all D_21 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_234),C_94)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_179),D_21)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_234),B_179)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_94),D_21))) # label(fact_107_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 155 (all A_233 all B_178 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_233),B_178)),B_178) = A_233) # label(fact_108_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 156 (all A_233 all B_178 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_233),B_178)),B_178) = A_233) # label(fact_109_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 157 (all A_233 all B_178 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_233),B_178)),B_178) = A_233) # label(fact_110_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 158 (all A_233 all B_178 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_233),B_178)),B_178) = A_233) # label(fact_111_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 159 (all W_1 all Y_2 all X_1 all Z_2 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,W_1),Y_2)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_1),Z_2)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,W_1),Z_2)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_1),Y_2)) <-> W_1 = X_1 | Y_2 = Z_2)) # label(fact_112_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 160 (all W_1 all Y_2 all X_1 all Z_2 (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,W_1),Y_2)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_1),Z_2)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,W_1),Z_2)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_1),Y_2)) <-> W_1 = X_1 | Y_2 = Z_2)) # label(fact_113_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 161 (all W_1 all Y_2 all X_1 all Z_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,W_1),Y_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),Z_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,W_1),Z_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),Y_2)) <-> W_1 = X_1 | Y_2 = Z_2)) # label(fact_114_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 162 (all W_1 all Y_2 all X_1 all Z_2 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,W_1),Y_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),Z_2)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,W_1),Z_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),Y_2)) <-> W_1 = X_1 | Y_2 = Z_2)) # label(fact_115_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 163 (all W_1 all Y_2 all X_1 all Z_2 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Y_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Z_2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W_1),Z_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2)) <-> W_1 = X_1 | Y_2 = Z_2)) # label(fact_116_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 164 (all A_232 all M_11 all B_177 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_232),M_11)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_177),M_11)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_232),B_177)),M_11)) # label(fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 165 (all A_232 all M_11 all B_177 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_232),M_11)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_177),M_11)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_232),B_177)),M_11)) # label(fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 166 (all A_232 all M_11 all B_177 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_232),M_11)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_177),M_11)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_232),B_177)),M_11)) # label(fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 167 (all A_232 all M_11 all B_177 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_232),M_11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_177),M_11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_232),B_177)),M_11)) # label(fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 168 (all A_232 all M_11 all B_177 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_232),M_11)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_177),M_11)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_232),B_177)),M_11)) # label(fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 169 (all A_232 all M_11 all B_177 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_232),M_11)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_177),M_11)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_232),B_177)),M_11)) # label(fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 170 (all A_231 all B_176 all C_93 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_231),B_176)),C_93) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_231),C_93)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_176),C_93))) # label(fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 171 (all A_231 all B_176 all C_93 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_231),B_176)),C_93) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_231),C_93)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_176),C_93))) # label(fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 172 (all A_231 all B_176 all C_93 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_231),B_176)),C_93) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_231),C_93)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_176),C_93))) # label(fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 173 (all A_231 all B_176 all C_93 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_231),B_176)),C_93) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_231),C_93)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_176),C_93))) # label(fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 174 (all A_231 all B_176 all C_93 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_231),B_176)),C_93) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_231),C_93)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_176),C_93))) # label(fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 175 (all A_231 all B_176 all C_93 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_231),B_176)),C_93) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_231),C_93)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_176),C_93))) # label(fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 176 (all C all D all Aa all Ba (Aa != Ba & C != D <-> hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),D)) != hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),D)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),C)))) # label(fact_129_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 177 (all C all D all Aa all Ba (Aa != Ba & C != D <-> hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Aa),C)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ba),D)) != hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Aa),D)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ba),C)))) # label(fact_130_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 178 (all C all D all Aa all Ba (Aa != Ba & C != D <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ba),D)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),D)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ba),C)))) # label(fact_131_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 179 (all C all D all Aa all Ba (Aa != Ba & C != D <-> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),C)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),D)) != hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),D)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),C)))) # label(fact_132_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 180 (all C all D all Aa all Ba (Aa != Ba & C != D <-> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),C)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),D)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),D)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),C)))) # label(fact_133_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 181 (all X_72 all Y_59 all Z_22 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_72),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Y_59),Z_22)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_72),Y_59)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_72),Z_22))) # label(fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 182 (all X_72 all Y_59 all Z_22 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,X_72),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Y_59),Z_22)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,X_72),Y_59)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,X_72),Z_22))) # label(fact_135_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 183 (all X_72 all Y_59 all Z_22 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_72),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Y_59),Z_22)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_72),Y_59)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_72),Z_22))) # label(fact_136_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 184 (all X_72 all Y_59 all Z_22 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_72),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_59),Z_22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_72),Y_59)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_72),Z_22))) # label(fact_137_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 185 (all X_72 all Y_59 all Z_22 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_72),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Y_59),Z_22)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_72),Y_59)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_72),Z_22))) # label(fact_138_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 186 (all X_72 all Y_59 all Z_22 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_72),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y_59),Z_22)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_72),Y_59)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_72),Z_22))) # label(fact_139_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 187 (all Aa all Ba all A_228 all B_173 (hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,Aa),Ba) = hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,A_228),B_173) -> -(Aa = A_228 -> Ba != B_173))) # label(fact_140_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 188 (all A_230 all B_175 all A_229 all B_174 (hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_230),B_175) = hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_141_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 189 (all A_230 all B_175 all A_229 all B_174 (hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,A_230),B_175) = hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_142_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 190 (all A_230 all B_175 all A_229 all B_174 (hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,A_230),B_175) = hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_143_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 191 (all A_230 all B_175 all A_229 all B_174 (hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_230),B_175) = hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_144_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 192 (all A_230 all B_175 all A_229 all B_174 (hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_230),B_175) = hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_145_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 193 (all A_230 all B_175 all A_229 all B_174 (hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,A_230),B_175) = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_146_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 194 (all A_230 all B_175 all A_229 all B_174 (hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_230),B_175) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_147_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 195 (all A_230 all B_175 all A_229 all B_174 (hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_230),B_175) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_229),B_174) -> -(A_230 = A_229 -> B_175 != B_174))) # label(fact_148_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 196 (all Aa all Ba all A_228 all B_173 (hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,Aa),Ba) = hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_149_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 197 (all Aa all Ba all A_228 all B_173 (hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,Aa),Ba) = hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_150_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 198 (all Aa all Ba all A_228 all B_173 (hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,Aa),Ba) = hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_151_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.66 199 (all Aa all Ba all A_228 all B_173 (hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,Aa),Ba) = hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_152_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 200 (all Aa all Ba all A_228 all B_173 (hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba) = hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_153_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 201 (all Aa all Ba all A_228 all B_173 (hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,Aa),Ba) = hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_154_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 202 (all Aa all Ba all A_228 all B_173 (hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),Ba) = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_155_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 203 (all Aa all Ba all A_228 all B_173 (hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,Aa),Ba) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_156_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 204 (all Aa all Ba all A_228 all B_173 (hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aa),Ba) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_228),B_173) <-> Aa = A_228 & Ba = B_173)) # label(fact_157_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 205 (all P_1 ((all X1 hBOOL(hAPP_P880235623l_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P880235623l_bool(P_1,hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,A_1),B_3)))))) # label(fact_158_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 206 (all P_1 ((all X1 hBOOL(hAPP_P62333565t_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P62333565t_bool(P_1,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_1),B_3)))))) # label(fact_159_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 207 (all P_1 ((all X1 hBOOL(hAPP_P1709355527t_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P1709355527t_bool(P_1,hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,A_1),B_3)))))) # label(fact_160_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 208 (all P_1 ((all X1 hBOOL(hAPP_P1164677895l_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P1164677895l_bool(P_1,hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,A_1),B_3)))))) # label(fact_161_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 209 (all P_1 ((all X1 hBOOL(hAPP_P1333854989l_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3)))))) # label(fact_162_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 210 (all P_1 ((all X1 hBOOL(hAPP_P1463840893t_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P1463840893t_bool(P_1,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_1),B_3)))))) # label(fact_163_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 211 (all P_1 ((all X1 hBOOL(hAPP_P1555980039t_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P1555980039t_bool(P_1,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,A_1),B_3)))))) # label(fact_164_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 212 (all P_1 ((all X1 hBOOL(hAPP_P178748804t_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P178748804t_bool(P_1,hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_1),B_3)))))) # label(fact_165_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 213 (all P_1 ((all X1 hBOOL(hAPP_P603027463t_bool(P_1,X1))) <-> (all A_1 all B_3 hBOOL(hAPP_P603027463t_bool(P_1,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_1),B_3)))))) # label(fact_166_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 214 (all A_227 all B_172 all C_92 all D_20 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_227),B_172)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_92),D_20)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_227),C_92)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_172),D_20))) # label(fact_167_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 215 (all A_227 all B_172 all C_92 all D_20 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_227),B_172)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_92),D_20)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_227),C_92)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_172),D_20))) # label(fact_168_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 216 (all A_227 all B_172 all C_92 all D_20 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_227),B_172)),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,C_92),D_20)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_227),C_92)),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_172),D_20))) # label(fact_169_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 217 (all A_227 all B_172 all C_92 all D_20 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_227),B_172)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_92),D_20)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_227),C_92)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_172),D_20))) # label(fact_170_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 218 (all A_227 all B_172 all C_92 all D_20 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_227),B_172)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_92),D_20)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_227),C_92)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_172),D_20))) # label(fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 219 (all A_227 all B_172 all C_92 all D_20 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_227),B_172)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_92),D_20)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_227),C_92)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_172),D_20))) # label(fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 220 (all A_226 all B_171 all C_91 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_226),B_171)),C_91) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_226),C_91)),B_171)) # label(fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 221 (all A_226 all B_171 all C_91 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_226),B_171)),C_91) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_226),C_91)),B_171)) # label(fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 222 (all A_226 all B_171 all C_91 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_226),B_171)),C_91) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_226),C_91)),B_171)) # label(fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 223 (all A_226 all B_171 all C_91 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_226),B_171)),C_91) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_226),C_91)),B_171)) # label(fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 224 (all A_226 all B_171 all C_91 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_226),B_171)),C_91) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_226),C_91)),B_171)) # label(fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 225 (all A_226 all B_171 all C_91 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_226),B_171)),C_91) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_226),C_91)),B_171)) # label(fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 226 (all A_225 all B_170 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_225),B_170) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_170),A_225)) # label(fact_179_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 227 (all A_225 all B_170 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_225),B_170) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_170),A_225)) # label(fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 228 (all A_225 all B_170 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_225),B_170) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_170),A_225)) # label(fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 229 (all A_225 all B_170 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_225),B_170) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_170),A_225)) # label(fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 230 (all A_225 all B_170 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_225),B_170) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_170),A_225)) # label(fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 231 (all A_225 all B_170 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_225),B_170) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_170),A_225)) # label(fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 232 (all Lx_6 all Rx_6 all Ry_4 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_6),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx_6),Ry_4)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx_6),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_6),Ry_4))) # label(fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 233 (all Lx_6 all Rx_6 all Ry_4 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_6),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx_6),Ry_4)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx_6),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_6),Ry_4))) # label(fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 234 (all Lx_6 all Rx_6 all Ry_4 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_6),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx_6),Ry_4)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx_6),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_6),Ry_4))) # label(fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 235 (all Lx_6 all Rx_6 all Ry_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_6),Ry_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_6),Ry_4))) # label(fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 236 (all Lx_6 all Rx_6 all Ry_4 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_6),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx_6),Ry_4)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx_6),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_6),Ry_4))) # label(fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 237 (all Lx_6 all Rx_6 all Ry_4 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_6),Ry_4)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_6),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_6),Ry_4))) # label(fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 238 (all Lx_5 all Rx_5 all Ry_3 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_5),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx_5),Ry_3)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_5),Rx_5)),Ry_3)) # label(fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 239 (all Lx_5 all Rx_5 all Ry_3 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_5),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx_5),Ry_3)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_5),Rx_5)),Ry_3)) # label(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 240 (all Lx_5 all Rx_5 all Ry_3 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_5),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx_5),Ry_3)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_5),Rx_5)),Ry_3)) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 241 (all Lx_5 all Rx_5 all Ry_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_5),Ry_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_5),Rx_5)),Ry_3)) # label(fact_194_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 242 (all Lx_5 all Rx_5 all Ry_3 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_5),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx_5),Ry_3)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_5),Rx_5)),Ry_3)) # label(fact_195_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 243 (all Lx_5 all Rx_5 all Ry_3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_5),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_5),Ry_3)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_5),Rx_5)),Ry_3)) # label(fact_196_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 244 (all Lx_4 all Ly_4 all Rx_4 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_4),Ly_4)),Rx_4) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_4),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ly_4),Rx_4))) # label(fact_197_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 245 (all Lx_4 all Ly_4 all Rx_4 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_4),Ly_4)),Rx_4) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_4),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Ly_4),Rx_4))) # label(fact_198_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 246 (all Lx_4 all Ly_4 all Rx_4 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_4),Ly_4)),Rx_4) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_4),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ly_4),Rx_4))) # label(fact_199_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 247 (all Lx_4 all Ly_4 all Rx_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_4),Ly_4)),Rx_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly_4),Rx_4))) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 248 (all Lx_4 all Ly_4 all Rx_4 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_4),Ly_4)),Rx_4) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_4),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ly_4),Rx_4))) # label(fact_201_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 249 (all Lx_4 all Ly_4 all Rx_4 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_4),Ly_4)),Rx_4) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly_4),Rx_4))) # label(fact_202_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 250 (all Lx_3 all Ly_3 all Rx_3 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_3),Ly_3)),Rx_3) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_3),Rx_3)),Ly_3)) # label(fact_203_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 251 (all Lx_3 all Ly_3 all Rx_3 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_3),Ly_3)),Rx_3) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_3),Rx_3)),Ly_3)) # label(fact_204_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 252 (all Lx_3 all Ly_3 all Rx_3 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_3),Ly_3)),Rx_3) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_3),Rx_3)),Ly_3)) # label(fact_205_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 253 (all Lx_3 all Ly_3 all Rx_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_3),Ly_3)),Rx_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_3),Rx_3)),Ly_3)) # label(fact_206_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 254 (all Lx_3 all Ly_3 all Rx_3 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_3),Ly_3)),Rx_3) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_3),Rx_3)),Ly_3)) # label(fact_207_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 255 (all Lx_3 all Ly_3 all Rx_3 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_3),Ly_3)),Rx_3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_3),Rx_3)),Ly_3)) # label(fact_208_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 256 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_2),Ly_2)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx_2),Ry_2)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_2),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ly_2),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx_2),Ry_2)))) # label(fact_209_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 257 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_2),Ly_2)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx_2),Ry_2)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_2),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Ly_2),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx_2),Ry_2)))) # label(fact_210_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 258 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_2),Ly_2)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx_2),Ry_2)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_2),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ly_2),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx_2),Ry_2)))) # label(fact_211_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 259 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_2),Ly_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_2),Ry_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_2),Ry_2)))) # label(fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 260 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_2),Ly_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx_2),Ry_2)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_2),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ly_2),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx_2),Ry_2)))) # label(fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 261 (all Lx_2 all Ly_2 all Rx_2 all Ry_2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_2),Ly_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_2),Ry_2)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_2),Ry_2)))) # label(fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 262 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_1),Ly_1)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx_1),Ry_1)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx_1),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx_1),Ly_1)),Ry_1))) # label(fact_215_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 263 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_1),Ly_1)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx_1),Ry_1)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx_1),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx_1),Ly_1)),Ry_1))) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 264 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_1),Ly_1)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx_1),Ry_1)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx_1),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx_1),Ly_1)),Ry_1))) # label(fact_217_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 265 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_1),Ly_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_1),Ry_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx_1),Ly_1)),Ry_1))) # label(fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 266 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_1),Ly_1)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx_1),Ry_1)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx_1),Ly_1)),Ry_1))) # label(fact_219_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 267 (all Lx_1 all Ly_1 all Rx_1 all Ry_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_1),Ly_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_1),Ry_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx_1),Ly_1)),Ry_1))) # label(fact_220_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 268 (all Lx all Ly all Rx all Ry hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx),Ly)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Rx),Ry)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Lx),Rx)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ly),Ry))) # label(fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 269 (all Lx all Ly all Rx all Ry hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx),Ly)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Rx),Ry)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Lx),Rx)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,Ly),Ry))) # label(fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 270 (all Lx all Ly all Rx all Ry hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx),Ly)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Rx),Ry)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Lx),Rx)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ly),Ry))) # label(fact_223_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 271 (all Lx all Ly all Rx all Ry hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),Ly)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Rx),Ry)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Lx),Rx)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ly),Ry))) # label(fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 272 (all Lx all Ly all Rx all Ry hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx),Ly)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Rx),Ry)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Lx),Rx)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ly),Ry))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 273 (all Lx all Ly all Rx all Ry hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),Ly)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Rx),Ry)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Lx),Rx)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ly),Ry))) # label(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 274 (all A_224 all C_90 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_224),C_90) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_90),A_224)) # label(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 275 (all A_224 all C_90 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_224),C_90) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_90),A_224)) # label(fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 276 (all A_224 all C_90 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_224),C_90) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,C_90),A_224)) # label(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 277 (all A_224 all C_90 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_224),C_90) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_90),A_224)) # label(fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 278 (all A_224 all C_90 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_224),C_90) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_90),A_224)) # label(fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 279 (all A_224 all C_90 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_224),C_90) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_90),A_224)) # label(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 280 (all A_223 all C_89 all D_19 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_223),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_89),D_19)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_89),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_223),D_19))) # label(fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 281 (all A_223 all C_89 all D_19 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_223),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_89),D_19)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_89),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_223),D_19))) # label(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 282 (all A_223 all C_89 all D_19 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_223),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,C_89),D_19)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,C_89),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_223),D_19))) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 283 (all A_223 all C_89 all D_19 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_223),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_89),D_19)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_89),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_223),D_19))) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 284 (all A_223 all C_89 all D_19 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_223),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_89),D_19)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_89),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_223),D_19))) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 285 (all A_223 all C_89 all D_19 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_223),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_89),D_19)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_89),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_223),D_19))) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 286 (all A_222 all C_88 all D_18 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_222),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_88),D_18)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_222),C_88)),D_18)) # label(fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 287 (all A_222 all C_88 all D_18 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_222),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_88),D_18)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_222),C_88)),D_18)) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 288 (all A_222 all C_88 all D_18 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_222),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,C_88),D_18)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_222),C_88)),D_18)) # label(fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 289 (all A_222 all C_88 all D_18 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_222),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_88),D_18)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_222),C_88)),D_18)) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 290 (all A_222 all C_88 all D_18 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_222),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_88),D_18)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_222),C_88)),D_18)) # label(fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 291 (all A_222 all C_88 all D_18 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_222),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_88),D_18)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_222),C_88)),D_18)) # label(fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 292 (all A_221 all B_169 all C_87 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_221),B_169)),C_87) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_221),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_169),C_87))) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 293 (all A_221 all B_169 all C_87 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_221),B_169)),C_87) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_221),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_169),C_87))) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 294 (all A_221 all B_169 all C_87 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_221),B_169)),C_87) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_221),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_169),C_87))) # label(fact_247_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 295 (all A_221 all B_169 all C_87 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_221),B_169)),C_87) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_221),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_169),C_87))) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 296 (all A_221 all B_169 all C_87 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_221),B_169)),C_87) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_221),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_169),C_87))) # label(fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 297 (all A_221 all B_169 all C_87 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_221),B_169)),C_87) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_221),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_169),C_87))) # label(fact_250_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 298 (all P_1 ((exists X1 hBOOL(hAPP_P880235623l_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P880235623l_bool(P_1,hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,A_1),B_3)))))) # label(fact_251_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 299 (all P_1 ((exists X1 hBOOL(hAPP_P62333565t_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P62333565t_bool(P_1,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_1),B_3)))))) # label(fact_252_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 300 (all P_1 ((exists X1 hBOOL(hAPP_P1709355527t_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P1709355527t_bool(P_1,hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,A_1),B_3)))))) # label(fact_253_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 301 (all P_1 ((exists X1 hBOOL(hAPP_P1164677895l_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P1164677895l_bool(P_1,hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,A_1),B_3)))))) # label(fact_254_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 302 (all P_1 ((exists X1 hBOOL(hAPP_P1333854989l_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3)))))) # label(fact_255_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 303 (all P_1 ((exists X1 hBOOL(hAPP_P1463840893t_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P1463840893t_bool(P_1,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_1),B_3)))))) # label(fact_256_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 304 (all P_1 ((exists X1 hBOOL(hAPP_P1555980039t_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P1555980039t_bool(P_1,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,A_1),B_3)))))) # label(fact_257_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 305 (all P_1 ((exists X1 hBOOL(hAPP_P178748804t_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P178748804t_bool(P_1,hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_1),B_3)))))) # label(fact_258_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 306 (all P_1 ((exists X1 hBOOL(hAPP_P603027463t_bool(P_1,X1))) <-> (exists A_1 exists B_3 hBOOL(hAPP_P603027463t_bool(P_1,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_1),B_3)))))) # label(fact_259_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 307 (all X_1 all P_1 ((all A_1 all B_3 all C_3 hBOOL(hAPP_P62333565t_bool(P_1,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,B_3),C_3))))) -> hBOOL(hAPP_P62333565t_bool(P_1,X_1)))) # label(fact_260_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 308 (all X_1 all P_1 ((all A_1 all B_3 all C_3 hBOOL(hAPP_P1463840893t_bool(P_1,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,B_3),C_3))))) -> hBOOL(hAPP_P1463840893t_bool(P_1,X_1)))) # label(fact_261_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 309 (all X_1 all P_1 ((all A_1 all B_3 all C_3 hBOOL(hAPP_P178748804t_bool(P_1,hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,B_3),C_3))))) -> hBOOL(hAPP_P178748804t_bool(P_1,X_1)))) # label(fact_262_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 310 (all Y_58 -(all A_1 all B_3 all C_3 Y_58 != hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,B_3),C_3)))) # label(fact_263_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 311 (all Y_58 -(all A_1 all B_3 all C_3 Y_58 != hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,B_3),C_3)))) # label(fact_264_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 312 (all Y_58 -(all A_1 all B_3 all C_3 Y_58 != hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,B_3),C_3)))) # label(fact_265_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 313 (all Pa -(all X_2 all Y_1 Pa != hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,X_2),Y_1))) # label(fact_266_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 314 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,X_2),Y_1))) # label(fact_267_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 315 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,X_2),Y_1))) # label(fact_268_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 316 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,X_2),Y_1))) # label(fact_269_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 317 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,X_2),Y_1))) # label(fact_270_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 318 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,X_2),Y_1))) # label(fact_271_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 319 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_2),Y_1))) # label(fact_272_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 320 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,X_2),Y_1))) # label(fact_273_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 321 (all P_7 -(all X_2 all Y_1 P_7 != hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,X_2),Y_1))) # label(fact_274_PairE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 322 (all X_1 all A (hBOOL(hAPP_f1469637905l_bool(hAPP_P1681069257l_bool(member308914164t_bool,X_1),A)) <-> hBOOL(hAPP_P880235623l_bool(A,X_1)))) # label(fact_275_mem__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 323 (all X_1 all A (hBOOL(hAPP_f526364711l_bool(hAPP_P1062890741l_bool(member2143287562nt_int,X_1),A)) <-> hBOOL(hAPP_P62333565t_bool(A,X_1)))) # label(fact_276_mem__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 324 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_nat_bool(A,X_1)))) # label(fact_277_mem__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 325 (all X_1 all A (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A)) <-> hBOOL(hAPP_f448129468l_bool(A,X_1)))) # label(fact_278_mem__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 326 (all X_1 all A (hBOOL(hAPP_f115998247l_bool(hAPP_P1876494581l_bool(member180897546at_nat,X_1),A)) <-> hBOOL(hAPP_P1463840893t_bool(A,X_1)))) # label(fact_279_mem__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 327 (all X_1 all A (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_1),A)) <-> hBOOL(hAPP_real_bool(A,X_1)))) # label(fact_280_mem__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 328 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) <-> hBOOL(hAPP_int_bool(A,X_1)))) # label(fact_281_mem__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 329 (all P_1 collec1979865426at_nat(P_1) = P_1) # label(fact_282_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 330 (all P_1 collect_real(P_1) = P_1) # label(fact_283_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 331 (all P_1 collec1347809874nt_int(P_1) = P_1) # label(fact_284_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 332 (all P_1 collec50511176nt_int(P_1) = P_1) # label(fact_285_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 333 (all P_1 collect_nat(P_1) = P_1) # label(fact_286_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 334 (all P_1 collect_int(P_1) = P_1) # label(fact_287_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 335 (all Y_2 -(all A_1 all B_3 Y_2 != hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,A_1),B_3))) # label(fact_288_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 336 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,A_1),B_3))) # label(fact_289_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 337 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,A_1),B_3))) # label(fact_290_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 338 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,A_1),B_3))) # label(fact_291_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 339 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))) # label(fact_292_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 340 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,A_1),B_3))) # label(fact_293_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 341 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,A_1),B_3))) # label(fact_294_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 342 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,A_1),B_3))) # label(fact_295_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 343 (all Y_57 -(all A_1 all B_3 Y_57 != hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_1),B_3))) # label(fact_296_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 344 (all F all Aa all Ba (hBOOL(hAPP_P880235623l_bool(F,hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,Aa),Ba))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(produc1775888740l_bool(F),Aa),Ba)))) # label(fact_297_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 345 (all F all Aa all Ba (hBOOL(hAPP_P62333565t_bool(F,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,Aa),Ba))) -> hBOOL(hAPP_P603027463t_bool(hAPP_P989584703t_bool(produc353512698t_bool(F),Aa),Ba)))) # label(fact_298_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 346 (all F all Aa all Ba (hBOOL(hAPP_P1709355527t_bool(F,hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,Aa),Ba))) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(produc2013771390t_bool(F),Aa),Ba)))) # label(fact_299_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 347 (all F all Aa all Ba (hBOOL(hAPP_P1164677895l_bool(F,hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,Aa),Ba))) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(produc609372286l_bool(F),Aa),Ba)))) # label(fact_300_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 348 (all F all Aa all Ba (hBOOL(hAPP_P1333854989l_bool(F,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(produc748992778l_bool(F),Aa),Ba)))) # label(fact_301_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 349 (all F all Aa all Ba (hBOOL(hAPP_P1463840893t_bool(F,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,Aa),Ba))) -> hBOOL(hAPP_P1555980039t_bool(hAPP_P705731903t_bool(produc1319041786t_bool(F),Aa),Ba)))) # label(fact_302_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 350 (all F all Aa all Ba (hBOOL(hAPP_P1555980039t_bool(F,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),Ba))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(produc2091540094t_bool(F),Aa),Ba)))) # label(fact_303_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 351 (all F all Aa all Ba (hBOOL(hAPP_P178748804t_bool(F,hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,Aa),Ba))) -> hBOOL(hAPP_P603027463t_bool(hAPP_i119638232t_bool(produc97574839t_bool(F),Aa),Ba)))) # label(fact_304_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 352 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(F,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aa),Ba))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(produc262399358t_bool(F),Aa),Ba)))) # label(fact_305_curryI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 353 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),E_2)),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),E_2)),D))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba)),E_2)),C)),D)))) # label(fact_306_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 354 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),E_2)),C)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),E_2)),D))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba)),E_2)),C)),D)))) # label(fact_307_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 355 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),E_2)),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),E_2)),D))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),E_2)),C)),D)))) # label(fact_308_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 356 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),E_2)),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),E_2)),D))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Ba),Aa)),E_2)),D))))) # label(fact_309_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 357 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),E_2)),C)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),E_2)),D))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa)),E_2)),D))))) # label(fact_310_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 358 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),E_2)),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),E_2)),D))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ba),Aa)),E_2)),D))))) # label(fact_311_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 359 (all X_71 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_71),X_71)),one_one_rat) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_71),one_one_rat)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_71),one_one_rat))) # label(fact_312_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 360 (all X_71 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_71),X_71)),one_one_complex) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X_71),one_one_complex)),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_71),one_one_complex))) # label(fact_313_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 361 (all X_71 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_71),X_71)),one_one_real) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_71),one_one_real)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_71),one_one_real))) # label(fact_314_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 362 (all X_71 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_71),X_71)),one_one_int) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_71),one_one_int)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_71),one_one_int))) # label(fact_315_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 363 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),E_2)),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),E_2)),D))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba)),E_2)),C)),D)))) # label(fact_316_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 364 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),E_2)),C)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),E_2)),D))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba)),E_2)),C)),D)))) # label(fact_317_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 365 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),E_2)),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),E_2)),D))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),E_2)),C)),D)))) # label(fact_318_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 366 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),E_2)),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),E_2)),D))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Ba),Aa)),E_2)),D))))) # label(fact_319_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 367 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),E_2)),C)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),E_2)),D))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa)),E_2)),D))))) # label(fact_320_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 368 (all Aa all E_2 all C all Ba all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),E_2)),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),E_2)),D))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ba),Aa)),E_2)),D))))) # label(fact_321_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 369 (all V_25 all W_17 all C_86 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,V_25)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_int_rat(number_number_of_rat,W_17)),C_86)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_25),W_17))),C_86)) # label(fact_322_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 370 (all V_25 all W_17 all C_86 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,V_25)),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_int_complex(number528085621omplex,W_17)),C_86)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_25),W_17))),C_86)) # label(fact_323_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 371 (all V_25 all W_17 all C_86 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,V_25)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(number267125858f_real,W_17)),C_86)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_25),W_17))),C_86)) # label(fact_324_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 372 (all V_25 all W_17 all C_86 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_25)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(number_number_of_int,W_17)),C_86)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_25),W_17))),C_86)) # label(fact_325_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 373 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(in_rel512175208t_bool(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f1469637905l_bool(hAPP_P1681069257l_bool(member308914164t_bool,hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,X_1),Y_2)),R_4)))) # label(fact_326_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 374 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_P603027463t_bool(hAPP_P989584703t_bool(in_rel682537726nt_int(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f526364711l_bool(hAPP_P1062890741l_bool(member2143287562nt_int,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,X_1),Y_2)),R_4)))) # label(fact_327_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 375 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_P1555980039t_bool(hAPP_P705731903t_bool(in_rel293241086at_nat(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f115998247l_bool(hAPP_P1876494581l_bool(member180897546at_nat,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,X_1),Y_2)),R_4)))) # label(fact_328_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 376 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(in_rel1707483778de_int(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f222989233l_bool(hAPP_P1879777545l_bool(member2092545300de_int,hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,X_1),Y_2)),R_4)))) # label(fact_329_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 377 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(in_rel1251239042umeral(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f251496625l_bool(hAPP_P2045320969l_bool(member1246959636umeral,hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,X_1),Y_2)),R_4)))) # label(fact_330_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 378 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(in_rel_real_real(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f46817975l_bool(hAPP_P1946311189l_bool(member1344826522l_real,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,X_1),Y_2)),R_4)))) # label(fact_331_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 379 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(in_rel_nat_nat(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f879361201l_bool(hAPP_P1251024649l_bool(member232255508at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_1),Y_2)),R_4)))) # label(fact_332_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 380 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_P603027463t_bool(hAPP_i119638232t_bool(in_rel1239871883nt_int(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f928428050l_bool(hAPP_P2074576781l_bool(member791087631nt_int,hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,X_1),Y_2)),R_4)))) # label(fact_333_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 381 (all R_4 all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(in_rel_int_int(R_4),X_1),Y_2)) <-> hBOOL(hAPP_f851219889l_bool(hAPP_P1268961545l_bool(member1747683604nt_int,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,X_1),Y_2)),R_4)))) # label(fact_334_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 382 (all F all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(produc1775888740l_bool(F),Aa),Ba)) -> hBOOL(hAPP_P880235623l_bool(F,hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,Aa),Ba))))) # label(fact_335_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 383 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(hAPP_P989584703t_bool(produc353512698t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P62333565t_bool(F,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,Aa),Ba))))) # label(fact_336_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 384 (all F all Aa all Ba (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(produc2013771390t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1709355527t_bool(F,hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,Aa),Ba))))) # label(fact_337_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 385 (all F all Aa all Ba (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(produc609372286l_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1164677895l_bool(F,hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,Aa),Ba))))) # label(fact_338_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 386 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(produc748992778l_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1333854989l_bool(F,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba))))) # label(fact_339_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 387 (all F all Aa all Ba (hBOOL(hAPP_P1555980039t_bool(hAPP_P705731903t_bool(produc1319041786t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1463840893t_bool(F,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,Aa),Ba))))) # label(fact_340_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 388 (all F all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(produc2091540094t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1555980039t_bool(F,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),Ba))))) # label(fact_341_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 389 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(hAPP_i119638232t_bool(produc97574839t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P178748804t_bool(F,hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,Aa),Ba))))) # label(fact_342_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 390 (all F all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(produc262399358t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P603027463t_bool(F,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aa),Ba))))) # label(fact_343_curryE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 391 (all X_1 (one_one_rat = X_1 <-> X_1 = one_one_rat)) # label(fact_344_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 392 (all X_1 (one_on1684967323de_int = X_1 <-> X_1 = one_on1684967323de_int)) # label(fact_345_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 393 (all X_1 (one_one_complex = X_1 <-> X_1 = one_one_complex)) # label(fact_346_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 394 (all X_1 (one_on1645066479umeral = X_1 <-> X_1 = one_on1645066479umeral)) # label(fact_347_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 395 (all X_1 (one_one_nat = X_1 <-> X_1 = one_one_nat)) # label(fact_348_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 396 (all X_1 (one_one_real = X_1 <-> X_1 = one_one_real)) # label(fact_349_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 397 (all X_1 (one_one_int = X_1 <-> X_1 = one_one_int)) # label(fact_350_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 398 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2)))) # label(fact_351_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 399 (all W_1 all X_1 (hAPP_int_rat(number_number_of_rat,W_1) = X_1 <-> X_1 = hAPP_int_rat(number_number_of_rat,W_1))) # label(fact_352_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 400 (all W_1 all X_1 (hAPP_i1732201573de_int(number1226105091de_int,W_1) = X_1 <-> X_1 = hAPP_i1732201573de_int(number1226105091de_int,W_1))) # label(fact_353_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 401 (all W_1 all X_1 (hAPP_int_complex(number528085621omplex,W_1) = X_1 <-> X_1 = hAPP_int_complex(number528085621omplex,W_1))) # label(fact_354_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 402 (all W_1 all X_1 (hAPP_i769753017umeral(number1443263063umeral,W_1) = X_1 <-> X_1 = hAPP_i769753017umeral(number1443263063umeral,W_1))) # label(fact_355_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 403 (all W_1 all X_1 (hAPP_int_nat(number_number_of_nat,W_1) = X_1 <-> X_1 = hAPP_int_nat(number_number_of_nat,W_1))) # label(fact_356_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 404 (all W_1 all X_1 (hAPP_int_real(number267125858f_real,W_1) = X_1 <-> X_1 = hAPP_int_real(number267125858f_real,W_1))) # label(fact_357_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 405 (all W_1 all X_1 (hAPP_int_int(number_number_of_int,W_1) = X_1 <-> X_1 = hAPP_int_int(number_number_of_int,W_1))) # label(fact_358_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 406 (all V all W_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) <-> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V))))) # label(fact_359_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 407 (all V all W_1 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_i1732201573de_int(number1226105091de_int,V)),hAPP_i1732201573de_int(number1226105091de_int,W_1))) <-> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_i1732201573de_int(number1226105091de_int,W_1)),hAPP_i1732201573de_int(number1226105091de_int,V))))) # label(fact_360_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 408 (all V all W_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_int_nat(number_number_of_nat,W_1))) <-> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(number_number_of_nat,W_1)),hAPP_int_nat(number_number_of_nat,V))))) # label(fact_361_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 409 (all V all W_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,V)),hAPP_int_real(number267125858f_real,W_1))) <-> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,W_1)),hAPP_int_real(number267125858f_real,V))))) # label(fact_362_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 410 (all V all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,V)),hAPP_int_int(number_number_of_int,W_1))) <-> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,W_1)),hAPP_int_int(number_number_of_int,V))))) # label(fact_363_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 411 (all V all W_1 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_i769753017umeral(number1443263063umeral,V)),hAPP_i769753017umeral(number1443263063umeral,W_1))) <-> -hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_i769753017umeral(number1443263063umeral,W_1)),hAPP_i769753017umeral(number1443263063umeral,V))))) # label(fact_364_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 412 (all X_1 all Y_2 (hAPP_int_rat(number_number_of_rat,X_1) = hAPP_int_rat(number_number_of_rat,Y_2) <-> X_1 = Y_2)) # label(fact_365_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 413 (all X_1 all Y_2 (hAPP_int_complex(number528085621omplex,X_1) = hAPP_int_complex(number528085621omplex,Y_2) <-> X_1 = Y_2)) # label(fact_366_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 414 (all X_1 all Y_2 (hAPP_int_real(number267125858f_real,X_1) = hAPP_int_real(number267125858f_real,Y_2) <-> X_1 = Y_2)) # label(fact_367_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 415 (all X_1 all Y_2 (hAPP_int_int(number_number_of_int,X_1) = hAPP_int_int(number_number_of_int,Y_2) <-> X_1 = Y_2)) # label(fact_368_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 416 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)))) # label(fact_369_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 417 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,X_1)),hAPP_int_real(number267125858f_real,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)))) # label(fact_370_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 418 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,X_1)),hAPP_int_int(number_number_of_int,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)))) # label(fact_371_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 419 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)))) # label(fact_372_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 420 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,X_1)),hAPP_int_real(number267125858f_real,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)))) # label(fact_373_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 421 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,X_1)),hAPP_int_int(number_number_of_int,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)))) # label(fact_374_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 422 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),one_one_int)),Z_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)))) # label(fact_375_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 423 (all X_70 all Y_56 (X_70 != Y_56 -> (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_70),Y_56)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_56),X_70))))) # label(fact_376_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 424 (all X_70 all Y_56 (X_70 != Y_56 -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_70),Y_56)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_56),X_70))))) # label(fact_377_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 425 (all X_70 all Y_56 (X_70 != Y_56 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_70),Y_56)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_56),X_70))))) # label(fact_378_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 426 (all W all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),one_one_int)),Z_1)))) # label(fact_379_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 427 (all X_69 all Y_55 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_69),Y_55)) -> (X_69 != Y_55 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_69),Y_55))))) # label(fact_380_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 428 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) -> (X_1 != Y_2 -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2))))) # label(fact_381_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 429 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) -> (X_1 != Y_2 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2))))) # label(fact_382_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 430 (all X_69 all Y_55 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_69),Y_55)) -> (X_69 != Y_55 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_69),Y_55))))) # label(fact_383_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 431 (all X_69 all Y_55 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_69),Y_55)) -> (X_69 != Y_55 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_69),Y_55))))) # label(fact_384_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 432 (all X_69 all Y_55 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_69),Y_55)) -> (X_69 != Y_55 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_69),Y_55))))) # label(fact_385_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 433 (all X_69 all Y_55 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_69),Y_55)) -> (X_69 != Y_55 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_69),Y_55))))) # label(fact_386_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 434 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_2),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)))) # label(fact_387_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 435 (all N_8 all M_10 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,one_one_rat),M_10)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,one_one_rat),N_8)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,one_one_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,M_10),N_8)))))) # label(fact_388_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 436 (all N_8 all M_10 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,one_on1684967323de_int),M_10)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,one_on1684967323de_int),N_8)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,one_on1684967323de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,M_10),N_8)))))) # label(fact_389_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 437 (all N_8 all M_10 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,one_on1645066479umeral),M_10)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,one_on1645066479umeral),N_8)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,one_on1645066479umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,M_10),N_8)))))) # label(fact_390_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 438 (all N_8 all M_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),M_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_10),N_8)))))) # label(fact_391_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 439 (all N_8 all M_10 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),M_10)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),N_8)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,M_10),N_8)))))) # label(fact_392_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 440 (all N_8 all M_10 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M_10)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),N_8)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_10),N_8)))))) # label(fact_393_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 441 (all A_220 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_220),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_220),one_one_rat)))) # label(fact_394_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 442 (all A_220 hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_220),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_220),one_on1684967323de_int)))) # label(fact_395_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 443 (all A_220 hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_220),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_220),one_on1645066479umeral)))) # label(fact_396_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 444 (all A_220 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_220),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_220),one_one_nat)))) # label(fact_397_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 445 (all A_220 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_220),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_220),one_one_real)))) # label(fact_398_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 446 (all A_220 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_220),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_220),one_one_int)))) # label(fact_399_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 447 (all C_85 all D_17 all A_219 all B_168 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_219),B_168)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_85),D_17)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_219),C_85)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_168),D_17)))))) # label(fact_400_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 448 (all C_85 all D_17 all A_219 all B_168 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_219),B_168)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_85),D_17)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_219),C_85)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_168),D_17)))))) # label(fact_401_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 449 (all C_85 all D_17 all A_219 all B_168 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_219),B_168)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_85),D_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_219),C_85)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_168),D_17)))))) # label(fact_402_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 450 (all C_85 all D_17 all A_219 all B_168 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_219),B_168)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_85),D_17)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_219),C_85)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_168),D_17)))))) # label(fact_403_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 451 (all C_85 all D_17 all A_219 all B_168 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_219),B_168)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_85),D_17)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_219),C_85)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_168),D_17)))))) # label(fact_404_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 452 (all C_84 all D_16 all A_218 all B_167 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_218),B_167)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_84),D_16)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_218),C_84)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_167),D_16)))))) # label(fact_405_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 453 (all C_84 all D_16 all A_218 all B_167 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_218),B_167)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_84),D_16)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_218),C_84)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_167),D_16)))))) # label(fact_406_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 454 (all C_84 all D_16 all A_218 all B_167 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_218),B_167)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_84),D_16)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_218),C_84)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_167),D_16)))))) # label(fact_407_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 455 (all C_84 all D_16 all A_218 all B_167 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_218),B_167)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_84),D_16)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_218),C_84)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_167),D_16)))))) # label(fact_408_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 456 (all C_84 all D_16 all A_218 all B_167 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_218),B_167)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_84),D_16)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_218),C_84)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_167),D_16)))))) # label(fact_409_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 457 (all Z_4 all Z_1 all W_16 all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_16),W)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_4),Z_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_16),Z_4)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z_1)))))) # label(fact_410_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 458 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) | W_1 = Z_2)) # label(fact_411_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 459 (all Aa all C all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Ba),C))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)))) # label(fact_412_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 460 (all Aa all C all Ba (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Aa),C)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Ba),C))) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Aa),Ba)))) # label(fact_413_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 461 (all Aa all C all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),C))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_414_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 462 (all Aa all C all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),C)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Ba),C))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)))) # label(fact_415_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 463 (all Aa all C all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),C))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)))) # label(fact_416_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 464 (all C all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C),Aa)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)))) # label(fact_417_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 465 (all C all Aa all Ba (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C),Aa)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C),Ba))) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Aa),Ba)))) # label(fact_418_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 466 (all C all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_419_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 467 (all C all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C),Aa)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)))) # label(fact_420_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 468 (all C all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C),Aa)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)))) # label(fact_421_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 469 (all C_83 all A_217 all B_166 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_217),B_166)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_217),C_83)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_166),C_83))))) # label(fact_422_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.67 470 (all C_83 all A_217 all B_166 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_217),B_166)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_217),C_83)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_166),C_83))))) # label(fact_423_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 471 (all C_83 all A_217 all B_166 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_217),B_166)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_217),C_83)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_166),C_83))))) # label(fact_424_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 472 (all C_83 all A_217 all B_166 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_217),B_166)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_217),C_83)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_166),C_83))))) # label(fact_425_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 473 (all C_83 all A_217 all B_166 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_217),B_166)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_217),C_83)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_166),C_83))))) # label(fact_426_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 474 (all C_82 all A_216 all B_165 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_216),B_165)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_82),A_216)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_82),B_165))))) # label(fact_427_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 475 (all C_82 all A_216 all B_165 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_216),B_165)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_82),A_216)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_82),B_165))))) # label(fact_428_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 476 (all C_82 all A_216 all B_165 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_216),B_165)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_82),A_216)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_82),B_165))))) # label(fact_429_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 477 (all C_82 all A_216 all B_165 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_216),B_165)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_82),A_216)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_82),B_165))))) # label(fact_430_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 478 (all C_82 all A_216 all B_165 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_216),B_165)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_82),A_216)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_82),B_165))))) # label(fact_431_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 479 (all C_81 all D_15 all A_215 all B_164 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_215),B_164)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_81),D_15)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_215),C_81)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_164),D_15)))))) # label(fact_432_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 480 (all C_81 all D_15 all A_215 all B_164 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_215),B_164)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_81),D_15)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_215),C_81)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_164),D_15)))))) # label(fact_433_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 481 (all C_81 all D_15 all A_215 all B_164 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_215),B_164)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_81),D_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_215),C_81)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_164),D_15)))))) # label(fact_434_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 482 (all C_81 all D_15 all A_215 all B_164 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_215),B_164)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_81),D_15)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_215),C_81)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_164),D_15)))))) # label(fact_435_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 483 (all C_81 all D_15 all A_215 all B_164 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_215),B_164)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_81),D_15)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_215),C_81)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_164),D_15)))))) # label(fact_436_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 484 (all A_214 all C_80 all B_163 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_214),C_80)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_163),C_80))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_214),B_163)))) # label(fact_437_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 485 (all A_214 all C_80 all B_163 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_214),C_80)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_163),C_80))) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_214),B_163)))) # label(fact_438_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 486 (all A_214 all C_80 all B_163 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_214),C_80)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_163),C_80))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_214),B_163)))) # label(fact_439_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 487 (all A_214 all C_80 all B_163 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_214),C_80)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_163),C_80))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_214),B_163)))) # label(fact_440_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 488 (all A_214 all C_80 all B_163 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_214),C_80)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_163),C_80))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_214),B_163)))) # label(fact_441_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 489 (all C_79 all A_213 all B_162 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_79),A_213)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_79),B_162))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_213),B_162)))) # label(fact_442_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 490 (all C_79 all A_213 all B_162 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_79),A_213)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_79),B_162))) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_213),B_162)))) # label(fact_443_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 491 (all C_79 all A_213 all B_162 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_79),A_213)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_79),B_162))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_213),B_162)))) # label(fact_444_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 492 (all C_79 all A_213 all B_162 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_79),A_213)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_79),B_162))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_213),B_162)))) # label(fact_445_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 493 (all C_79 all A_213 all B_162 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_79),A_213)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_79),B_162))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_213),B_162)))) # label(fact_446_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 494 (all A_212 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,one_one_rat),A_212) = A_212) # label(fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 495 (all A_212 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,one_on1684967323de_int),A_212) = A_212) # label(fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 496 (all A_212 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,one_one_complex),A_212) = A_212) # label(fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 497 (all A_212 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,one_on1645066479umeral),A_212) = A_212) # label(fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 498 (all A_212 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_212) = A_212) # label(fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 499 (all A_212 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,one_one_real),A_212) = A_212) # label(fact_452_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 500 (all A_212 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_212) = A_212) # label(fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 501 (all A_211 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_211),one_one_rat) = A_211) # label(fact_454_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 502 (all A_211 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_211),one_on1684967323de_int) = A_211) # label(fact_455_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 503 (all A_211 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_211),one_one_complex) = A_211) # label(fact_456_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 504 (all A_211 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_211),one_on1645066479umeral) = A_211) # label(fact_457_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 505 (all A_211 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_211),one_one_nat) = A_211) # label(fact_458_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 506 (all A_211 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_211),one_one_real) = A_211) # label(fact_459_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 507 (all A_211 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_211),one_one_int) = A_211) # label(fact_460_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 508 (all A_210 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,one_one_rat),A_210) = A_210) # label(fact_461_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 509 (all A_210 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,one_on1684967323de_int),A_210) = A_210) # label(fact_462_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 510 (all A_210 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,one_one_complex),A_210) = A_210) # label(fact_463_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 511 (all A_210 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,one_on1645066479umeral),A_210) = A_210) # label(fact_464_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 512 (all A_210 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_210) = A_210) # label(fact_465_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 513 (all A_210 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,one_one_real),A_210) = A_210) # label(fact_466_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 514 (all A_210 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_210) = A_210) # label(fact_467_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 515 (all A_209 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,one_one_rat),A_209) = A_209) # label(fact_468_mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 516 (all A_209 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,one_on1684967323de_int),A_209) = A_209) # label(fact_469_mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 517 (all A_209 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,one_one_complex),A_209) = A_209) # label(fact_470_mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 518 (all A_209 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,one_on1645066479umeral),A_209) = A_209) # label(fact_471_mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 519 (all A_209 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),A_209) = A_209) # label(fact_472_mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 520 (all A_209 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,one_one_real),A_209) = A_209) # label(fact_473_mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 521 (all A_209 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),A_209) = A_209) # label(fact_474_mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 522 (all A_208 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_208),one_one_rat) = A_208) # label(fact_475_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 523 (all A_208 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_208),one_on1684967323de_int) = A_208) # label(fact_476_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 524 (all A_208 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_208),one_one_complex) = A_208) # label(fact_477_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 525 (all A_208 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_208),one_on1645066479umeral) = A_208) # label(fact_478_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 526 (all A_208 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_208),one_one_nat) = A_208) # label(fact_479_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 527 (all A_208 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_208),one_one_real) = A_208) # label(fact_480_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 528 (all A_208 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_208),one_one_int) = A_208) # label(fact_481_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 529 (all A_207 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_207),one_one_rat) = A_207) # label(fact_482_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 530 (all A_207 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_207),one_on1684967323de_int) = A_207) # label(fact_483_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 531 (all A_207 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_207),one_one_complex) = A_207) # label(fact_484_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 532 (all A_207 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_207),one_on1645066479umeral) = A_207) # label(fact_485_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 533 (all A_207 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_207),one_one_nat) = A_207) # label(fact_486_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 534 (all A_207 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_207),one_one_real) = A_207) # label(fact_487_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 535 (all A_207 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_207),one_one_int) = A_207) # label(fact_488_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 536 (all Aa all Ba all C all D (hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,C),D) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C),D))))) # label(fact_489_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 537 (all Aa all Ba all C all D (hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C),D) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C),D))))) # label(fact_490_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 538 (all Aa all Ba all C all D (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C),D) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),D))))) # label(fact_491_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 539 (all Aa all C all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Ba),C))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),Ba)))) # label(fact_492_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 540 (all Aa all C all Ba (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Aa),C)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,Ba),C))) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Aa),Ba)))) # label(fact_493_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 541 (all Aa all C all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),C))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_494_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 542 (all Aa all C all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),C)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Ba),C))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)))) # label(fact_495_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 543 (all Aa all C all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),C)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),C))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)))) # label(fact_496_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 544 (all C all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C),Aa)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),Ba)))) # label(fact_497_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 545 (all C all Aa all Ba (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C),Aa)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C),Ba))) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Aa),Ba)))) # label(fact_498_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 546 (all C all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_499_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 547 (all C all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C),Aa)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)))) # label(fact_500_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 548 (all C all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C),Aa)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)))) # label(fact_501_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 549 (all C_78 all A_206 all B_161 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_206),B_161)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_206),C_78)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_161),C_78))))) # label(fact_502_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 550 (all C_78 all A_206 all B_161 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_206),B_161)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_206),C_78)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_161),C_78))))) # label(fact_503_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 551 (all C_78 all A_206 all B_161 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_206),B_161)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_206),C_78)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_161),C_78))))) # label(fact_504_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 552 (all C_78 all A_206 all B_161 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_206),B_161)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_206),C_78)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_161),C_78))))) # label(fact_505_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 553 (all C_78 all A_206 all B_161 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_206),B_161)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_206),C_78)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_161),C_78))))) # label(fact_506_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 554 (all C_77 all A_205 all B_160 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_205),B_160)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_77),A_205)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_77),B_160))))) # label(fact_507_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 555 (all C_77 all A_205 all B_160 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_205),B_160)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_77),A_205)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_77),B_160))))) # label(fact_508_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 556 (all C_77 all A_205 all B_160 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_205),B_160)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_77),A_205)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_77),B_160))))) # label(fact_509_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 557 (all C_77 all A_205 all B_160 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_205),B_160)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_77),A_205)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_77),B_160))))) # label(fact_510_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 558 (all C_77 all A_205 all B_160 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_205),B_160)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_77),A_205)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_77),B_160))))) # label(fact_511_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 559 (all C_76 all D_14 all A_204 all B_159 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_204),B_159)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_76),D_14)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_204),C_76)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_159),D_14)))))) # label(fact_512_add__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 560 (all C_76 all D_14 all A_204 all B_159 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_204),B_159)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_76),D_14)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_204),C_76)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_159),D_14)))))) # label(fact_513_add__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 561 (all C_76 all D_14 all A_204 all B_159 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_204),B_159)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_76),D_14)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_204),C_76)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_159),D_14)))))) # label(fact_514_add__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 562 (all C_76 all D_14 all A_204 all B_159 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_204),B_159)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_76),D_14)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_204),C_76)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_159),D_14)))))) # label(fact_515_add__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 563 (all C_76 all D_14 all A_204 all B_159 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_204),B_159)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_76),D_14)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_204),C_76)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_159),D_14)))))) # label(fact_516_add__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 564 (all A_203 all C_75 all B_158 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_203),C_75)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_158),C_75))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_203),B_158)))) # label(fact_517_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 565 (all A_203 all C_75 all B_158 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_203),C_75)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_158),C_75))) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_203),B_158)))) # label(fact_518_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 566 (all A_203 all C_75 all B_158 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_203),C_75)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_158),C_75))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_203),B_158)))) # label(fact_519_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 567 (all A_203 all C_75 all B_158 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_203),C_75)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_158),C_75))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_203),B_158)))) # label(fact_520_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 568 (all A_203 all C_75 all B_158 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_203),C_75)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_158),C_75))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_203),B_158)))) # label(fact_521_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 569 (all C_74 all A_202 all B_157 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_74),A_202)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_74),B_157))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_202),B_157)))) # label(fact_522_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 570 (all C_74 all A_202 all B_157 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_74),A_202)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_74),B_157))) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_202),B_157)))) # label(fact_523_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 571 (all C_74 all A_202 all B_157 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_74),A_202)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_74),B_157))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_202),B_157)))) # label(fact_524_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 572 (all C_74 all A_202 all B_157 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_74),A_202)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_74),B_157))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_202),B_157)))) # label(fact_525_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 573 (all C_74 all A_202 all B_157 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_74),A_202)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_74),B_157))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_202),B_157)))) # label(fact_526_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 574 (all Aa all Ba all C all D (hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,C),D) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C),D))))) # label(fact_527_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 575 (all Aa all Ba all C all D (hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C),D) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C),D))))) # label(fact_528_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 576 (all Aa all Ba all C all D (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C),D) -> (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),D))))) # label(fact_529_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 577 (all V_2 all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,W)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_2),W))) # label(fact_530_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 578 (all V_2 all W hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,W)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_2),W))) # label(fact_531_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 579 (all K_2 all I all J_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),J_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),K_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,J_2),K_2))))) # label(fact_532_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 580 (all K_2 all I all J_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),J_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),I)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),J_2))))) # label(fact_533_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 581 (all Z_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),Z_1) = Z_1) # label(fact_534_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 582 (all Z_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),one_one_int) = Z_1) # label(fact_535_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 583 (all V_24 all B_156 all C_73 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_24)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_156),C_73)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_24)),B_156)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_24)),C_73))) # label(fact_536_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 584 (all V_24 all B_156 all C_73 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_i1732201573de_int(number1226105091de_int,V_24)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_156),C_73)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_i1732201573de_int(number1226105091de_int,V_24)),B_156)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_i1732201573de_int(number1226105091de_int,V_24)),C_73))) # label(fact_537_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 585 (all V_24 all B_156 all C_73 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_24)),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_156),C_73)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_24)),B_156)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_24)),C_73))) # label(fact_538_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 586 (all V_24 all B_156 all C_73 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_156),C_73)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_24)),B_156)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_24)),C_73))) # label(fact_539_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 587 (all V_24 all B_156 all C_73 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_24)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_156),C_73)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_24)),B_156)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_24)),C_73))) # label(fact_540_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 588 (all V_24 all B_156 all C_73 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_24)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_156),C_73)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_24)),B_156)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_24)),C_73))) # label(fact_541_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 589 (all V_24 all B_156 all C_73 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_i769753017umeral(number1443263063umeral,V_24)),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,B_156),C_73)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_i769753017umeral(number1443263063umeral,V_24)),B_156)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_i769753017umeral(number1443263063umeral,V_24)),C_73))) # label(fact_542_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 590 (all A_201 all B_155 all V_23 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_201),B_155)),hAPP_int_rat(number_number_of_rat,V_23)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_201),hAPP_int_rat(number_number_of_rat,V_23))),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_155),hAPP_int_rat(number_number_of_rat,V_23)))) # label(fact_543_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 591 (all A_201 all B_155 all V_23 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_201),B_155)),hAPP_i1732201573de_int(number1226105091de_int,V_23)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_201),hAPP_i1732201573de_int(number1226105091de_int,V_23))),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_155),hAPP_i1732201573de_int(number1226105091de_int,V_23)))) # label(fact_544_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 592 (all A_201 all B_155 all V_23 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_201),B_155)),hAPP_int_complex(number528085621omplex,V_23)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_201),hAPP_int_complex(number528085621omplex,V_23))),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_155),hAPP_int_complex(number528085621omplex,V_23)))) # label(fact_545_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 593 (all A_201 all B_155 all V_23 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_201),B_155)),hAPP_int_nat(number_number_of_nat,V_23)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_201),hAPP_int_nat(number_number_of_nat,V_23))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_155),hAPP_int_nat(number_number_of_nat,V_23)))) # label(fact_546_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 594 (all A_201 all B_155 all V_23 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_201),B_155)),hAPP_int_real(number267125858f_real,V_23)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_201),hAPP_int_real(number267125858f_real,V_23))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_155),hAPP_int_real(number267125858f_real,V_23)))) # label(fact_547_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 595 (all A_201 all B_155 all V_23 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_201),B_155)),hAPP_int_int(number_number_of_int,V_23)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_201),hAPP_int_int(number_number_of_int,V_23))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_155),hAPP_int_int(number_number_of_int,V_23)))) # label(fact_548_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 596 (all A_201 all B_155 all V_23 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_201),B_155)),hAPP_i769753017umeral(number1443263063umeral,V_23)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_201),hAPP_i769753017umeral(number1443263063umeral,V_23))),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_155),hAPP_i769753017umeral(number1443263063umeral,V_23)))) # label(fact_549_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 597 (all V_22 all B_154 all C_72 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_22)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,B_154),C_72)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_22)),B_154)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_22)),C_72))) # label(fact_550_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 598 (all V_22 all B_154 all C_72 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_22)),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,B_154),C_72)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_22)),B_154)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_22)),C_72))) # label(fact_551_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 599 (all V_22 all B_154 all C_72 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_22)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_154),C_72)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_22)),B_154)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_22)),C_72))) # label(fact_552_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 600 (all V_22 all B_154 all C_72 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_22)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_154),C_72)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_22)),B_154)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_22)),C_72))) # label(fact_553_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 601 (all A_200 all B_153 all V_21 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_200),B_153)),hAPP_int_rat(number_number_of_rat,V_21)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_200),hAPP_int_rat(number_number_of_rat,V_21))),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_153),hAPP_int_rat(number_number_of_rat,V_21)))) # label(fact_554_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 602 (all A_200 all B_153 all V_21 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_200),B_153)),hAPP_int_complex(number528085621omplex,V_21)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_200),hAPP_int_complex(number528085621omplex,V_21))),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,B_153),hAPP_int_complex(number528085621omplex,V_21)))) # label(fact_555_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 603 (all A_200 all B_153 all V_21 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_200),B_153)),hAPP_int_real(number267125858f_real,V_21)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_200),hAPP_int_real(number267125858f_real,V_21))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_153),hAPP_int_real(number267125858f_real,V_21)))) # label(fact_556_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 604 (all A_200 all B_153 all V_21 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_200),B_153)),hAPP_int_int(number_number_of_int,V_21)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_200),hAPP_int_int(number_number_of_int,V_21))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_153),hAPP_int_int(number_number_of_int,V_21)))) # label(fact_557_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 605 (all V_20 all W_15 hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_20),W_15)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_20)),hAPP_int_rat(number_number_of_rat,W_15))) # label(fact_558_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 606 (all V_20 all W_15 hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_20),W_15)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_20)),hAPP_int_complex(number528085621omplex,W_15))) # label(fact_559_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 607 (all V_20 all W_15 hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_20),W_15)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_20)),hAPP_int_real(number267125858f_real,W_15))) # label(fact_560_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 608 (all V_20 all W_15 hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_20),W_15)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_20)),hAPP_int_int(number_number_of_int,W_15))) # label(fact_561_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 609 (all V_19 all W_14 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_19)),hAPP_int_rat(number_number_of_rat,W_14)) = hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_19),W_14))) # label(fact_562_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 610 (all V_19 all W_14 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_19)),hAPP_int_complex(number528085621omplex,W_14)) = hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_19),W_14))) # label(fact_563_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 611 (all V_19 all W_14 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_19)),hAPP_int_real(number267125858f_real,W_14)) = hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_19),W_14))) # label(fact_564_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 612 (all V_19 all W_14 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_19)),hAPP_int_int(number_number_of_int,W_14)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_19),W_14))) # label(fact_565_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 613 (all V_18 all W_13 all Z_21 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,V_18)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,W_13)),Z_21)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_18),W_13))),Z_21)) # label(fact_566_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 614 (all V_18 all W_13 all Z_21 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,V_18)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,W_13)),Z_21)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_18),W_13))),Z_21)) # label(fact_567_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 615 (all V_18 all W_13 all Z_21 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,V_18)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,W_13)),Z_21)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_18),W_13))),Z_21)) # label(fact_568_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 616 (all V_18 all W_13 all Z_21 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,V_18)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,W_13)),Z_21)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_18),W_13))),Z_21)) # label(fact_569_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 617 (all V_17 all W_12 hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_17),W_12)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,V_17)),hAPP_int_rat(number_number_of_rat,W_12))) # label(fact_570_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 618 (all V_17 all W_12 hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_17),W_12)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,V_17)),hAPP_int_complex(number528085621omplex,W_12))) # label(fact_571_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 619 (all V_17 all W_12 hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_17),W_12)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,V_17)),hAPP_int_real(number267125858f_real,W_12))) # label(fact_572_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 620 (all V_17 all W_12 hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_17),W_12)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_17)),hAPP_int_int(number_number_of_int,W_12))) # label(fact_573_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 621 (all V_16 all W_11 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,V_16)),hAPP_int_rat(number_number_of_rat,W_11)) = hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_16),W_11))) # label(fact_574_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 622 (all V_16 all W_11 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,V_16)),hAPP_int_complex(number528085621omplex,W_11)) = hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_16),W_11))) # label(fact_575_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 623 (all V_16 all W_11 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,V_16)),hAPP_int_real(number267125858f_real,W_11)) = hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_16),W_11))) # label(fact_576_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 624 (all V_16 all W_11 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_16)),hAPP_int_int(number_number_of_int,W_11)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_16),W_11))) # label(fact_577_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 625 (all V_15 all W_10 all Z_20 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,V_15)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,W_10)),Z_20)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_15),W_10))),Z_20)) # label(fact_578_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 626 (all V_15 all W_10 all Z_20 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,V_15)),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,W_10)),Z_20)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_15),W_10))),Z_20)) # label(fact_579_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 627 (all V_15 all W_10 all Z_20 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,V_15)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,W_10)),Z_20)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_15),W_10))),Z_20)) # label(fact_580_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 628 (all V_15 all W_10 all Z_20 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_15)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),Z_20)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_15),W_10))),Z_20)) # label(fact_581_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 629 (all V_14 all W_9 hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,V_14),W_9)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_int_rat(number_number_of_rat,V_14)),hAPP_int_rat(number_number_of_rat,W_9))) # label(fact_582_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 630 (all V_14 all W_9 hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,V_14),W_9)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_int_complex(number528085621omplex,V_14)),hAPP_int_complex(number528085621omplex,W_9))) # label(fact_583_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 631 (all V_14 all W_9 hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,V_14),W_9)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(number267125858f_real,V_14)),hAPP_int_real(number267125858f_real,W_9))) # label(fact_584_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 632 (all V_14 all W_9 hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,V_14),W_9)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(number_number_of_int,V_14)),hAPP_int_int(number_number_of_int,W_9))) # label(fact_585_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 633 (all M_9 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,M_9),M_9) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,one_one_rat),one_one_rat)),M_9)) # label(fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 634 (all M_9 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,M_9),M_9) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,one_on1684967323de_int),one_on1684967323de_int)),M_9)) # label(fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 635 (all M_9 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,M_9),M_9) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,one_one_complex),one_one_complex)),M_9)) # label(fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 636 (all M_9 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,M_9),M_9) = hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,one_on1645066479umeral),one_on1645066479umeral)),M_9)) # label(fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 637 (all M_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_9),M_9) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),M_9)) # label(fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 638 (all M_9 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,M_9),M_9) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),one_one_real)),M_9)) # label(fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 639 (all M_9 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_9),M_9) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_9)) # label(fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 640 (all M_8 all A_199 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,M_8),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_199),M_8)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_199),one_one_rat)),M_8)) # label(fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 641 (all M_8 all A_199 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,M_8),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_199),M_8)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_199),one_on1684967323de_int)),M_8)) # label(fact_594_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 642 (all M_8 all A_199 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,M_8),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_199),M_8)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_199),one_one_complex)),M_8)) # label(fact_595_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 643 (all M_8 all A_199 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,M_8),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_199),M_8)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_199),one_on1645066479umeral)),M_8)) # label(fact_596_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 644 (all M_8 all A_199 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_8),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_199),M_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_199),one_one_nat)),M_8)) # label(fact_597_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 645 (all M_8 all A_199 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,M_8),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_199),M_8)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_199),one_one_real)),M_8)) # label(fact_598_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 646 (all M_8 all A_199 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_8),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_199),M_8)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_199),one_one_int)),M_8)) # label(fact_599_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 647 (all A_198 all M_7 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_198),M_7)),M_7) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_198),one_one_rat)),M_7)) # label(fact_600_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 648 (all A_198 all M_7 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_198),M_7)),M_7) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_198),one_on1684967323de_int)),M_7)) # label(fact_601_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 649 (all A_198 all M_7 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_198),M_7)),M_7) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_198),one_one_complex)),M_7)) # label(fact_602_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 650 (all A_198 all M_7 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_198),M_7)),M_7) = hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_198),one_on1645066479umeral)),M_7)) # label(fact_603_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 651 (all A_198 all M_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_198),M_7)),M_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_198),one_one_nat)),M_7)) # label(fact_604_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 652 (all A_198 all M_7 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_198),M_7)),M_7) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_198),one_one_real)),M_7)) # label(fact_605_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 653 (all A_198 all M_7 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_198),M_7)),M_7) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_198),one_one_int)),M_7)) # label(fact_606_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 654 (all F all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(produc1775888740l_bool(F),Aa),Ba)) -> hBOOL(hAPP_P880235623l_bool(F,hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,Aa),Ba))))) # label(fact_607_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 655 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(hAPP_P989584703t_bool(produc353512698t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P62333565t_bool(F,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,Aa),Ba))))) # label(fact_608_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 656 (all F all Aa all Ba (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(produc2013771390t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1709355527t_bool(F,hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,Aa),Ba))))) # label(fact_609_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 657 (all F all Aa all Ba (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(produc609372286l_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1164677895l_bool(F,hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,Aa),Ba))))) # label(fact_610_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 658 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(produc748992778l_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1333854989l_bool(F,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba))))) # label(fact_611_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 659 (all F all Aa all Ba (hBOOL(hAPP_P1555980039t_bool(hAPP_P705731903t_bool(produc1319041786t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1463840893t_bool(F,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,Aa),Ba))))) # label(fact_612_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 660 (all F all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(produc2091540094t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P1555980039t_bool(F,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),Ba))))) # label(fact_613_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 661 (all F all Aa all Ba (hBOOL(hAPP_P603027463t_bool(hAPP_i119638232t_bool(produc97574839t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P178748804t_bool(F,hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,Aa),Ba))))) # label(fact_614_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 662 (all F all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(produc262399358t_bool(F),Aa),Ba)) -> hBOOL(hAPP_P603027463t_bool(F,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aa),Ba))))) # label(fact_615_curryD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 663 (all X_68 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_68),X_68))) # label(fact_616_order__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 664 (all X_1 hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),X_1))) # label(fact_617_order__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 665 (all X_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),X_1))) # label(fact_618_order__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 666 (all X_68 hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_68),X_68))) # label(fact_619_order__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 667 (all X_68 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_68),X_68))) # label(fact_620_order__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 668 (all X_68 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_68),X_68))) # label(fact_621_order__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 669 (all X_68 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_68),X_68))) # label(fact_622_order__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 670 (all Z_19 all Y_54 all X_67 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_54),X_67)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z_19),Y_54)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z_19),X_67))))) # label(fact_623_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 671 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Z_2),X_1))))) # label(fact_624_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 672 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_1))))) # label(fact_625_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 673 (all Z_19 all Y_54 all X_67 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_54),X_67)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Z_19),Y_54)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Z_19),X_67))))) # label(fact_626_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 674 (all Z_19 all Y_54 all X_67 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_54),X_67)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_19),Y_54)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_19),X_67))))) # label(fact_627_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 675 (all Z_19 all Y_54 all X_67 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_54),X_67)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_19),Y_54)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_19),X_67))))) # label(fact_628_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 676 (all Z_19 all Y_54 all X_67 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_54),X_67)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_19),Y_54)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_19),X_67))))) # label(fact_629_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 677 (all Z_18 all X_66 all Y_53 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_66),Y_53)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_53),Z_18)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_66),Z_18))))) # label(fact_630_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 678 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Z_2))))) # label(fact_631_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 679 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Z_2))))) # label(fact_632_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 680 (all Z_18 all X_66 all Y_53 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_66),Y_53)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_53),Z_18)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_66),Z_18))))) # label(fact_633_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 681 (all Z_18 all X_66 all Y_53 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_66),Y_53)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_53),Z_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_66),Z_18))))) # label(fact_634_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 682 (all Z_18 all X_66 all Y_53 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_66),Y_53)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_53),Z_18)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_66),Z_18))))) # label(fact_635_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 683 (all Z_18 all X_66 all Y_53 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_66),Y_53)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_53),Z_18)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_66),Z_18))))) # label(fact_636_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 684 (all Z_17 all Y_52 all X_65 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_52),X_65)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Z_17),Y_52)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z_17),X_65))))) # label(fact_637_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 685 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Z_2),X_1))))) # label(fact_638_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 686 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_1))))) # label(fact_639_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 687 (all Z_17 all Y_52 all X_65 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_52),X_65)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Z_17),Y_52)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Z_17),X_65))))) # label(fact_640_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 688 (all Z_17 all Y_52 all X_65 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_52),X_65)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_17),Y_52)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_17),X_65))))) # label(fact_641_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 689 (all Z_17 all Y_52 all X_65 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_52),X_65)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_17),Y_52)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_17),X_65))))) # label(fact_642_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 690 (all Z_17 all Y_52 all X_65 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_52),X_65)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_17),Y_52)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_17),X_65))))) # label(fact_643_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 691 (all Z_16 all X_64 all Y_51 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_64),Y_51)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_51),Z_16)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_64),Z_16))))) # label(fact_644_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 692 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Z_2))))) # label(fact_645_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 693 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Z_2))))) # label(fact_646_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 694 (all Z_16 all X_64 all Y_51 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_64),Y_51)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_51),Z_16)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_64),Z_16))))) # label(fact_647_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 695 (all Z_16 all X_64 all Y_51 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_64),Y_51)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_51),Z_16)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_64),Z_16))))) # label(fact_648_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 696 (all Z_16 all X_64 all Y_51 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_64),Y_51)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_51),Z_16)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_64),Z_16))))) # label(fact_649_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 697 (all Z_16 all X_64 all Y_51 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_64),Y_51)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_51),Z_16)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_64),Z_16))))) # label(fact_650_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 698 (all B_152 all A_197 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_152),A_197)) -> (A_197 != B_152 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_152),A_197))))) # label(fact_651_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 699 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ba),Aa)) -> (Aa != Ba -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Ba),Aa))))) # label(fact_652_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 700 (all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) -> (Aa != Ba -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))))) # label(fact_653_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 701 (all B_152 all A_197 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_152),A_197)) -> (A_197 != B_152 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_152),A_197))))) # label(fact_654_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 702 (all B_152 all A_197 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_152),A_197)) -> (A_197 != B_152 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_152),A_197))))) # label(fact_655_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 703 (all B_152 all A_197 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_152),A_197)) -> (A_197 != B_152 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_152),A_197))))) # label(fact_656_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 704 (all B_152 all A_197 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_152),A_197)) -> (A_197 != B_152 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_152),A_197))))) # label(fact_657_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 705 (all A_196 all B_151 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_196),B_151)) -> (A_196 != B_151 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_196),B_151))))) # label(fact_658_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 706 (all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Aa),Ba)) -> (Aa != Ba -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Aa),Ba))))) # label(fact_659_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 707 (all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) -> (Aa != Ba -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))))) # label(fact_660_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 708 (all A_196 all B_151 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_196),B_151)) -> (A_196 != B_151 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_196),B_151))))) # label(fact_661_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 709 (all A_196 all B_151 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_196),B_151)) -> (A_196 != B_151 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_196),B_151))))) # label(fact_662_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 710 (all A_196 all B_151 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_196),B_151)) -> (A_196 != B_151 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_196),B_151))))) # label(fact_663_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 711 (all A_196 all B_151 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_196),B_151)) -> (A_196 != B_151 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_196),B_151))))) # label(fact_664_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 712 (all X_63 all Y_50 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_63),Y_50)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_63),Y_50)) | X_63 = Y_50)) # label(fact_665_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 713 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) | X_1 = Y_2)) # label(fact_666_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 714 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) | X_1 = Y_2)) # label(fact_667_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 715 (all X_63 all Y_50 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_63),Y_50)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_63),Y_50)) | X_63 = Y_50)) # label(fact_668_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 716 (all X_63 all Y_50 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_63),Y_50)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_63),Y_50)) | X_63 = Y_50)) # label(fact_669_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 717 (all X_63 all Y_50 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_63),Y_50)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_63),Y_50)) | X_63 = Y_50)) # label(fact_670_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 718 (all X_63 all Y_50 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_63),Y_50)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_63),Y_50)) | X_63 = Y_50)) # label(fact_671_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 719 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) -> (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_672_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 720 (all X_1 all Y_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) -> (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_673_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 721 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_674_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 722 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_675_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 723 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_676_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 724 (all X_62 all Y_49 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_62),Y_49)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_62),Y_49)))) # label(fact_677_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 725 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)))) # label(fact_678_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 726 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)))) # label(fact_679_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 727 (all X_62 all Y_49 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_62),Y_49)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_62),Y_49)))) # label(fact_680_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 728 (all X_62 all Y_49 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_62),Y_49)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_62),Y_49)))) # label(fact_681_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 729 (all X_62 all Y_49 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_62),Y_49)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_62),Y_49)))) # label(fact_682_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 730 (all X_62 all Y_49 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_62),Y_49)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_62),Y_49)))) # label(fact_683_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 731 (all Y_48 all X_61 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_48),X_61)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_61),Y_48)))) # label(fact_684_leD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 732 (all Y_48 all X_61 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_48),X_61)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_61),Y_48)))) # label(fact_685_leD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 733 (all Y_48 all X_61 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_48),X_61)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_61),Y_48)))) # label(fact_686_leD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 734 (all Y_48 all X_61 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_48),X_61)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_61),Y_48)))) # label(fact_687_leD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 735 (all Y_48 all X_61 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_48),X_61)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_61),Y_48)))) # label(fact_688_leD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 736 (all A_195 all B_150 (A_195 != B_150 -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_150),A_195)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_150),A_195))))) # label(fact_689_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 737 (all Aa all Ba (Aa != Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ba),Aa)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Ba),Aa))))) # label(fact_690_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 738 (all Aa all Ba (Aa != Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))))) # label(fact_691_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 739 (all A_195 all B_150 (A_195 != B_150 -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_150),A_195)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_150),A_195))))) # label(fact_692_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 740 (all A_195 all B_150 (A_195 != B_150 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_150),A_195)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_150),A_195))))) # label(fact_693_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 741 (all A_195 all B_150 (A_195 != B_150 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_150),A_195)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_150),A_195))))) # label(fact_694_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 742 (all A_195 all B_150 (A_195 != B_150 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_150),A_195)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_150),A_195))))) # label(fact_695_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 743 (all W hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),W))) # label(fact_696_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 744 (all K_2 hAPP_int_int(number_number_of_int,K_2) = K_2) # label(fact_697_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 745 (all Z_1 all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z_1)))) # label(fact_698_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 746 (all Z_2 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1)) & Z_2 != W_1)) # label(fact_699_zless__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 747 (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_700_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 748 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,K_1)),hAPP_int_int(number_number_of_int,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)))) # label(fact_701_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 749 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,K_1)),hAPP_int_int(number_number_of_int,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)))) # label(fact_702_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 750 (all K_2 all I all J_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),J_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J_2),K_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K_2))))) # label(fact_703_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 751 (all Z_1 all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z_1)) -> Z_1 = W))) # label(fact_704_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 752 (all F all G (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G,X_2)))))) # label(fact_705_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 753 (all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2)))))) # label(fact_706_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 754 (all X_60 all Y_47 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_60),Y_47)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_47),X_60)))) # label(fact_707_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 755 (all X_60 all Y_47 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_60),Y_47)) | hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_47),X_60)))) # label(fact_708_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 756 (all X_60 all Y_47 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_60),Y_47)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_47),X_60)))) # label(fact_709_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 757 (all X_60 all Y_47 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_60),Y_47)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_47),X_60)))) # label(fact_710_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 758 (all X_60 all Y_47 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_60),Y_47)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_47),X_60)))) # label(fact_711_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 759 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_2),X_1)))) # label(fact_712_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 760 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)))) # label(fact_713_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 761 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)))) # label(fact_714_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 762 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) & hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_2),X_1)))) # label(fact_715_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 763 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)))) # label(fact_716_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 764 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),X_1)))) # label(fact_717_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 765 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_2),X_1)))) # label(fact_718_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 766 (all X_59 all Y_46 (X_59 = Y_46 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_59),Y_46)))) # label(fact_719_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 767 (all X_1 all Y_2 (X_1 = Y_2 -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)))) # label(fact_720_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 768 (all X_1 all Y_2 (X_1 = Y_2 -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)))) # label(fact_721_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 769 (all X_59 all Y_46 (X_59 = Y_46 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_59),Y_46)))) # label(fact_722_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 770 (all X_59 all Y_46 (X_59 = Y_46 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_59),Y_46)))) # label(fact_723_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 771 (all X_59 all Y_46 (X_59 = Y_46 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_59),Y_46)))) # label(fact_724_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 772 (all X_59 all Y_46 (X_59 = Y_46 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_59),Y_46)))) # label(fact_725_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 773 (all X_1 all F all G (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G,X_1))))) # label(fact_726_le__funD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 774 (all X_1 all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))))) # label(fact_727_le__funD) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 775 (all Y_2 all X_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_2),X_1)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_728_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 776 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_729_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 777 (all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_730_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 778 (all Y_2 all X_1 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_2),X_1)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_731_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 779 (all Y_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_732_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 780 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_733_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 781 (all Y_2 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_2),X_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_734_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 782 (all C_71 all A_194 all B_149 (A_194 = B_149 -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_149),C_71)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_194),C_71))))) # label(fact_735_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 783 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ba),C)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Aa),C))))) # label(fact_736_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.68 784 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),C)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),C))))) # label(fact_737_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 785 (all C_71 all A_194 all B_149 (A_194 = B_149 -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_149),C_71)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_194),C_71))))) # label(fact_738_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 786 (all C_71 all A_194 all B_149 (A_194 = B_149 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_149),C_71)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_194),C_71))))) # label(fact_739_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 787 (all C_71 all A_194 all B_149 (A_194 = B_149 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_149),C_71)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_194),C_71))))) # label(fact_740_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 788 (all C_71 all A_194 all B_149 (A_194 = B_149 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_149),C_71)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_194),C_71))))) # label(fact_741_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 789 (all C_70 all A_193 all B_148 (A_193 = B_148 -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_70),B_148)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_70),A_193))))) # label(fact_742_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 790 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C),Ba)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C),Aa))))) # label(fact_743_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 791 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),Ba)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),Aa))))) # label(fact_744_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 792 (all C_70 all A_193 all B_148 (A_193 = B_148 -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_70),B_148)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_70),A_193))))) # label(fact_745_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 793 (all C_70 all A_193 all B_148 (A_193 = B_148 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_70),B_148)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_70),A_193))))) # label(fact_746_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 794 (all C_70 all A_193 all B_148 (A_193 = B_148 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_70),B_148)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_70),A_193))))) # label(fact_747_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 795 (all C_70 all A_193 all B_148 (A_193 = B_148 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_70),B_148)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_70),A_193))))) # label(fact_748_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 796 (all C_69 all A_192 all B_147 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_192),B_147)) -> (B_147 = C_69 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_192),C_69))))) # label(fact_749_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 797 (all C all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Aa),Ba)) -> (Ba = C -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Aa),C))))) # label(fact_750_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 798 (all C all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) -> (Ba = C -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),C))))) # label(fact_751_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 799 (all C_69 all A_192 all B_147 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_192),B_147)) -> (B_147 = C_69 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_192),C_69))))) # label(fact_752_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 800 (all C_69 all A_192 all B_147 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_192),B_147)) -> (B_147 = C_69 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_192),C_69))))) # label(fact_753_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 801 (all C_69 all A_192 all B_147 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_192),B_147)) -> (B_147 = C_69 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_192),C_69))))) # label(fact_754_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 802 (all C_69 all A_192 all B_147 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_192),B_147)) -> (B_147 = C_69 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_192),C_69))))) # label(fact_755_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 803 (all C_68 all B_146 all A_191 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_146),A_191)) -> (B_146 = C_68 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_68),A_191))))) # label(fact_756_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 804 (all C all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Ba),Aa)) -> (Ba = C -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C),Aa))))) # label(fact_757_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 805 (all C all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa)) -> (Ba = C -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),Aa))))) # label(fact_758_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 806 (all C_68 all B_146 all A_191 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_146),A_191)) -> (B_146 = C_68 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_68),A_191))))) # label(fact_759_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 807 (all C_68 all B_146 all A_191 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_146),A_191)) -> (B_146 = C_68 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_68),A_191))))) # label(fact_760_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 808 (all C_68 all B_146 all A_191 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_146),A_191)) -> (B_146 = C_68 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_68),A_191))))) # label(fact_761_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 809 (all C_68 all B_146 all A_191 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_146),A_191)) -> (B_146 = C_68 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_68),A_191))))) # label(fact_762_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 810 (all X_58 all Y_45 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_58),Y_45)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_45),X_58)) -> X_58 = Y_45))) # label(fact_763_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 811 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)) -> X_1 = Y_2))) # label(fact_764_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 812 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)) -> X_1 = Y_2))) # label(fact_765_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 813 (all X_58 all Y_45 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_58),Y_45)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_45),X_58)) -> X_58 = Y_45))) # label(fact_766_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 814 (all X_58 all Y_45 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_58),Y_45)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_45),X_58)) -> X_58 = Y_45))) # label(fact_767_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 815 (all X_58 all Y_45 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_58),Y_45)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_45),X_58)) -> X_58 = Y_45))) # label(fact_768_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 816 (all X_58 all Y_45 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_58),Y_45)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_45),X_58)) -> X_58 = Y_45))) # label(fact_769_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 817 (all Z_15 all X_57 all Y_44 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_57),Y_44)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_44),Z_15)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_57),Z_15))))) # label(fact_770_order__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 818 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Z_2))))) # label(fact_771_order__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 819 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Z_2))))) # label(fact_772_order__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 820 (all Z_15 all X_57 all Y_44 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_57),Y_44)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_44),Z_15)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_57),Z_15))))) # label(fact_773_order__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 821 (all Z_15 all X_57 all Y_44 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_57),Y_44)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_44),Z_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_57),Z_15))))) # label(fact_774_order__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 822 (all Z_15 all X_57 all Y_44 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_57),Y_44)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_44),Z_15)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_57),Z_15))))) # label(fact_775_order__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 823 (all Z_15 all X_57 all Y_44 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_57),Y_44)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_44),Z_15)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_57),Z_15))))) # label(fact_776_order__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 824 (all Y_43 all X_56 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_43),X_56)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_56),Y_43)) -> X_56 = Y_43))) # label(fact_777_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 825 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) -> X_1 = Y_2))) # label(fact_778_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 826 (all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) -> X_1 = Y_2))) # label(fact_779_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 827 (all Y_43 all X_56 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_43),X_56)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_56),Y_43)) -> X_56 = Y_43))) # label(fact_780_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 828 (all Y_43 all X_56 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_43),X_56)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_56),Y_43)) -> X_56 = Y_43))) # label(fact_781_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 829 (all Y_43 all X_56 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_43),X_56)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_56),Y_43)) -> X_56 = Y_43))) # label(fact_782_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 830 (all Y_43 all X_56 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_43),X_56)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_56),Y_43)) -> X_56 = Y_43))) # label(fact_783_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 831 (all Z_14 all Y_42 all X_55 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_42),X_55)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Z_14),Y_42)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Z_14),X_55))))) # label(fact_784_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 832 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),X_1))))) # label(fact_785_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 833 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_1))))) # label(fact_786_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 834 (all Z_14 all Y_42 all X_55 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_42),X_55)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Z_14),Y_42)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Z_14),X_55))))) # label(fact_787_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 835 (all Z_14 all Y_42 all X_55 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_42),X_55)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_14),Y_42)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_14),X_55))))) # label(fact_788_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 836 (all Z_14 all Y_42 all X_55 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_42),X_55)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_14),Y_42)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_14),X_55))))) # label(fact_789_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 837 (all Z_14 all Y_42 all X_55 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_42),X_55)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_14),Y_42)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_14),X_55))))) # label(fact_790_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 838 (all X_1 all F all G (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G,X_1))))) # label(fact_791_le__funE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 839 (all X_1 all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))))) # label(fact_792_le__funE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 840 (all X_54 all Y_41 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_54),Y_41)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_41),X_54)))) # label(fact_793_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 841 (all X_54 all Y_41 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_54),Y_41)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_41),X_54)))) # label(fact_794_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 842 (all X_54 all Y_41 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_54),Y_41)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_41),X_54)))) # label(fact_795_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 843 (all X_54 all Y_41 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_54),Y_41)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_41),X_54)))) # label(fact_796_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 844 (all X_54 all Y_41 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_54),Y_41)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_41),X_54)))) # label(fact_797_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 845 (all X_53 -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_53),X_53))) # label(fact_798_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 846 (all X_1 -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),X_1))) # label(fact_799_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 847 (all X_1 -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),X_1))) # label(fact_800_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 848 (all X_53 -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_53),X_53))) # label(fact_801_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 849 (all X_53 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_53),X_53))) # label(fact_802_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 850 (all X_53 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_53),X_53))) # label(fact_803_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 851 (all X_53 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_53),X_53))) # label(fact_804_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 852 (all X_1 all Y_2 (X_1 != Y_2 <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_2),X_1)))) # label(fact_805_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 853 (all X_1 all Y_2 (X_1 != Y_2 <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) | hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_2),X_1)))) # label(fact_806_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 854 (all X_1 all Y_2 (X_1 != Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)))) # label(fact_807_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 855 (all X_1 all Y_2 (X_1 != Y_2 <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)))) # label(fact_808_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 856 (all X_1 all Y_2 (X_1 != Y_2 <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_2),X_1)))) # label(fact_809_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 857 (all X_1 all Y_2 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_2),X_1)) | X_1 = Y_2)) # label(fact_810_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 858 (all X_1 all Y_2 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_2),X_1)) | X_1 = Y_2)) # label(fact_811_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 859 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)) | X_1 = Y_2)) # label(fact_812_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 860 (all X_1 all Y_2 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)) | X_1 = Y_2)) # label(fact_813_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 861 (all X_1 all Y_2 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_2),X_1)) | X_1 = Y_2)) # label(fact_814_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 862 (all X_52 all Y_40 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_52),Y_40)) | X_52 = Y_40 | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_40),X_52)))) # label(fact_815_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 863 (all X_52 all Y_40 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_52),Y_40)) | X_52 = Y_40 | hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_40),X_52)))) # label(fact_816_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 864 (all X_52 all Y_40 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_52),Y_40)) | X_52 = Y_40 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_40),X_52)))) # label(fact_817_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 865 (all X_52 all Y_40 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_52),Y_40)) | X_52 = Y_40 | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_40),X_52)))) # label(fact_818_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 866 (all X_52 all Y_40 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_52),Y_40)) | X_52 = Y_40 | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_40),X_52)))) # label(fact_819_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 867 (all Y_2 all X_1 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_2),X_1)) -> (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_820_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 868 (all Y_2 all X_1 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_2),X_1)) -> (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_821_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 869 (all Y_2 all X_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_822_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 870 (all Y_2 all X_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)) -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_823_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 871 (all Y_2 all X_1 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_2),X_1)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_824_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 872 (all X_51 all Y_39 (X_51 != Y_39 -> (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_51),Y_39)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_39),X_51))))) # label(fact_825_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 873 (all X_51 all Y_39 (X_51 != Y_39 -> (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_51),Y_39)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_39),X_51))))) # label(fact_826_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 874 (all X_51 all Y_39 (X_51 != Y_39 -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_51),Y_39)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_39),X_51))))) # label(fact_827_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 875 (all X_51 all Y_39 (X_51 != Y_39 -> (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_51),Y_39)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_39),X_51))))) # label(fact_828_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 876 (all X_51 all Y_39 (X_51 != Y_39 -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_51),Y_39)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_39),X_51))))) # label(fact_829_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 877 (all X_50 all Y_38 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_50),Y_38)) -> X_50 != Y_38)) # label(fact_830_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 878 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> X_1 != Y_2)) # label(fact_831_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 879 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> X_1 != Y_2)) # label(fact_832_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 880 (all X_50 all Y_38 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_50),Y_38)) -> X_50 != Y_38)) # label(fact_833_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 881 (all X_50 all Y_38 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_50),Y_38)) -> X_50 != Y_38)) # label(fact_834_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 882 (all X_50 all Y_38 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_50),Y_38)) -> X_50 != Y_38)) # label(fact_835_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 883 (all X_50 all Y_38 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_50),Y_38)) -> X_50 != Y_38)) # label(fact_836_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 884 (all X_49 all Y_37 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_49),Y_37)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_37),X_49)))) # label(fact_837_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 885 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),X_1)))) # label(fact_838_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 886 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_1)))) # label(fact_839_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 887 (all X_49 all Y_37 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_49),Y_37)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_37),X_49)))) # label(fact_840_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 888 (all X_49 all Y_37 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_49),Y_37)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_37),X_49)))) # label(fact_841_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 889 (all X_49 all Y_37 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_49),Y_37)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_37),X_49)))) # label(fact_842_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 890 (all X_49 all Y_37 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_49),Y_37)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_37),X_49)))) # label(fact_843_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 891 (all X_48 all Y_36 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_48),Y_36)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_36),X_48)))) # label(fact_844_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 892 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),X_1)))) # label(fact_845_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 893 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_1)))) # label(fact_846_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 894 (all X_48 all Y_36 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_48),Y_36)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_36),X_48)))) # label(fact_847_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 895 (all X_48 all Y_36 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_48),Y_36)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_36),X_48)))) # label(fact_848_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 896 (all X_48 all Y_36 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_48),Y_36)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_36),X_48)))) # label(fact_849_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 897 (all X_48 all Y_36 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_48),Y_36)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_36),X_48)))) # label(fact_850_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 898 (all X_47 all Y_35 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_47),Y_35)) -> X_47 != Y_35)) # label(fact_851_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 899 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> X_1 != Y_2)) # label(fact_852_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 900 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> X_1 != Y_2)) # label(fact_853_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 901 (all X_47 all Y_35 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_47),Y_35)) -> X_47 != Y_35)) # label(fact_854_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 902 (all X_47 all Y_35 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_47),Y_35)) -> X_47 != Y_35)) # label(fact_855_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 903 (all X_47 all Y_35 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_47),Y_35)) -> X_47 != Y_35)) # label(fact_856_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 904 (all X_47 all Y_35 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_47),Y_35)) -> X_47 != Y_35)) # label(fact_857_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 905 (all X_46 all Y_34 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_46),Y_34)) -> Y_34 != X_46)) # label(fact_858_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 906 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> Y_2 != X_1)) # label(fact_859_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 907 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> Y_2 != X_1)) # label(fact_860_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 908 (all X_46 all Y_34 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_46),Y_34)) -> Y_34 != X_46)) # label(fact_861_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 909 (all X_46 all Y_34 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_46),Y_34)) -> Y_34 != X_46)) # label(fact_862_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 910 (all X_46 all Y_34 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_46),Y_34)) -> Y_34 != X_46)) # label(fact_863_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 911 (all X_46 all Y_34 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_46),Y_34)) -> Y_34 != X_46)) # label(fact_864_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 912 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_865_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 913 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_866_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 914 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_867_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 915 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_868_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 916 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_869_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 917 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_870_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 918 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_871_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 919 (all A_190 all B_145 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_190),B_145)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_145),A_190)))) # label(fact_872_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 920 (all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Aa),Ba)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Ba),Aa)))) # label(fact_873_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 921 (all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)))) # label(fact_874_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 922 (all A_190 all B_145 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_190),B_145)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_145),A_190)))) # label(fact_875_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 923 (all A_190 all B_145 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_190),B_145)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_145),A_190)))) # label(fact_876_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 924 (all A_190 all B_145 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_190),B_145)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_145),A_190)))) # label(fact_877_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 925 (all A_190 all B_145 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_190),B_145)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_145),A_190)))) # label(fact_878_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 926 (all B_144 all A_189 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_144),A_189)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_189),B_144)))) # label(fact_879_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 927 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Ba),Aa)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Aa),Ba)))) # label(fact_880_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 928 (all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)))) # label(fact_881_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 929 (all B_144 all A_189 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_144),A_189)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_189),B_144)))) # label(fact_882_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 930 (all B_144 all A_189 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_144),A_189)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_189),B_144)))) # label(fact_883_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 931 (all B_144 all A_189 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_144),A_189)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_189),B_144)))) # label(fact_884_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 932 (all B_144 all A_189 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_144),A_189)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_189),B_144)))) # label(fact_885_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 933 (all C_67 all A_188 all B_143 (A_188 = B_143 -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_143),C_67)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_188),C_67))))) # label(fact_886_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 934 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Ba),C)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Aa),C))))) # label(fact_887_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 935 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),C)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),C))))) # label(fact_888_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 936 (all C_67 all A_188 all B_143 (A_188 = B_143 -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_143),C_67)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_188),C_67))))) # label(fact_889_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 937 (all C_67 all A_188 all B_143 (A_188 = B_143 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_143),C_67)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_188),C_67))))) # label(fact_890_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 938 (all C_67 all A_188 all B_143 (A_188 = B_143 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_143),C_67)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_188),C_67))))) # label(fact_891_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 939 (all C_67 all A_188 all B_143 (A_188 = B_143 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_143),C_67)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_188),C_67))))) # label(fact_892_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 940 (all C_66 all A_187 all B_142 (A_187 = B_142 -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_66),B_142)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_66),A_187))))) # label(fact_893_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 941 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,C),Ba)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,C),Aa))))) # label(fact_894_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 942 (all C all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,C),Ba)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,C),Aa))))) # label(fact_895_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 943 (all C_66 all A_187 all B_142 (A_187 = B_142 -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_66),B_142)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_66),A_187))))) # label(fact_896_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 944 (all C_66 all A_187 all B_142 (A_187 = B_142 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_66),B_142)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_66),A_187))))) # label(fact_897_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 945 (all C_66 all A_187 all B_142 (A_187 = B_142 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_66),B_142)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_66),A_187))))) # label(fact_898_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 946 (all C_66 all A_187 all B_142 (A_187 = B_142 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_66),B_142)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_66),A_187))))) # label(fact_899_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 947 (all C_65 all A_186 all B_141 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_186),B_141)) -> (B_141 = C_65 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_186),C_65))))) # label(fact_900_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 948 (all C all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Aa),Ba)) -> (Ba = C -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Aa),C))))) # label(fact_901_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 949 (all C all Aa all Ba (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) -> (Ba = C -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),C))))) # label(fact_902_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 950 (all C_65 all A_186 all B_141 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_186),B_141)) -> (B_141 = C_65 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_186),C_65))))) # label(fact_903_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 951 (all C_65 all A_186 all B_141 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_186),B_141)) -> (B_141 = C_65 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_186),C_65))))) # label(fact_904_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 952 (all C_65 all A_186 all B_141 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_186),B_141)) -> (B_141 = C_65 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_186),C_65))))) # label(fact_905_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 953 (all C_65 all A_186 all B_141 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_186),B_141)) -> (B_141 = C_65 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_186),C_65))))) # label(fact_906_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 954 (all C_64 all B_140 all A_185 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_140),A_185)) -> (B_140 = C_64 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_64),A_185))))) # label(fact_907_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 955 (all C all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Ba),Aa)) -> (Ba = C -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,C),Aa))))) # label(fact_908_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 956 (all C all Ba all Aa (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) -> (Ba = C -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,C),Aa))))) # label(fact_909_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 957 (all C_64 all B_140 all A_185 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_140),A_185)) -> (B_140 = C_64 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_64),A_185))))) # label(fact_910_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 958 (all C_64 all B_140 all A_185 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_140),A_185)) -> (B_140 = C_64 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_64),A_185))))) # label(fact_911_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 959 (all C_64 all B_140 all A_185 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_140),A_185)) -> (B_140 = C_64 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_64),A_185))))) # label(fact_912_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 960 (all C_64 all B_140 all A_185 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_140),A_185)) -> (B_140 = C_64 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_64),A_185))))) # label(fact_913_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 961 (all Z_13 all X_45 all Y_33 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_45),Y_33)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_33),Z_13)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_45),Z_13))))) # label(fact_914_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 962 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Z_2))))) # label(fact_915_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 963 (all Z_2 all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Z_2))))) # label(fact_916_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 964 (all Z_13 all X_45 all Y_33 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_45),Y_33)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_33),Z_13)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_45),Z_13))))) # label(fact_917_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 965 (all Z_13 all X_45 all Y_33 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_45),Y_33)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_33),Z_13)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_45),Z_13))))) # label(fact_918_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 966 (all Z_13 all X_45 all Y_33 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_45),Y_33)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_33),Z_13)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_45),Z_13))))) # label(fact_919_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 967 (all Z_13 all X_45 all Y_33 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_45),Y_33)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_33),Z_13)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_45),Z_13))))) # label(fact_920_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 968 (all Z_12 all Y_32 all X_44 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_32),X_44)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z_12),Y_32)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z_12),X_44))))) # label(fact_921_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 969 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Z_2),X_1))))) # label(fact_922_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 970 (all Z_2 all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_1))))) # label(fact_923_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 971 (all Z_12 all Y_32 all X_44 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_32),X_44)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Z_12),Y_32)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Z_12),X_44))))) # label(fact_924_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 972 (all Z_12 all Y_32 all X_44 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_32),X_44)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_12),Y_32)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_12),X_44))))) # label(fact_925_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 973 (all Z_12 all Y_32 all X_44 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_32),X_44)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_12),Y_32)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_12),X_44))))) # label(fact_926_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 974 (all Z_12 all Y_32 all X_44 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_32),X_44)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_12),Y_32)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_12),X_44))))) # label(fact_927_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 975 (all X_43 all Y_31 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_43),Y_31)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_31),X_43)))) # label(fact_928_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 976 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),X_1)))) # label(fact_929_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 977 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_1)))) # label(fact_930_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 978 (all X_43 all Y_31 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_43),Y_31)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_31),X_43)))) # label(fact_931_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 979 (all X_43 all Y_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_43),Y_31)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_31),X_43)))) # label(fact_932_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 980 (all X_43 all Y_31 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_43),Y_31)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_31),X_43)))) # label(fact_933_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 981 (all X_43 all Y_31 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_43),Y_31)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_31),X_43)))) # label(fact_934_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 982 (all X_42 all Y_30 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_42),Y_30)) -> (X_42 != Y_30 -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_30),X_42))))) # label(fact_935_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 983 (all X_42 all Y_30 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_42),Y_30)) -> (X_42 != Y_30 -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_30),X_42))))) # label(fact_936_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 984 (all X_42 all Y_30 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_42),Y_30)) -> (X_42 != Y_30 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_30),X_42))))) # label(fact_937_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 985 (all X_42 all Y_30 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_42),Y_30)) -> (X_42 != Y_30 -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_30),X_42))))) # label(fact_938_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 986 (all X_42 all Y_30 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_42),Y_30)) -> (X_42 != Y_30 -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_30),X_42))))) # label(fact_939_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 987 (all X_1 all Y_2 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_2),X_1)))) # label(fact_940_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 988 (all X_1 all Y_2 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_2),X_1)))) # label(fact_941_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 989 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)))) # label(fact_942_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 990 (all X_1 all Y_2 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),X_1)))) # label(fact_943_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 991 (all X_1 all Y_2 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_2),X_1)))) # label(fact_944_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 992 (all X_1 all Y_2 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_2),X_1)))) # label(fact_945_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 993 (all X_1 all Y_2 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_2),X_1)))) # label(fact_946_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 994 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)))) # label(fact_947_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 995 (all X_1 all Y_2 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)))) # label(fact_948_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 996 (all X_1 all Y_2 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_2),X_1)))) # label(fact_949_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 997 (all X_41 all Y_29 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_41),Y_29)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_29),X_41)))) # label(fact_950_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 998 (all X_41 all Y_29 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_41),Y_29)) | hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Y_29),X_41)))) # label(fact_951_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 999 (all X_41 all Y_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_41),Y_29)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_29),X_41)))) # label(fact_952_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1000 (all X_41 all Y_29 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_41),Y_29)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_29),X_41)))) # label(fact_953_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1001 (all X_41 all Y_29 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_41),Y_29)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_29),X_41)))) # label(fact_954_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1002 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) & X_1 != Y_2)) # label(fact_955_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1003 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) & X_1 != Y_2)) # label(fact_956_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1004 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) & X_1 != Y_2)) # label(fact_957_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1005 (all X_1 all Y_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) & X_1 != Y_2)) # label(fact_958_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1006 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & X_1 != Y_2)) # label(fact_959_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1007 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) & X_1 != Y_2)) # label(fact_960_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1008 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) & X_1 != Y_2)) # label(fact_961_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1009 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) & -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_2),X_1)))) # label(fact_962_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1010 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) & -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)))) # label(fact_963_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1011 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)))) # label(fact_964_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1012 (all X_1 all Y_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) & -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_2),X_1)))) # label(fact_965_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1013 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)))) # label(fact_966_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1014 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) & -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),X_1)))) # label(fact_967_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1015 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) & -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_2),X_1)))) # label(fact_968_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1016 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) | X_1 = Y_2)) # label(fact_969_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1017 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),Y_2)) | X_1 = Y_2)) # label(fact_970_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1018 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_2)) | X_1 = Y_2)) # label(fact_971_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1019 (all X_1 all Y_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) <-> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) | X_1 = Y_2)) # label(fact_972_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1020 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) | X_1 = Y_2)) # label(fact_973_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1021 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) | X_1 = Y_2)) # label(fact_974_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1022 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) | X_1 = Y_2)) # label(fact_975_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1023 (all X_40 all Y_28 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_40),Y_28)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_28),X_40)))) # label(fact_976_leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1024 (all X_40 all Y_28 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_40),Y_28)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_28),X_40)))) # label(fact_977_leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1025 (all X_40 all Y_28 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_40),Y_28)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_28),X_40)))) # label(fact_978_leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1026 (all X_40 all Y_28 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_40),Y_28)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_28),X_40)))) # label(fact_979_leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1027 (all X_40 all Y_28 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_40),Y_28)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_28),X_40)))) # label(fact_980_leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1028 (all Y_27 all X_39 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_27),X_39)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_39),Y_27)))) # label(fact_981_not__leE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1029 (all Y_27 all X_39 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,Y_27),X_39)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_39),Y_27)))) # label(fact_982_not__leE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1030 (all Y_27 all X_39 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_27),X_39)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_39),Y_27)))) # label(fact_983_not__leE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1031 (all Y_27 all X_39 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_27),X_39)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_39),Y_27)))) # label(fact_984_not__leE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1032 (all Y_27 all X_39 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_27),X_39)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_39),Y_27)))) # label(fact_985_not__leE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1033 (all X_1 all Y_2 (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_986_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1034 (all X_1 all Y_2 (-hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_1),Y_2)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_987_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1035 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_988_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1036 (all X_1 all Y_2 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_989_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1037 (all X_1 all Y_2 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_990_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1038 (all A_184 all B_139 (A_184 != B_139 -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_184),B_139)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_184),B_139))))) # label(fact_991_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1039 (all Aa all Ba (Aa != Ba -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Aa),Ba)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Aa),Ba))))) # label(fact_992_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1040 (all Aa all Ba (Aa != Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))))) # label(fact_993_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1041 (all A_184 all B_139 (A_184 != B_139 -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_184),B_139)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_184),B_139))))) # label(fact_994_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1042 (all A_184 all B_139 (A_184 != B_139 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_184),B_139)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_184),B_139))))) # label(fact_995_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1043 (all A_184 all B_139 (A_184 != B_139 -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_184),B_139)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_184),B_139))))) # label(fact_996_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1044 (all A_184 all B_139 (A_184 != B_139 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_184),B_139)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_184),B_139))))) # label(fact_997_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1045 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_1),one_one_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_1)))) # label(fact_998_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1046 (all P_1 all I_1 all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1)) -> (hBOOL(hAPP_int_bool(P_1,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K_1)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_999_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1047 (all P_1 all I_1 all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),K_1)) -> (hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_1),one_one_int))) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K_1)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_1000_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1048 (all P_1 all K_1 all I_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_1)) -> (hBOOL(hAPP_int_bool(P_1,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_1001_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1049 (all P_1 all K_1 all I_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),I_1)) -> (hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),one_one_int))) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_1002_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1050 (all Z_11 all Y_26 ((all X_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_2),Y_26)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_2),Z_11)))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_26),Z_11)))) # label(fact_1003_dense__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1051 (all Z_11 all Y_26 ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_26)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Z_11)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_26),Z_11)))) # label(fact_1004_dense__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1052 (all Z_10 all X_38 all Y_25 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_38),Y_25)) -> ((all W_8 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_38),W_8)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,W_8),Y_25)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,W_8),Z_10))))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_25),Z_10))))) # label(fact_1005_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1053 (all Z_10 all X_38 all Y_25 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_38),Y_25)) -> ((all W_8 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_38),W_8)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,W_8),Y_25)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W_8),Z_10))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_25),Z_10))))) # label(fact_1006_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1054 (all F all G (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,F),G)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)) & -hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,G),F)))) # label(fact_1007_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1055 (all F all G (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) & -hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F)))) # label(fact_1008_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1056 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G,X_2)))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G)))) # label(fact_1009_le__funI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1057 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)))) # label(fact_1010_le__funI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1058 (all I_1 all P_1 all K_1 (hBOOL(hAPP_int_bool(P_1,K_1)) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_2)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)))))) -> ((all I_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K_1)) -> (hBOOL(hAPP_int_bool(P_1,I_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I_2),one_one_int)))))) -> hBOOL(hAPP_int_bool(P_1,I_1)))))) # label(fact_1011_int__induct) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1059 (all B_1 all A_2 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),C_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),A_2))))) # label(fact_1012_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1060 (all X_1 all P_1 ((all A_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_1)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_1),one_one_int)))) -> hBOOL(hAPP_int_bool(P_1,A_1)))) -> hBOOL(hAPP_int_bool(P_1,X_1)))) # label(fact_1013_d22set__induct__old) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1061 (all V_13 all U_3 all Y_24 all X_37 all A_183 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_37),A_183)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Y_24),A_183)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),U_3)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),V_13)) -> (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,U_3),V_13) = one_one_rat -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,U_3),X_37)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,V_13),Y_24))),A_183)))))))) # label(fact_1014_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1062 (all V_13 all U_3 all Y_24 all X_37 all A_183 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_37),A_183)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_24),A_183)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_3)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),V_13)) -> (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,U_3),V_13) = one_one_real -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,U_3),X_37)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,V_13),Y_24))),A_183)))))))) # label(fact_1015_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1063 (all V_13 all U_3 all Y_24 all X_37 all A_183 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_37),A_183)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_24),A_183)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_13)) -> (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3),V_13) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3),X_37)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_13),Y_24))),A_183)))))))) # label(fact_1016_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1064 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,V)),archim1419379755ng_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_int_rat(number_number_of_rat,V)),one_one_rat)),X_1)))) # label(fact_1017_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1065 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,V)),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(number267125858f_real,V)),one_one_real)),X_1)))) # label(fact_1018_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1066 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1419379755ng_rat(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_int_rat(number_number_of_rat,V)),one_one_rat))))) # label(fact_1019_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1067 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(number267125858f_real,V)),one_one_real))))) # label(fact_1020_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1068 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),archim1419379755ng_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),X_1)))) # label(fact_1021_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1069 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)))) # label(fact_1022_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1070 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1419379755ng_rat(X_1)),zero_zero_int)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),zero_zero_rat)))) # label(fact_1023_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1071 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X_1)),zero_zero_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real)))) # label(fact_1024_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1072 (all X_1 (zero_zero_rat = X_1 <-> X_1 = zero_zero_rat)) # label(fact_1027_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1073 (all X_1 (zero_z891286103de_int = X_1 <-> X_1 = zero_z891286103de_int)) # label(fact_1028_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1074 (all X_1 (zero_zero_complex = X_1 <-> X_1 = zero_zero_complex)) # label(fact_1029_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1075 (all X_1 (zero_z126310315umeral = X_1 <-> X_1 = zero_z126310315umeral)) # label(fact_1030_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1076 (all X_1 (zero_zero_nat = X_1 <-> X_1 = zero_zero_nat)) # label(fact_1031_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1077 (all X_1 (zero_zero_real = X_1 <-> X_1 = zero_zero_real)) # label(fact_1032_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1078 (all X_1 (zero_zero_int = X_1 <-> X_1 = zero_zero_int)) # label(fact_1033_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1079 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1419379755ng_rat(X_1)),one_one_int)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),zero_zero_rat)))) # label(fact_1034_ceiling__less__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1080 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_1)),one_one_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real)))) # label(fact_1035_ceiling__less__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1081 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),archim1419379755ng_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),X_1)))) # label(fact_1036_one__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1082 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)))) # label(fact_1037_one__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1083 (all A_182 all B_138 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_182),B_138) = zero_zero_rat -> A_182 = zero_zero_rat | B_138 = zero_zero_rat)) # label(fact_1038_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1084 (all A_182 all B_138 (hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_182),B_138) = zero_z891286103de_int -> A_182 = zero_z891286103de_int | B_138 = zero_z891286103de_int)) # label(fact_1039_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1085 (all A_182 all B_138 (hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_182),B_138) = zero_zero_complex -> A_182 = zero_zero_complex | B_138 = zero_zero_complex)) # label(fact_1040_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1086 (all A_182 all B_138 (hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_182),B_138) = zero_z126310315umeral -> A_182 = zero_z126310315umeral | B_138 = zero_z126310315umeral)) # label(fact_1041_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1087 (all A_182 all B_138 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_182),B_138) = zero_zero_nat -> A_182 = zero_zero_nat | B_138 = zero_zero_nat)) # label(fact_1042_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1088 (all A_182 all B_138 (hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_182),B_138) = zero_zero_real -> A_182 = zero_zero_real | B_138 = zero_zero_real)) # label(fact_1043_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1089 (all A_182 all B_138 (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_182),B_138) = zero_zero_int -> A_182 = zero_zero_int | B_138 = zero_zero_int)) # label(fact_1044_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1090 (all B_137 all A_181 (A_181 != zero_zero_rat -> (B_137 != zero_zero_rat -> hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_181),B_137) != zero_zero_rat))) # label(fact_1045_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1091 (all B_137 all A_181 (A_181 != zero_z891286103de_int -> (B_137 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_181),B_137) != zero_z891286103de_int))) # label(fact_1046_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1092 (all B_137 all A_181 (A_181 != zero_zero_complex -> (B_137 != zero_zero_complex -> hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_181),B_137) != zero_zero_complex))) # label(fact_1047_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.69 1093 (all B_137 all A_181 (A_181 != zero_z126310315umeral -> (B_137 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_181),B_137) != zero_z126310315umeral))) # label(fact_1048_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1094 (all B_137 all A_181 (A_181 != zero_zero_nat -> (B_137 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_181),B_137) != zero_zero_nat))) # label(fact_1049_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1095 (all B_137 all A_181 (A_181 != zero_zero_real -> (B_137 != zero_zero_real -> hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_181),B_137) != zero_zero_real))) # label(fact_1050_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1096 (all B_137 all A_181 (A_181 != zero_zero_int -> (B_137 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_181),B_137) != zero_zero_int))) # label(fact_1051_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1097 (all Aa all Ba (hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),Ba) = zero_zero_rat <-> Aa = zero_zero_rat | Ba = zero_zero_rat)) # label(fact_1052_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1098 (all Aa all Ba (hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Aa),Ba) = zero_zero_complex <-> Aa = zero_zero_complex | Ba = zero_zero_complex)) # label(fact_1053_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1099 (all Aa all Ba (hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),Ba) = zero_zero_real <-> Aa = zero_zero_real | Ba = zero_zero_real)) # label(fact_1054_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1100 (all Aa all Ba (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),Ba) = zero_zero_int <-> Aa = zero_zero_int | Ba = zero_zero_int)) # label(fact_1055_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1101 (all X_36 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_36),zero_zero_complex) = zero_zero_complex) # label(fact_1056_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1102 (all X_36 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_36),zero_zero_real) = zero_zero_real) # label(fact_1057_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1103 (all A_180 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_180),zero_zero_complex) = zero_zero_complex) # label(fact_1058_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1104 (all A_180 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_180),zero_zero_real) = zero_zero_real) # label(fact_1059_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1105 (all A_179 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_179),zero_zero_rat) = zero_zero_rat) # label(fact_1060_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1106 (all A_179 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_179),zero_z891286103de_int) = zero_z891286103de_int) # label(fact_1061_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1107 (all A_179 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_179),zero_zero_complex) = zero_zero_complex) # label(fact_1062_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1108 (all A_179 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_179),zero_z126310315umeral) = zero_z126310315umeral) # label(fact_1063_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1109 (all A_179 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_179),zero_zero_nat) = zero_zero_nat) # label(fact_1064_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1110 (all A_179 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_179),zero_zero_real) = zero_zero_real) # label(fact_1065_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1111 (all A_179 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_179),zero_zero_int) = zero_zero_int) # label(fact_1066_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1112 (all Y_23 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,zero_zero_complex),Y_23) = zero_zero_complex) # label(fact_1067_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1113 (all Y_23 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,zero_zero_real),Y_23) = zero_zero_real) # label(fact_1068_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1114 (all B_136 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,zero_zero_complex),B_136) = zero_zero_complex) # label(fact_1069_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1115 (all B_136 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,zero_zero_real),B_136) = zero_zero_real) # label(fact_1070_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1116 (all A_178 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,zero_zero_rat),A_178) = zero_zero_rat) # label(fact_1071_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1117 (all A_178 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,zero_z891286103de_int),A_178) = zero_z891286103de_int) # label(fact_1072_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1118 (all A_178 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,zero_zero_complex),A_178) = zero_zero_complex) # label(fact_1073_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1119 (all A_178 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,zero_z126310315umeral),A_178) = zero_z126310315umeral) # label(fact_1074_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1120 (all A_178 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),A_178) = zero_zero_nat) # label(fact_1075_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1121 (all A_178 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,zero_zero_real),A_178) = zero_zero_real) # label(fact_1076_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1122 (all A_178 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,zero_zero_int),A_178) = zero_zero_int) # label(fact_1077_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1123 (all A_177 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_177),zero_zero_rat) = zero_zero_rat) # label(fact_1078_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1124 (all A_177 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_177),zero_z891286103de_int) = zero_z891286103de_int) # label(fact_1079_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1125 (all A_177 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_177),zero_zero_complex) = zero_zero_complex) # label(fact_1080_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1126 (all A_177 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_177),zero_z126310315umeral) = zero_z126310315umeral) # label(fact_1081_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1127 (all A_177 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_177),zero_zero_nat) = zero_zero_nat) # label(fact_1082_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1128 (all A_177 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_177),zero_zero_real) = zero_zero_real) # label(fact_1083_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1129 (all A_177 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_177),zero_zero_int) = zero_zero_int) # label(fact_1084_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1130 (all A_176 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,zero_zero_rat),A_176) = zero_zero_rat) # label(fact_1085_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1131 (all A_176 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,zero_z891286103de_int),A_176) = zero_z891286103de_int) # label(fact_1086_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1132 (all A_176 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,zero_zero_complex),A_176) = zero_zero_complex) # label(fact_1087_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1133 (all A_176 hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,zero_z126310315umeral),A_176) = zero_z126310315umeral) # label(fact_1088_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1134 (all A_176 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),A_176) = zero_zero_nat) # label(fact_1089_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1135 (all A_176 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,zero_zero_real),A_176) = zero_zero_real) # label(fact_1090_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1136 (all A_176 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,zero_zero_int),A_176) = zero_zero_int) # label(fact_1091_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1137 (all Aa (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa) = zero_zero_rat <-> Aa = zero_zero_rat)) # label(fact_1092_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1138 (all Aa (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa) = zero_zero_real <-> Aa = zero_zero_real)) # label(fact_1093_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1139 (all Aa (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa) = zero_zero_int <-> Aa = zero_zero_int)) # label(fact_1094_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1140 (all A_175 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_175),zero_zero_rat) = A_175) # label(fact_1095_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1141 (all A_175 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_175),zero_z891286103de_int) = A_175) # label(fact_1096_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1142 (all A_175 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_175),zero_zero_complex) = A_175) # label(fact_1097_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1143 (all A_175 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_175),zero_zero_nat) = A_175) # label(fact_1098_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1144 (all A_175 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_175),zero_zero_real) = A_175) # label(fact_1099_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1145 (all A_175 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_175),zero_zero_int) = A_175) # label(fact_1100_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1146 (all A_175 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_175),zero_z126310315umeral) = A_175) # label(fact_1101_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1147 (all A_174 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_174),zero_zero_rat) = A_174) # label(fact_1102_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1148 (all A_174 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_174),zero_z891286103de_int) = A_174) # label(fact_1103_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1149 (all A_174 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_174),zero_zero_complex) = A_174) # label(fact_1104_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1150 (all A_174 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_174),zero_zero_nat) = A_174) # label(fact_1105_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1151 (all A_174 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_174),zero_zero_real) = A_174) # label(fact_1106_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1152 (all A_174 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_174),zero_zero_int) = A_174) # label(fact_1107_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1153 (all A_174 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_174),zero_z126310315umeral) = A_174) # label(fact_1108_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1154 (all Aa (zero_zero_rat = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa) <-> Aa = zero_zero_rat)) # label(fact_1109_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1155 (all Aa (zero_zero_real = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa) <-> Aa = zero_zero_real)) # label(fact_1110_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1156 (all Aa (zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa) <-> Aa = zero_zero_int)) # label(fact_1111_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1157 (all A_173 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,zero_zero_rat),A_173) = A_173) # label(fact_1112_add__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1158 (all A_173 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,zero_z891286103de_int),A_173) = A_173) # label(fact_1113_add__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1159 (all A_173 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,zero_zero_complex),A_173) = A_173) # label(fact_1114_add__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1160 (all A_173 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_173) = A_173) # label(fact_1115_add__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1161 (all A_173 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,zero_zero_real),A_173) = A_173) # label(fact_1116_add__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1162 (all A_173 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),A_173) = A_173) # label(fact_1117_add__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1163 (all A_173 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,zero_z126310315umeral),A_173) = A_173) # label(fact_1118_add__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1164 (all A_172 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,zero_zero_rat),A_172) = A_172) # label(fact_1119_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1165 (all A_172 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,zero_z891286103de_int),A_172) = A_172) # label(fact_1120_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1166 (all A_172 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,zero_zero_complex),A_172) = A_172) # label(fact_1121_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1167 (all A_172 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_172) = A_172) # label(fact_1122_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1168 (all A_172 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,zero_zero_real),A_172) = A_172) # label(fact_1123_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1169 (all A_172 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),A_172) = A_172) # label(fact_1124_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1170 (all A_172 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,zero_z126310315umeral),A_172) = A_172) # label(fact_1125_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1171 (all Ba all Aa (Ba = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Ba),Aa) <-> Aa = zero_zero_rat)) # label(fact_1126_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1172 (all Ba all Aa (Ba = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Ba),Aa) <-> Aa = zero_zero_complex)) # label(fact_1127_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1173 (all Ba all Aa (Ba = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) <-> Aa = zero_zero_nat)) # label(fact_1128_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1174 (all Ba all Aa (Ba = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Ba),Aa) <-> Aa = zero_zero_real)) # label(fact_1129_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1175 (all Ba all Aa (Ba = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),Aa) <-> Aa = zero_zero_int)) # label(fact_1130_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1176 (all A_171 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_171),zero_zero_rat) = A_171) # label(fact_1131_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1177 (all A_171 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_171),zero_z891286103de_int) = A_171) # label(fact_1132_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1178 (all A_171 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_171),zero_zero_complex) = A_171) # label(fact_1133_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1179 (all A_171 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_171),zero_zero_nat) = A_171) # label(fact_1134_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1180 (all A_171 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_171),zero_zero_real) = A_171) # label(fact_1135_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1181 (all A_171 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_171),zero_zero_int) = A_171) # label(fact_1136_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1182 (all A_171 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_171),zero_z126310315umeral) = A_171) # label(fact_1137_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1183 (all A_170 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,zero_zero_rat),A_170) = A_170) # label(fact_1138_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1184 (all A_170 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,zero_z891286103de_int),A_170) = A_170) # label(fact_1139_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1185 (all A_170 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,zero_zero_complex),A_170) = A_170) # label(fact_1140_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1186 (all A_170 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_170) = A_170) # label(fact_1141_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1187 (all A_170 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,zero_zero_real),A_170) = A_170) # label(fact_1142_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1188 (all A_170 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),A_170) = A_170) # label(fact_1143_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1189 (all A_170 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,zero_z126310315umeral),A_170) = A_170) # label(fact_1144_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1190 (all Aa all Ba (hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba) = zero_zero_rat <-> Aa = Ba)) # label(fact_1159_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1191 (all Aa all Ba (hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Aa),Ba) = zero_zero_complex <-> Aa = Ba)) # label(fact_1160_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1192 (all Aa all Ba (hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba) = zero_zero_real <-> Aa = Ba)) # label(fact_1161_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1193 (all Aa all Ba (hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = zero_zero_int <-> Aa = Ba)) # label(fact_1162_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1194 (all Aa all Ba (Aa = Ba <-> hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba) = zero_zero_rat)) # label(fact_1163_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1195 (all Aa all Ba (Aa = Ba <-> hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Aa),Ba) = zero_zero_complex)) # label(fact_1164_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1196 (all Aa all Ba (Aa = Ba <-> hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba) = zero_zero_real)) # label(fact_1165_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1197 (all Aa all Ba (Aa = Ba <-> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = zero_zero_int)) # label(fact_1166_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1198 (all A_169 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_169),A_169) = zero_zero_rat) # label(fact_1167_diff__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1199 (all A_169 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_169),A_169) = zero_zero_complex) # label(fact_1168_diff__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1200 (all A_169 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_169),A_169) = zero_zero_real) # label(fact_1169_diff__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1201 (all A_169 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_169),A_169) = zero_zero_int) # label(fact_1170_diff__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1202 (all A_168 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_168),zero_zero_rat) = A_168) # label(fact_1171_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1203 (all A_168 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_168),zero_zero_complex) = A_168) # label(fact_1172_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1204 (all A_168 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_168),zero_zero_real) = A_168) # label(fact_1173_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1205 (all A_168 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_168),zero_zero_int) = A_168) # label(fact_1174_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1206 (all Z_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),zero_zero_int) = Z_1) # label(fact_1176_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1207 (all Z_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),Z_1) = Z_1) # label(fact_1177_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1208 (all X_35 all Y_22 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1419379755ng_rat(X_35)),archim1419379755ng_rat(Y_22))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_35),Y_22)))) # label(fact_1178_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1209 (all X_35 all Y_22 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_35)),archim856651990g_real(Y_22))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_35),Y_22)))) # label(fact_1179_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1210 (all Y_21 all X_34 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_21),X_34)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(Y_21)),archim856651990g_real(X_34))))) # label(fact_1180_ceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1211 (all Y_21 all X_34 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_21),X_34)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1419379755ng_rat(Y_21)),archim1419379755ng_rat(X_34))))) # label(fact_1181_ceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1212 (all V_12 archim856651990g_real(hAPP_int_real(number267125858f_real,V_12)) = hAPP_int_int(number_number_of_int,V_12)) # label(fact_1184_ceiling__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1213 (all V_12 archim1419379755ng_rat(hAPP_int_rat(number_number_of_rat,V_12)) = hAPP_int_int(number_number_of_int,V_12)) # label(fact_1185_ceiling__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1214 (all A_167 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_167),A_167)))) # label(fact_1186_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1215 (all A_167 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_167),A_167)))) # label(fact_1187_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1216 (all A_167 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_167),A_167)))) # label(fact_1188_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1217 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Aa)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Ba)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),zero_zero_rat)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Ba),zero_zero_rat)))) # label(fact_1189_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1218 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Ba)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Ba),zero_zero_real)))) # label(fact_1190_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1219 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,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_1191_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1220 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),Ba)),zero_zero_rat)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Aa)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Ba),zero_zero_rat)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),zero_zero_rat)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Ba)))) # label(fact_1192_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1221 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),Ba)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Ba),zero_zero_real)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Ba)))) # label(fact_1193_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1222 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),Ba)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),zero_zero_int)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ba)))) # label(fact_1194_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1223 (all B_135 all A_166 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_166)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_135)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_166),B_135)))))) # label(fact_1195_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1224 (all B_135 all A_166 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_166)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),B_135)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_166),B_135)))))) # label(fact_1196_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1225 (all B_135 all A_166 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_166)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),B_135)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_166),B_135)))))) # label(fact_1197_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1226 (all B_135 all A_166 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_166)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_135)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_166),B_135)))))) # label(fact_1198_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1227 (all B_135 all A_166 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_166)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_135)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_166),B_135)))))) # label(fact_1199_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1228 (all B_135 all A_166 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_166)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_135)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_166),B_135)))))) # label(fact_1200_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1229 (all B_134 all A_165 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_165)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_134),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_165),B_134)),zero_zero_rat))))) # label(fact_1201_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1230 (all B_134 all A_165 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_165)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_134),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_165),B_134)),zero_z891286103de_int))))) # label(fact_1202_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1231 (all B_134 all A_165 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_165)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_134),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_165),B_134)),zero_z126310315umeral))))) # label(fact_1203_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1232 (all B_134 all A_165 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_165)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_134),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_165),B_134)),zero_zero_nat))))) # label(fact_1204_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1233 (all B_134 all A_165 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_165)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_134),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_165),B_134)),zero_zero_real))))) # label(fact_1205_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1234 (all B_134 all A_165 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_165)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_134),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_165),B_134)),zero_zero_int))))) # label(fact_1206_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1235 (all B_133 all A_164 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_164)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_133),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_133),A_164)),zero_zero_rat))))) # label(fact_1207_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1236 (all B_133 all A_164 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_164)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_133),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_133),A_164)),zero_z891286103de_int))))) # label(fact_1208_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1237 (all B_133 all A_164 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_164)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_133),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_133),A_164)),zero_z126310315umeral))))) # label(fact_1209_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1238 (all B_133 all A_164 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_164)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_133),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_133),A_164)),zero_zero_nat))))) # label(fact_1210_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1239 (all B_133 all A_164 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_164)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_133),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_133),A_164)),zero_zero_real))))) # label(fact_1211_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1240 (all B_133 all A_164 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_164)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_133),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_133),A_164)),zero_zero_int))))) # label(fact_1212_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1241 (all B_132 all A_163 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_163),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_132)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_163),B_132)),zero_zero_rat))))) # label(fact_1213_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1242 (all B_132 all A_163 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_163),zero_z891286103de_int)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),B_132)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_163),B_132)),zero_z891286103de_int))))) # label(fact_1214_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1243 (all B_132 all A_163 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_163),zero_z126310315umeral)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),B_132)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_163),B_132)),zero_z126310315umeral))))) # label(fact_1215_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1244 (all B_132 all A_163 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_163),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_132)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_163),B_132)),zero_zero_nat))))) # label(fact_1216_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1245 (all B_132 all A_163 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_163),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_132)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_163),B_132)),zero_zero_real))))) # label(fact_1217_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1246 (all B_132 all A_163 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_163),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_132)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_163),B_132)),zero_zero_int))))) # label(fact_1218_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1247 (all B_131 all A_162 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_162),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_131),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_162),B_131)))))) # label(fact_1219_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1248 (all B_131 all A_162 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_162),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_131),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_162),B_131)))))) # label(fact_1220_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1249 (all B_131 all A_162 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_162),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_131),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_162),B_131)))))) # label(fact_1221_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1250 (all C_63 all A_161 all B_130 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_161),B_130)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_63)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_161),C_63)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_130),C_63)))))) # label(fact_1222_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1251 (all C_63 all A_161 all B_130 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_161),B_130)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_63)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_161),C_63)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_130),C_63)))))) # label(fact_1223_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1252 (all C_63 all A_161 all B_130 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_161),B_130)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_63)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_161),C_63)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_130),C_63)))))) # label(fact_1224_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1253 (all C_63 all A_161 all B_130 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_161),B_130)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_63)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_161),C_63)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_130),C_63)))))) # label(fact_1225_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1254 (all C_63 all A_161 all B_130 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_161),B_130)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_63)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_161),C_63)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_130),C_63)))))) # label(fact_1226_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1255 (all C_63 all A_161 all B_130 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_161),B_130)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_63)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_161),C_63)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_130),C_63)))))) # label(fact_1227_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1256 (all C_62 all A_160 all B_129 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_160),B_129)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_62)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_62),A_160)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_62),B_129)))))) # label(fact_1228_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1257 (all C_62 all A_160 all B_129 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_160),B_129)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_62)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_62),A_160)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_62),B_129)))))) # label(fact_1229_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1258 (all C_62 all A_160 all B_129 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_160),B_129)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_62)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_62),A_160)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_62),B_129)))))) # label(fact_1230_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1259 (all C_62 all A_160 all B_129 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_160),B_129)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_62)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_62),A_160)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_62),B_129)))))) # label(fact_1231_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1260 (all C_62 all A_160 all B_129 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_160),B_129)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_62)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_62),A_160)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_62),B_129)))))) # label(fact_1232_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1261 (all C_62 all A_160 all B_129 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_160),B_129)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_62)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_62),A_160)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_62),B_129)))))) # label(fact_1233_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1262 (all C_61 all A_159 all B_128 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_159),B_128)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_61)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_61),A_159)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_61),B_128)))))) # label(fact_1234_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1263 (all C_61 all A_159 all B_128 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_159),B_128)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_61)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_61),A_159)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_61),B_128)))))) # label(fact_1235_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1264 (all C_61 all A_159 all B_128 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_159),B_128)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_61)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_61),A_159)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_61),B_128)))))) # label(fact_1236_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1265 (all C_61 all A_159 all B_128 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_159),B_128)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_61)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_61),A_159)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_61),B_128)))))) # label(fact_1237_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1266 (all C_61 all A_159 all B_128 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_159),B_128)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_61)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_61),A_159)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_61),B_128)))))) # label(fact_1238_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1267 (all C_61 all A_159 all B_128 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_159),B_128)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_61)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_61),A_159)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_61),B_128)))))) # label(fact_1239_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1268 (all C_60 all B_127 all A_158 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_127),A_158)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_60),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_158),C_60)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_127),C_60)))))) # label(fact_1240_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1269 (all C_60 all B_127 all A_158 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_127),A_158)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_60),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_158),C_60)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_127),C_60)))))) # label(fact_1241_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1270 (all C_60 all B_127 all A_158 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_127),A_158)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_60),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),C_60)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_127),C_60)))))) # label(fact_1242_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1271 (all C_59 all B_126 all A_157 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_126),A_157)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_59),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_59),A_157)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_59),B_126)))))) # label(fact_1243_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1272 (all C_59 all B_126 all A_157 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_126),A_157)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_59),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_59),A_157)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_59),B_126)))))) # label(fact_1244_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1273 (all C_59 all B_126 all A_157 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_126),A_157)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_59),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_59),A_157)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_59),B_126)))))) # label(fact_1245_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1274 (all C_58 all D_13 all A_156 all B_125 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_156),B_125)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_58),D_13)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_156)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_58)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_156),C_58)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_125),D_13)))))))) # label(fact_1246_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1275 (all C_58 all D_13 all A_156 all B_125 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_156),B_125)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_58),D_13)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_156)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_58)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_156),C_58)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_125),D_13)))))))) # label(fact_1247_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1276 (all C_58 all D_13 all A_156 all B_125 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_156),B_125)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,C_58),D_13)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_156)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_58)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_156),C_58)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_125),D_13)))))))) # label(fact_1248_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1277 (all C_58 all D_13 all A_156 all B_125 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_156),B_125)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_58),D_13)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_156)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_58)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_156),C_58)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_125),D_13)))))))) # label(fact_1249_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1278 (all C_58 all D_13 all A_156 all B_125 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_156),B_125)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_58),D_13)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_156)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_58)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_156),C_58)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_125),D_13)))))))) # label(fact_1250_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1279 (all C_58 all D_13 all A_156 all B_125 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_156),B_125)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_58),D_13)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_156)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_58)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_156),C_58)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_125),D_13)))))))) # label(fact_1251_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1280 (all C_57 all D_12 all A_155 all B_124 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_155),B_124)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_57),D_12)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_124)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_57)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_155),C_57)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_124),D_12)))))))) # label(fact_1252_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1281 (all C_57 all D_12 all A_155 all B_124 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_155),B_124)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_57),D_12)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),B_124)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_57)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_155),C_57)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_124),D_12)))))))) # label(fact_1253_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1282 (all C_57 all D_12 all A_155 all B_124 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_155),B_124)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,C_57),D_12)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),B_124)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_57)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_155),C_57)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_124),D_12)))))))) # label(fact_1254_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1283 (all C_57 all D_12 all A_155 all B_124 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_155),B_124)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_57),D_12)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_124)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_57)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_155),C_57)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_124),D_12)))))))) # label(fact_1255_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1284 (all C_57 all D_12 all A_155 all B_124 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_155),B_124)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_57),D_12)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_124)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_57)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_155),C_57)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_124),D_12)))))))) # label(fact_1256_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1285 (all C_57 all D_12 all A_155 all B_124 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_155),B_124)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_57),D_12)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_124)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_57)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_155),C_57)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_124),D_12)))))))) # label(fact_1257_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1286 (all B_123 all A_154 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_154)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_123)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_154),zero_zero_rat)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_123),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_154),B_123))))) # label(fact_1258_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1287 (all B_123 all A_154 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_154)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_123)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_154),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_123),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_154),B_123))))) # label(fact_1259_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1288 (all B_123 all A_154 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_154)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_123)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_154),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_123),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_154),B_123))))) # label(fact_1260_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1289 (all B_122 all A_153 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_153)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_122),zero_zero_rat)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_153),zero_zero_rat)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_122)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_153),B_122)),zero_zero_rat)))) # label(fact_1261_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1290 (all B_122 all A_153 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_153)) & hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_122),zero_z891286103de_int)) | hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_153),zero_z891286103de_int)) & hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),B_122)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_153),B_122)),zero_z891286103de_int)))) # label(fact_1262_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1291 (all B_122 all A_153 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_153)) & hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_122),zero_z126310315umeral)) | hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_153),zero_z126310315umeral)) & hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),B_122)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_153),B_122)),zero_z126310315umeral)))) # label(fact_1263_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1292 (all B_122 all A_153 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_153)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_122),zero_zero_nat)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_153),zero_zero_nat)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_122)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_153),B_122)),zero_zero_nat)))) # label(fact_1264_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1293 (all B_122 all A_153 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_153)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_122),zero_zero_real)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_153),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_122)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_153),B_122)),zero_zero_real)))) # label(fact_1265_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1294 (all B_122 all A_153 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_153)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_122),zero_zero_int)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_153),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_122)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_153),B_122)),zero_zero_int)))) # label(fact_1266_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1295 (all A_152 -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_152),A_152)),zero_zero_rat))) # label(fact_1267_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1296 (all A_152 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_152),A_152)),zero_zero_real))) # label(fact_1268_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1297 (all A_152 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_152),A_152)),zero_zero_int))) # label(fact_1269_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1298 (all Aa all C all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),C)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),C))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C),zero_zero_rat)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Ba),Aa)))) # label(fact_1270_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1299 (all Aa all C all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),C)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),C))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),Aa)))) # label(fact_1271_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1300 (all Aa all C all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),C)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),C))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa)))) # label(fact_1272_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1301 (all C all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Aa)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C),zero_zero_rat)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Ba),Aa)))) # label(fact_1273_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1302 (all C all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Aa)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C),zero_zero_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),Aa)))) # label(fact_1274_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1303 (all C all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Aa)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa)))) # label(fact_1275_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1304 (all Aa all Ba all C (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Aa)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba))))) # label(fact_1276_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1305 (all Aa all Ba all C (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Aa)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba))))) # label(fact_1277_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1306 (all Aa all Ba all C (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Aa)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba))))) # label(fact_1278_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1307 (all B_121 all A_151 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_151)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),B_121)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_151),B_121)))))) # label(fact_1279_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1308 (all B_121 all A_151 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_151)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),B_121)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_151),B_121)))))) # label(fact_1280_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1309 (all B_121 all A_151 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_151)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),B_121)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_151),B_121)))))) # label(fact_1281_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1310 (all B_121 all A_151 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_151)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_121)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_151),B_121)))))) # label(fact_1282_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1311 (all B_121 all A_151 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_151)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_121)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_151),B_121)))))) # label(fact_1283_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1312 (all B_121 all A_151 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_151)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_121)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_151),B_121)))))) # label(fact_1284_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1313 (all B_120 all A_150 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_150)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_120),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_150),B_120)),zero_zero_rat))))) # label(fact_1285_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1314 (all B_120 all A_150 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_150)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_120),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_150),B_120)),zero_z891286103de_int))))) # label(fact_1286_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1315 (all B_120 all A_150 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_150)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_120),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_150),B_120)),zero_z126310315umeral))))) # label(fact_1287_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1316 (all B_120 all A_150 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_150)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_120),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_150),B_120)),zero_zero_nat))))) # label(fact_1288_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1317 (all B_120 all A_150 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_150)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_120),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_150),B_120)),zero_zero_real))))) # label(fact_1289_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1318 (all B_120 all A_150 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_150)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_120),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_150),B_120)),zero_zero_int))))) # label(fact_1290_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1319 (all B_119 all A_149 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_149)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_119),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_119),A_149)),zero_zero_rat))))) # label(fact_1291_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1320 (all B_119 all A_149 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_149)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_119),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_119),A_149)),zero_z891286103de_int))))) # label(fact_1292_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1321 (all B_119 all A_149 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_149)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_119),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_119),A_149)),zero_z126310315umeral))))) # label(fact_1293_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1322 (all B_119 all A_149 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_149)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_119),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_119),A_149)),zero_zero_nat))))) # label(fact_1294_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1323 (all B_119 all A_149 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_149)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_119),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_119),A_149)),zero_zero_real))))) # label(fact_1295_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1324 (all B_119 all A_149 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_149)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_119),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_119),A_149)),zero_zero_int))))) # label(fact_1296_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1325 (all A_148 all B_118 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_148),B_118))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_148)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),B_118))))) # label(fact_1297_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1326 (all A_148 all B_118 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_148),B_118))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_148)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),B_118))))) # label(fact_1298_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1327 (all A_148 all B_118 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_148),B_118))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_148)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),B_118))))) # label(fact_1299_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1328 (all A_148 all B_118 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_148),B_118))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_148)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_118))))) # label(fact_1300_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1329 (all A_148 all B_118 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_148),B_118))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_148)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_118))))) # label(fact_1301_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1330 (all A_148 all B_118 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_148),B_118))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_148)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_118))))) # label(fact_1302_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1331 (all B_117 all A_147 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_117),A_147))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_147)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),B_117))))) # label(fact_1303_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1332 (all B_117 all A_147 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_117),A_147))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_147)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),B_117))))) # label(fact_1304_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1333 (all B_117 all A_147 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_117),A_147))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_147)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),B_117))))) # label(fact_1305_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1334 (all B_117 all A_147 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_117),A_147))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_147)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_117))))) # label(fact_1306_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1335 (all B_117 all A_147 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_117),A_147))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_147)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_117))))) # label(fact_1307_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1336 (all B_117 all A_147 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_117),A_147))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_147)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_117))))) # label(fact_1308_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1337 (all Aa all Ba all C (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Aa)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Ba),Aa))))) # label(fact_1309_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1338 (all Aa all Ba all C (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Aa)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),Aa))))) # label(fact_1310_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1339 (all Aa all Ba all C (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Aa)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa))))) # label(fact_1311_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1340 (all B_116 all A_146 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_146),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),B_116)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_146),B_116)),zero_zero_rat))))) # label(fact_1312_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1341 (all B_116 all A_146 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_146),zero_z891286103de_int)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),B_116)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_146),B_116)),zero_z891286103de_int))))) # label(fact_1313_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1342 (all B_116 all A_146 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_146),zero_z126310315umeral)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),B_116)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_146),B_116)),zero_z126310315umeral))))) # label(fact_1314_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1343 (all B_116 all A_146 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_146),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_116)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_146),B_116)),zero_zero_nat))))) # label(fact_1315_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1344 (all B_116 all A_146 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_146),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_116)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_146),B_116)),zero_zero_real))))) # label(fact_1316_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1345 (all B_116 all A_146 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_146),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_116)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_146),B_116)),zero_zero_int))))) # label(fact_1317_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1346 (all B_115 all A_145 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_145),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_115),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_145),B_115)))))) # label(fact_1318_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1347 (all B_115 all A_145 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_145),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_115),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_145),B_115)))))) # label(fact_1319_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1348 (all B_115 all A_145 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_145),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_115),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_145),B_115)))))) # label(fact_1320_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1349 (all C_56 all A_144 all B_114 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_144),B_114)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C_56)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_144),C_56)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_114),C_56)))))) # label(fact_1321_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1350 (all C_56 all A_144 all B_114 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_144),B_114)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),C_56)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_144),C_56)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_114),C_56)))))) # label(fact_1322_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1351 (all C_56 all A_144 all B_114 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_144),B_114)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),C_56)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_144),C_56)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_114),C_56)))))) # label(fact_1323_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1352 (all C_56 all A_144 all B_114 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_144),B_114)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_56)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_144),C_56)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_114),C_56)))))) # label(fact_1324_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1353 (all C_56 all A_144 all B_114 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_144),B_114)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_56)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_144),C_56)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_114),C_56)))))) # label(fact_1325_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1354 (all C_56 all A_144 all B_114 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_144),B_114)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_56)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_144),C_56)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_114),C_56)))))) # label(fact_1326_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1355 (all C_55 all A_143 all B_113 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_143),B_113)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C_55)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_55),A_143)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_55),B_113)))))) # label(fact_1327_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1356 (all C_55 all A_143 all B_113 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_143),B_113)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),C_55)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_55),A_143)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_55),B_113)))))) # label(fact_1328_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1357 (all C_55 all A_143 all B_113 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_143),B_113)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),C_55)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_55),A_143)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_55),B_113)))))) # label(fact_1329_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.70 1358 (all C_55 all A_143 all B_113 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_143),B_113)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_55)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_55),A_143)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_55),B_113)))))) # label(fact_1330_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1359 (all C_55 all A_143 all B_113 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_143),B_113)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_55)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_55),A_143)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_55),B_113)))))) # label(fact_1331_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1360 (all C_55 all A_143 all B_113 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_143),B_113)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_55)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_55),A_143)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_55),B_113)))))) # label(fact_1332_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1361 (all C_54 all A_142 all B_112 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_142),B_112)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C_54)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_54),A_142)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_54),B_112)))))) # label(fact_1333_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1362 (all C_54 all A_142 all B_112 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_142),B_112)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),C_54)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_54),A_142)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_54),B_112)))))) # label(fact_1334_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1363 (all C_54 all A_142 all B_112 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_142),B_112)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),C_54)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_54),A_142)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_54),B_112)))))) # label(fact_1335_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1364 (all C_54 all A_142 all B_112 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_142),B_112)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_54)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_54),A_142)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_54),B_112)))))) # label(fact_1336_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1365 (all C_54 all A_142 all B_112 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_142),B_112)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_54)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_54),A_142)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_54),B_112)))))) # label(fact_1337_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1366 (all C_54 all A_142 all B_112 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_142),B_112)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_54)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_54),A_142)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_54),B_112)))))) # label(fact_1338_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1367 (all C_53 all B_111 all A_141 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_111),A_141)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_53),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_141),C_53)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_111),C_53)))))) # label(fact_1339_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1368 (all C_53 all B_111 all A_141 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_111),A_141)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_53),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_141),C_53)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_111),C_53)))))) # label(fact_1340_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1369 (all C_53 all B_111 all A_141 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_111),A_141)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_53),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_141),C_53)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_111),C_53)))))) # label(fact_1341_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1370 (all C_52 all B_110 all A_140 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_110),A_140)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_52),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_52),A_140)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_52),B_110)))))) # label(fact_1342_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1371 (all C_52 all B_110 all A_140 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_110),A_140)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_52),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_52),A_140)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_52),B_110)))))) # label(fact_1343_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1372 (all C_52 all B_110 all A_140 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_110),A_140)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_52),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_52),A_140)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_52),B_110)))))) # label(fact_1344_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1373 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Aa)))) # label(fact_1345_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1374 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)))) # label(fact_1346_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1375 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)))) # label(fact_1347_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1376 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa)),zero_zero_rat)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),zero_zero_rat)))) # label(fact_1348_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1377 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)))) # label(fact_1349_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1378 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int)))) # label(fact_1350_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1379 (all B_109 all A_139 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_139)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_109)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_139),B_109)))))) # label(fact_1351_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1380 (all B_109 all A_139 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_139)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),B_109)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_139),B_109)))))) # label(fact_1352_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1381 (all B_109 all A_139 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_139)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_109)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_139),B_109)))))) # label(fact_1353_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1382 (all B_109 all A_139 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_139)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_109)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_139),B_109)))))) # label(fact_1354_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1383 (all B_109 all A_139 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_139)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_109)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_139),B_109)))))) # label(fact_1355_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1384 (all B_109 all A_139 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_139)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),B_109)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_139),B_109)))))) # label(fact_1356_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1385 (all Y_2 all X_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),X_1)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Y_2)) -> (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_1),Y_2) = zero_zero_rat <-> X_1 = zero_zero_rat & Y_2 = zero_zero_rat)))) # label(fact_1357_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1386 (all Y_2 all X_1 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),X_1)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),Y_2)) -> (hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,X_1),Y_2) = zero_z891286103de_int <-> X_1 = zero_z891286103de_int & Y_2 = zero_z891286103de_int)))) # label(fact_1358_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1387 (all Y_2 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_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),Y_2) = zero_zero_nat <-> X_1 = zero_zero_nat & Y_2 = zero_zero_nat)))) # label(fact_1359_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1388 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_2)) -> (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2) = zero_zero_real <-> X_1 = zero_zero_real & Y_2 = zero_zero_real)))) # label(fact_1360_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1389 (all Y_2 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_2)) -> (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_1),Y_2) = zero_zero_int <-> X_1 = zero_zero_int & Y_2 = zero_zero_int)))) # label(fact_1361_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1390 (all Y_2 all X_1 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),X_1)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),Y_2)) -> (hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,X_1),Y_2) = zero_z126310315umeral <-> X_1 = zero_z126310315umeral & Y_2 = zero_z126310315umeral)))) # label(fact_1362_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1391 (all B_108 all C_51 all A_138 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_138)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_108),C_51)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_108),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_138),C_51)))))) # label(fact_1363_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1392 (all B_108 all C_51 all A_138 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_138)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_108),C_51)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_108),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_138),C_51)))))) # label(fact_1364_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1393 (all B_108 all C_51 all A_138 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_138)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_108),C_51)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_108),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_138),C_51)))))) # label(fact_1365_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1394 (all B_108 all C_51 all A_138 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_138)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_108),C_51)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_108),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_138),C_51)))))) # label(fact_1366_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1395 (all B_108 all C_51 all A_138 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_138)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_108),C_51)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_108),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_138),C_51)))))) # label(fact_1367_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1396 (all B_108 all C_51 all A_138 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_138)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_108),C_51)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_108),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_138),C_51)))))) # label(fact_1368_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1397 (all B_107 all A_137 all C_50 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_50)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_107),A_137)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_107),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_137),C_50)))))) # label(fact_1369_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1398 (all B_107 all A_137 all C_50 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_50)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_107),A_137)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_107),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_137),C_50)))))) # label(fact_1370_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1399 (all B_107 all A_137 all C_50 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_50)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_107),A_137)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_107),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_137),C_50)))))) # label(fact_1371_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1400 (all B_107 all A_137 all C_50 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_50)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_107),A_137)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_107),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_137),C_50)))))) # label(fact_1372_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1401 (all B_107 all A_137 all C_50 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_50)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_107),A_137)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_107),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_137),C_50)))))) # label(fact_1373_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1402 (all B_107 all A_137 all C_50 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_50)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_107),A_137)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_107),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_137),C_50)))))) # label(fact_1374_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1403 (all B_106 all A_136 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_136),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_106),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_136),B_106)),zero_zero_rat))))) # label(fact_1375_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1404 (all B_106 all A_136 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_136),zero_z891286103de_int)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_106),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_136),B_106)),zero_z891286103de_int))))) # label(fact_1376_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1405 (all B_106 all A_136 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_136),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_106),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_136),B_106)),zero_zero_nat))))) # label(fact_1377_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1406 (all B_106 all A_136 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_136),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_106),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_136),B_106)),zero_zero_real))))) # label(fact_1378_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1407 (all B_106 all A_136 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_136),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_106),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_136),B_106)),zero_zero_int))))) # label(fact_1379_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1408 (all B_106 all A_136 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_136),zero_z126310315umeral)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_106),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_136),B_106)),zero_z126310315umeral))))) # label(fact_1380_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1409 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),Aa)))) # label(fact_1381_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1410 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Aa)))) # label(fact_1382_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1411 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa)))) # label(fact_1383_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1412 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa)),zero_zero_rat)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),zero_zero_rat)))) # label(fact_1384_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1413 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),zero_zero_real)))) # label(fact_1385_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1414 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_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_1386_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1415 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa)),zero_zero_rat)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),zero_zero_rat)))) # label(fact_1387_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1416 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),zero_zero_real)))) # label(fact_1388_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1417 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_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_1389_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1418 (all B_105 all A_135 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_135)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),B_105)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_135),B_105)))))) # label(fact_1390_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1419 (all B_105 all A_135 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_135)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),B_105)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_135),B_105)))))) # label(fact_1391_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1420 (all B_105 all A_135 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_135)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_105)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_135),B_105)))))) # label(fact_1392_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1421 (all B_105 all A_135 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_135)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_105)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_135),B_105)))))) # label(fact_1393_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1422 (all B_105 all A_135 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_135)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_105)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_135),B_105)))))) # label(fact_1394_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1423 (all B_105 all A_135 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_135)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),B_105)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_135),B_105)))))) # label(fact_1395_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1424 (all B_104 all C_49 all A_134 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_134)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_104),C_49)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_104),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_134),C_49)))))) # label(fact_1396_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1425 (all B_104 all C_49 all A_134 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_134)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_104),C_49)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_104),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_134),C_49)))))) # label(fact_1397_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1426 (all B_104 all C_49 all A_134 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_134)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_104),C_49)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_104),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_134),C_49)))))) # label(fact_1398_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1427 (all B_104 all C_49 all A_134 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_134)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_104),C_49)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_104),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_134),C_49)))))) # label(fact_1399_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1428 (all B_104 all C_49 all A_134 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_134)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_104),C_49)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_104),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_134),C_49)))))) # label(fact_1400_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1429 (all B_104 all C_49 all A_134 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_134)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_104),C_49)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_104),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_134),C_49)))))) # label(fact_1401_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1430 (all B_103 all A_133 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_133),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_103),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_133),B_103)),zero_zero_rat))))) # label(fact_1402_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1431 (all B_103 all A_133 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_133),zero_z891286103de_int)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_103),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_133),B_103)),zero_z891286103de_int))))) # label(fact_1403_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1432 (all B_103 all A_133 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_133),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_103),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_133),B_103)),zero_zero_nat))))) # label(fact_1404_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1433 (all B_103 all A_133 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_133),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_103),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_133),B_103)),zero_zero_real))))) # label(fact_1405_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1434 (all B_103 all A_133 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_133),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_103),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_133),B_103)),zero_zero_int))))) # label(fact_1406_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1435 (all B_103 all A_133 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_133),zero_z126310315umeral)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_103),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_133),B_103)),zero_z126310315umeral))))) # label(fact_1407_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1436 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba)),zero_zero_rat)))) # label(fact_1432_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1437 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba)),zero_zero_real)))) # label(fact_1433_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1438 (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,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),zero_zero_int)))) # label(fact_1434_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1439 (all C_48 all D_11 all A_132 all B_102 all R_7 (R_7 != zero_zero_rat -> (A_132 = B_102 & C_48 != D_11 -> hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_132),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,R_7),C_48)) != hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,B_102),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,R_7),D_11))))) # label(fact_1435_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1440 (all C_48 all D_11 all A_132 all B_102 all R_7 (R_7 != zero_zero_complex -> (A_132 = B_102 & C_48 != D_11 -> hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_132),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,R_7),C_48)) != hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_102),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,R_7),D_11))))) # label(fact_1436_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1441 (all C_48 all D_11 all A_132 all B_102 all R_7 (R_7 != zero_zero_nat -> (A_132 = B_102 & C_48 != D_11 -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_132),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,R_7),C_48)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_102),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,R_7),D_11))))) # label(fact_1437_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1442 (all C_48 all D_11 all A_132 all B_102 all R_7 (R_7 != zero_zero_real -> (A_132 = B_102 & C_48 != D_11 -> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_132),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_7),C_48)) != hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_102),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_7),D_11))))) # label(fact_1438_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1443 (all C_48 all D_11 all A_132 all B_102 all R_7 (R_7 != zero_zero_int -> (A_132 = B_102 & C_48 != D_11 -> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_132),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,R_7),C_48)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_102),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,R_7),D_11))))) # label(fact_1439_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1444 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba)),zero_zero_rat)))) # label(fact_1440_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1445 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba)),zero_zero_real)))) # label(fact_1441_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1446 (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,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),zero_zero_int)))) # label(fact_1442_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1447 (all A_2 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_2)) -> (X != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),one_one_int) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),one_one_int))))))) # label(fact_1443_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1448 (all K_2 all I all J_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),J_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),I)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),J_2)))))) # label(fact_1445_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1449 (all Z_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_1)),Z_1) != zero_zero_int) # label(fact_1446_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1450 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_1),L)),zero_zero_int)))) # label(fact_1447_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1451 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),archim1419379755ng_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,one_one_rat),X_1)))) # label(fact_1448_one__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1452 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X_1)))) # label(fact_1449_one__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1453 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1419379755ng_rat(X_1)),one_one_int)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),one_one_rat)))) # label(fact_1450_ceiling__le__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1454 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X_1)),one_one_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),one_one_real)))) # label(fact_1451_ceiling__le__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1455 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,V)),archim1419379755ng_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,V)),X_1)))) # label(fact_1452_number__of__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1456 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,V)),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,V)),X_1)))) # label(fact_1453_number__of__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1457 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_int_real(number267125858f_real,V))))) # label(fact_1454_ceiling__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1458 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1419379755ng_rat(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),hAPP_int_rat(number_number_of_rat,V))))) # label(fact_1455_ceiling__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1459 (all X_33 archim1419379755ng_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_33),one_one_rat)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim1419379755ng_rat(X_33)),one_one_int)) # label(fact_1456_ceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1460 (all X_33 archim856651990g_real(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_33),one_one_real)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim856651990g_real(X_33)),one_one_int)) # label(fact_1457_ceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1461 (all X_32 all V_11 archim1419379755ng_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_32),hAPP_int_rat(number_number_of_rat,V_11))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim1419379755ng_rat(X_32)),hAPP_int_int(number_number_of_int,V_11))) # label(fact_1458_ceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1462 (all X_32 all V_11 archim856651990g_real(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_32),hAPP_int_real(number267125858f_real,V_11))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim856651990g_real(X_32)),hAPP_int_int(number_number_of_int,V_11))) # label(fact_1459_ceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1463 (all X_31 archim1419379755ng_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_31),one_one_rat)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim1419379755ng_rat(X_31)),one_one_int)) # label(fact_1460_ceiling__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1464 (all X_31 archim856651990g_real(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_31),one_one_real)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim856651990g_real(X_31)),one_one_int)) # label(fact_1461_ceiling__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1465 (all X_30 all V_10 archim1419379755ng_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_30),hAPP_int_rat(number_number_of_rat,V_10))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim1419379755ng_rat(X_30)),hAPP_int_int(number_number_of_int,V_10))) # label(fact_1462_ceiling__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1466 (all X_30 all V_10 archim856651990g_real(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_30),hAPP_int_real(number267125858f_real,V_10))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim856651990g_real(X_30)),hAPP_int_int(number_number_of_int,V_10))) # label(fact_1463_ceiling__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1467 (all C_47 all A_131 all B_101 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_47),A_131)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_47),B_101))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C_47)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_131),B_101))))) # label(fact_1464_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1468 (all C_47 all A_131 all B_101 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_47),A_131)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_47),B_101))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),C_47)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_131),B_101))))) # label(fact_1465_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1469 (all C_47 all A_131 all B_101 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_47),A_131)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_47),B_101))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),C_47)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_131),B_101))))) # label(fact_1466_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1470 (all C_47 all A_131 all B_101 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_47),A_131)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_47),B_101))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_47)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_131),B_101))))) # label(fact_1467_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1471 (all C_47 all A_131 all B_101 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_47),A_131)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_47),B_101))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_47)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_131),B_101))))) # label(fact_1468_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1472 (all C_47 all A_131 all B_101 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_47),A_131)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_47),B_101))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_47)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_131),B_101))))) # label(fact_1469_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1473 (all A_130 all C_46 all B_100 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_130),C_46)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_100),C_46))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C_46)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_130),B_100))))) # label(fact_1470_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1474 (all A_130 all C_46 all B_100 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_130),C_46)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_100),C_46))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),C_46)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_130),B_100))))) # label(fact_1471_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1475 (all A_130 all C_46 all B_100 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_130),C_46)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_100),C_46))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),C_46)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_130),B_100))))) # label(fact_1472_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1476 (all A_130 all C_46 all B_100 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_130),C_46)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_100),C_46))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_46)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_130),B_100))))) # label(fact_1473_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1477 (all A_130 all C_46 all B_100 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_130),C_46)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_100),C_46))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_46)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_130),B_100))))) # label(fact_1474_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1478 (all A_130 all C_46 all B_100 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_130),C_46)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_100),C_46))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_46)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_130),B_100))))) # label(fact_1475_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1479 (all C_45 all A_129 all B_99 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_45),A_129)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_45),B_99))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_45)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_129),B_99))))) # label(fact_1476_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1480 (all C_45 all A_129 all B_99 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_45),A_129)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_45),B_99))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_45)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_129),B_99))))) # label(fact_1477_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1481 (all C_45 all A_129 all B_99 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_45),A_129)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_45),B_99))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_45)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_129),B_99))))) # label(fact_1478_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1482 (all C_45 all A_129 all B_99 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_45),A_129)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_45),B_99))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_45)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_129),B_99))))) # label(fact_1479_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1483 (all C_45 all A_129 all B_99 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_45),A_129)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_45),B_99))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_45)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_129),B_99))))) # label(fact_1480_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1484 (all C_45 all A_129 all B_99 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_45),A_129)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_45),B_99))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_45)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_129),B_99))))) # label(fact_1481_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1485 (all C_44 all A_128 all B_98 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_44),A_128)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_44),B_98))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_44)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_128),B_98))))) # label(fact_1482_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1486 (all C_44 all A_128 all B_98 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_44),A_128)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_44),B_98))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_44)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_128),B_98))))) # label(fact_1483_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1487 (all C_44 all A_128 all B_98 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_44),A_128)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_44),B_98))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_44)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_128),B_98))))) # label(fact_1484_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1488 (all C_44 all A_128 all B_98 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_44),A_128)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_44),B_98))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_44)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_128),B_98))))) # label(fact_1485_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1489 (all C_44 all A_128 all B_98 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_44),A_128)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_44),B_98))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_44)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_128),B_98))))) # label(fact_1486_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1490 (all C_44 all A_128 all B_98 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_44),A_128)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_44),B_98))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_44)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_128),B_98))))) # label(fact_1487_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1491 (all A_127 all C_43 all B_97 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_127),C_43)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_97),C_43))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_43)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_127),B_97))))) # label(fact_1488_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1492 (all A_127 all C_43 all B_97 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_127),C_43)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_97),C_43))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_43)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_127),B_97))))) # label(fact_1489_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1493 (all A_127 all C_43 all B_97 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_127),C_43)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_97),C_43))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_43)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_127),B_97))))) # label(fact_1490_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1494 (all A_127 all C_43 all B_97 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_127),C_43)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_97),C_43))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_43)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_127),B_97))))) # label(fact_1491_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1495 (all A_127 all C_43 all B_97 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_127),C_43)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_97),C_43))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_43)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_127),B_97))))) # label(fact_1492_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1496 (all A_127 all C_43 all B_97 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_127),C_43)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_97),C_43))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_43)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_127),B_97))))) # label(fact_1493_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1497 (all A_126 all C_42 all B_96 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_126),C_42)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_96),C_42))) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_42)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_126),B_96))))) # label(fact_1494_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1498 (all A_126 all C_42 all B_96 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_126),C_42)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_96),C_42))) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_42)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_126),B_96))))) # label(fact_1495_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1499 (all A_126 all C_42 all B_96 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_126),C_42)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_96),C_42))) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_42)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_126),B_96))))) # label(fact_1496_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1500 (all A_126 all C_42 all B_96 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_126),C_42)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_96),C_42))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_42)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_126),B_96))))) # label(fact_1497_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1501 (all A_126 all C_42 all B_96 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_126),C_42)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_96),C_42))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_42)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_126),B_96))))) # label(fact_1498_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1502 (all A_126 all C_42 all B_96 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_126),C_42)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_96),C_42))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_42)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_126),B_96))))) # label(fact_1499_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1503 (all C_41 all D_10 all A_125 all B_95 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_125),B_95)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_41),D_10)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_125)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_41)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_125),C_41)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_95),D_10)))))))) # label(fact_1500_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1504 (all C_41 all D_10 all A_125 all B_95 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_125),B_95)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_41),D_10)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_125)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_41)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_125),C_41)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_95),D_10)))))))) # label(fact_1501_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1505 (all C_41 all D_10 all A_125 all B_95 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_125),B_95)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,C_41),D_10)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_125)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_41)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_125),C_41)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_95),D_10)))))))) # label(fact_1502_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1506 (all C_41 all D_10 all A_125 all B_95 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_125),B_95)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_41),D_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_125)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_41)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_125),C_41)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_95),D_10)))))))) # label(fact_1503_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1507 (all C_41 all D_10 all A_125 all B_95 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_125),B_95)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_41),D_10)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_125)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_41)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_125),C_41)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_95),D_10)))))))) # label(fact_1504_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1508 (all C_41 all D_10 all A_125 all B_95 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_125),B_95)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_41),D_10)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_125)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_41)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_125),C_41)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_95),D_10)))))))) # label(fact_1505_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1509 (all C_40 all D_9 all A_124 all B_94 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_124),B_94)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,C_40),D_9)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_124)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C_40)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_124),C_40)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_94),D_9)))))))) # label(fact_1506_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1510 (all C_40 all D_9 all A_124 all B_94 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_124),B_94)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,C_40),D_9)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_124)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),C_40)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_124),C_40)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_94),D_9)))))))) # label(fact_1507_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1511 (all C_40 all D_9 all A_124 all B_94 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_124),B_94)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,C_40),D_9)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_124)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),C_40)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_124),C_40)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_94),D_9)))))))) # label(fact_1508_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1512 (all C_40 all D_9 all A_124 all B_94 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_124),B_94)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_40),D_9)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_124)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_40)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_124),C_40)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_94),D_9)))))))) # label(fact_1509_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1513 (all C_40 all D_9 all A_124 all B_94 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_124),B_94)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_40),D_9)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_124)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_40)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_124),C_40)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_94),D_9)))))))) # label(fact_1510_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1514 (all C_40 all D_9 all A_124 all B_94 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_124),B_94)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_40),D_9)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_124)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_40)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_124),C_40)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_94),D_9)))))))) # label(fact_1511_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1515 (all C_39 all D_8 all A_123 all B_93 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_123),B_93)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_39),D_8)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_123)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_39)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_123),C_39)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_93),D_8)))))))) # label(fact_1512_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1516 (all C_39 all D_8 all A_123 all B_93 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_123),B_93)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_39),D_8)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_123)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_39)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_123),C_39)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_93),D_8)))))))) # label(fact_1513_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1517 (all C_39 all D_8 all A_123 all B_93 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_123),B_93)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,C_39),D_8)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_123)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_39)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_123),C_39)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_93),D_8)))))))) # label(fact_1514_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1518 (all C_39 all D_8 all A_123 all B_93 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_123),B_93)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_39),D_8)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_123)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_39)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_123),C_39)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_93),D_8)))))))) # label(fact_1515_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1519 (all C_39 all D_8 all A_123 all B_93 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_123),B_93)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_39),D_8)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_123)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_39)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_123),C_39)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_93),D_8)))))))) # label(fact_1516_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1520 (all C_39 all D_8 all A_123 all B_93 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_123),B_93)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_39),D_8)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_123)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_39)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_123),C_39)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_93),D_8)))))))) # label(fact_1517_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1521 (all C_38 all D_7 all A_122 all B_92 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_122),B_92)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C_38),D_7)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),B_92)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),C_38)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_122),C_38)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,B_92),D_7)))))))) # label(fact_1518_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1522 (all C_38 all D_7 all A_122 all B_92 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_122),B_92)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,C_38),D_7)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),B_92)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),C_38)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_122),C_38)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_92),D_7)))))))) # label(fact_1519_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1523 (all C_38 all D_7 all A_122 all B_92 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_122),B_92)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,C_38),D_7)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),B_92)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),C_38)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_122),C_38)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_92),D_7)))))))) # label(fact_1520_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1524 (all C_38 all D_7 all A_122 all B_92 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_122),B_92)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_38),D_7)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_92)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_38)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_122),C_38)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_92),D_7)))))))) # label(fact_1521_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1525 (all C_38 all D_7 all A_122 all B_92 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_122),B_92)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_38),D_7)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_92)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_38)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_122),C_38)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_92),D_7)))))))) # label(fact_1522_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1526 (all C_38 all D_7 all A_122 all B_92 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_122),B_92)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_38),D_7)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_92)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_38)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_122),C_38)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_92),D_7)))))))) # label(fact_1523_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1527 (all Aa all Ba all C (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,C),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Aa)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Ba),Aa))))) # label(fact_1524_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1528 (all Aa all Ba all C (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Aa)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Ba),Aa))))) # label(fact_1525_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1529 (all Aa all Ba all C (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Aa)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa))))) # label(fact_1526_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1530 (all Aa all Ba all C (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),C)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Aa)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C),Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),Ba))))) # label(fact_1527_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1531 (all Aa all Ba all C (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Aa)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba))))) # label(fact_1528_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1532 (all Aa all Ba all C (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Aa)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba))))) # label(fact_1529_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1533 (all B_91 all A_121 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_121),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_91),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_121),B_91)),zero_zero_rat))))) # label(fact_1530_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1534 (all B_91 all A_121 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,A_121),zero_z891286103de_int)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_91),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_121),B_91)),zero_z891286103de_int))))) # label(fact_1531_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1535 (all B_91 all A_121 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_121),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_91),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_121),B_91)),zero_zero_nat))))) # label(fact_1532_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1536 (all B_91 all A_121 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_121),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_91),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_121),B_91)),zero_zero_real))))) # label(fact_1533_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1537 (all B_91 all A_121 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_121),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_91),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_121),B_91)),zero_zero_int))))) # label(fact_1534_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1538 (all B_91 all A_121 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,A_121),zero_z126310315umeral)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_91),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_121),B_91)),zero_z126310315umeral))))) # label(fact_1535_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1539 (all B_90 all A_120 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_120),zero_zero_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_90),zero_zero_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_120),B_90)),zero_zero_rat))))) # label(fact_1536_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1540 (all B_90 all A_120 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,A_120),zero_z891286103de_int)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_90),zero_z891286103de_int)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_120),B_90)),zero_z891286103de_int))))) # label(fact_1537_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1541 (all B_90 all A_120 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_120),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_90),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_120),B_90)),zero_zero_nat))))) # label(fact_1538_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1542 (all B_90 all A_120 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_120),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_90),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_120),B_90)),zero_zero_real))))) # label(fact_1539_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1543 (all B_90 all A_120 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_120),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_90),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_120),B_90)),zero_zero_int))))) # label(fact_1540_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1544 (all B_90 all A_120 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,A_120),zero_z126310315umeral)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_90),zero_z126310315umeral)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_120),B_90)),zero_z126310315umeral))))) # label(fact_1541_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1545 (all B_89 all C_37 all A_119 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_119)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_89),C_37)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_89),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_119),C_37)))))) # label(fact_1542_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1546 (all B_89 all C_37 all A_119 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_119)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_89),C_37)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_89),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_119),C_37)))))) # label(fact_1543_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1547 (all B_89 all C_37 all A_119 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_119)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_89),C_37)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_89),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_119),C_37)))))) # label(fact_1544_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1548 (all B_89 all C_37 all A_119 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_119)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_89),C_37)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_89),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_119),C_37)))))) # label(fact_1545_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1549 (all B_89 all C_37 all A_119 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_119)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_89),C_37)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_89),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_119),C_37)))))) # label(fact_1546_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1550 (all B_89 all C_37 all A_119 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_119)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_89),C_37)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_89),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_119),C_37)))))) # label(fact_1547_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1551 (all B_88 all C_36 all A_118 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_118)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_88),C_36)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,B_88),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_118),C_36)))))) # label(fact_1548_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1552 (all B_88 all C_36 all A_118 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_118)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,B_88),C_36)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,B_88),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_118),C_36)))))) # label(fact_1549_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1553 (all B_88 all C_36 all A_118 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_118)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_88),C_36)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_88),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_118),C_36)))))) # label(fact_1550_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1554 (all B_88 all C_36 all A_118 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_118)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_88),C_36)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_88),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_118),C_36)))))) # label(fact_1551_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1555 (all B_88 all C_36 all A_118 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_118)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_88),C_36)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_88),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),C_36)))))) # label(fact_1552_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1556 (all B_88 all C_36 all A_118 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_118)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,B_88),C_36)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,B_88),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_118),C_36)))))) # label(fact_1553_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1557 (all B_87 all A_117 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_117)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),B_87)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_117),B_87)))))) # label(fact_1554_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1558 (all B_87 all A_117 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),A_117)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),B_87)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_117),B_87)))))) # label(fact_1555_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1559 (all B_87 all A_117 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_117)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_87)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_117),B_87)))))) # label(fact_1556_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1560 (all B_87 all A_117 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_117)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_87)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_117),B_87)))))) # label(fact_1557_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1561 (all B_87 all A_117 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_117)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_87)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_117),B_87)))))) # label(fact_1558_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1562 (all B_87 all A_117 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),A_117)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),B_87)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_117),B_87)))))) # label(fact_1559_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1563 (all B_86 all A_116 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_116)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_86)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_116),B_86)))))) # label(fact_1560_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1564 (all B_86 all A_116 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),A_116)) -> (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,zero_z891286103de_int),B_86)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,zero_z891286103de_int),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_116),B_86)))))) # label(fact_1561_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1565 (all B_86 all A_116 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_116)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_86)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_116),B_86)))))) # label(fact_1562_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1566 (all B_86 all A_116 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_116)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_86)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_116),B_86)))))) # label(fact_1563_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1567 (all B_86 all A_116 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_116)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_86)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_116),B_86)))))) # label(fact_1564_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1568 (all B_86 all A_116 (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),A_116)) -> (hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le565307924umeral,zero_z126310315umeral),B_86)) -> hBOOL(hAPP_C24501650l_bool(hAPP_C10902773l_bool(ord_le1304079648umeral,zero_z126310315umeral),hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_116),B_86)))))) # label(fact_1565_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1569 (all Y_20 all X_29 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),X_29)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Y_20)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_20),one_one_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_20),X_29)),X_29)))))) # label(fact_1566_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1570 (all Y_20 all X_29 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_29)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_20)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_20),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_20),X_29)),X_29)))))) # label(fact_1567_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1571 (all Y_20 all X_29 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_29)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_20)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_20),one_one_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y_20),X_29)),X_29)))))) # label(fact_1568_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1572 (all Y_19 all X_28 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),X_28)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Y_19)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_19),one_one_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_28),Y_19)),X_28)))))) # label(fact_1569_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1573 (all Y_19 all X_28 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_28)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_19)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_19),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_28),Y_19)),X_28)))))) # label(fact_1570_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1574 (all Y_19 all X_28 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_28)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_19)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_19),one_one_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_28),Y_19)),X_28)))))) # label(fact_1571_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1575 (all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)))) # label(fact_1578_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1576 (all N all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),N) = one_one_int <-> M = one_one_int & N = one_one_int))) # label(fact_1579_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1577 (all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_2)),Z_2)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),zero_zero_int)))) # label(fact_1580_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1578 (all V_9 all U_2 all Y_18 all X_27 all A_115 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_27),A_115)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Y_18),A_115)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),U_2)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),V_9)) -> (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,U_2),V_9) = one_one_rat -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,U_2),X_27)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,V_9),Y_18))),A_115)))))))) # label(fact_1581_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1579 (all V_9 all U_2 all Y_18 all X_27 all A_115 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_27),A_115)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_18),A_115)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),V_9)) -> (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,U_2),V_9) = one_one_real -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,U_2),X_27)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,V_9),Y_18))),A_115)))))))) # label(fact_1582_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1580 (all V_9 all U_2 all Y_18 all X_27 all A_115 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_27),A_115)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_18),A_115)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_9)) -> (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2),V_9) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_2),X_27)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_9),Y_18))),A_115)))))))) # label(fact_1583_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1581 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_1))))) # label(fact_1584_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1582 (all R_3 all Q_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (A_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),Q_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),A_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_1)))))) # label(fact_1585_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1583 (all R_3 all Q_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (A_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),Q_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),one_one_int)))))) # label(fact_1586_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1584 (all B_1 all Q_1 all R_3 all B_4 all Q_6 all R_5 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_4),Q_6)),R_5) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_4),Q_6)),R_5)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_4),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_6),Q_1))))))))) # label(fact_1587_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1585 (all B_1 all Q_6 all R_5 all Q_1 all R_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_6)),R_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_3))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_3),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_5)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_6))))))) # label(fact_1588_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1586 (all B_1 all Q_1 all R_3 all B_4 all Q_6 all R_5 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_4),Q_6)),R_5) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_4),Q_6)),R_5))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_5),B_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_4),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_6))))))))) # label(fact_1589_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1587 (all B_1 all Q_6 all R_5 all Q_1 all R_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_6)),R_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_3))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_5),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_6),Q_1))))))) # label(fact_1590_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1588 (all B_4 all Q_6 all R_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_4),Q_6)),R_5)),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_5)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_4)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_6),zero_zero_int)))))) # label(fact_1591_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1589 (all B_4 all Q_6 all R_5 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_4),Q_6)),R_5))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_5),B_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_4)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_6)))))) # label(fact_1592_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.71 1590 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_1),X_1)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_2),Y_2)))) <-> X_1 != zero_zero_rat | Y_2 != zero_zero_rat)) # label(fact_1593_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1591 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),X_1)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_2),Y_2)))) <-> X_1 != zero_zero_real | Y_2 != zero_zero_real)) # label(fact_1594_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1592 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),X_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y_2),Y_2)))) <-> X_1 != zero_zero_int | Y_2 != zero_zero_int)) # label(fact_1595_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1593 (all X_26 all Y_17 -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_26),X_26)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_17),Y_17))),zero_zero_rat))) # label(fact_1596_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1594 (all X_26 all Y_17 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_26),X_26)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_17),Y_17))),zero_zero_real))) # label(fact_1597_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1595 (all X_26 all Y_17 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_26),X_26)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y_17),Y_17))),zero_zero_int))) # label(fact_1598_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1596 (all X_1 all Y_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_1),X_1)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_2),Y_2))),zero_zero_rat)) <-> X_1 = zero_zero_rat & Y_2 = zero_zero_rat)) # label(fact_1599_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1597 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),X_1)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_2),Y_2))),zero_zero_real)) <-> X_1 = zero_zero_real & Y_2 = zero_zero_real)) # label(fact_1600_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1598 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),X_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y_2),Y_2))),zero_zero_int)) <-> X_1 = zero_zero_int & Y_2 = zero_zero_int)) # label(fact_1601_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1599 (all X_1 all Y_2 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_1),X_1)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_2),Y_2)) = zero_zero_rat <-> X_1 = zero_zero_rat & Y_2 = zero_zero_rat)) # label(fact_1602_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1600 (all X_1 all Y_2 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),X_1)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_2),Y_2)) = zero_zero_real <-> X_1 = zero_zero_real & Y_2 = zero_zero_real)) # label(fact_1603_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1601 (all X_1 all Y_2 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),X_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y_2),Y_2)) = zero_zero_int <-> X_1 = zero_zero_int & Y_2 = zero_zero_int)) # label(fact_1604_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1602 (all X_25 all Y_16 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_25),X_25)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_16),Y_16))))) # label(fact_1605_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1603 (all X_25 all Y_16 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_25),X_25)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_16),Y_16))))) # label(fact_1606_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1604 (all X_25 all Y_16 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_25),X_25)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y_16),Y_16))))) # label(fact_1607_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1605 (all M_1 all R_3 all S_2 all T_2 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> (xzgcd(M_1,N_1) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,R_3),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,S_2),T_2)) -> R_3 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,S_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,T_2),N_1))))) # label(fact_1608_xzgcd__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1606 (all M_1 all N_1 all R_5 all S_4 all S_2 all T_3 all T_2 all Rn all Sn_1 all Tn_1 all R_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),R_3)) -> (xzgcda(M_1,N_1,R_5,R_3,S_4,S_2,T_3,T_2) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,Rn),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Sn_1),Tn_1)) -> (R_5 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,S_4),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,T_3),N_1)) -> (R_3 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,S_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,T_2),N_1)) -> Rn = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Sn_1),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Tn_1),N_1))))))) # label(fact_1609_xzgcda__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1607 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_1610_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1608 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)))))) # label(fact_1611_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1609 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))))) # label(fact_1612_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1610 (all K_1 all P_1 all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> ((all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> (all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),D)))))))))) # label(fact_1614_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1611 (all K_1 all P_1 all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> ((all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) -> (all X_2 (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),D)))))))))) # label(fact_1615_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1612 (all X_24 all Y_15 ((all Z (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),Z)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z),one_one_rat)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Z),X_24)),Y_15))))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_24),Y_15)))) # label(fact_1616_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1613 (all X_24 all Y_15 ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z),X_24)),Y_15))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_24),Y_15)))) # label(fact_1617_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1614 (all A_2 all B_1 all Q_1 all R_3 (A_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_3) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_1))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_3)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_3),zero_zero_int))) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3)))))) # label(fact_1618_divmod__int__relI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1615 (all M_1 all N_1 xzgcd(M_1,N_1) = xzgcda(M_1,N_1,M_1,N_1,one_one_int,zero_zero_int,zero_zero_int,one_one_int)) # label(fact_1619_xzgcd__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1616 (all B_1 (B_1 != zero_zero_int -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(zero_zero_int,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),zero_zero_int))))) # label(fact_1620_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1617 (all A_2 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,A_2),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (A_2 != zero_zero_int -> R_3 = zero_zero_int))) # label(fact_1621_self__remainder) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1618 (all Q_6 all R_5 all A_2 all B_1 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_6),R_5))) -> (B_1 != zero_zero_int -> Q_1 = Q_6)))) # label(fact_1622_unique__quotient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1619 (all Q_6 all R_5 all A_2 all B_1 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_6),R_5))) -> (B_1 != zero_zero_int -> R_3 = R_5)))) # label(fact_1623_unique__remainder) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1620 (all A_2 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,A_2),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (A_2 != zero_zero_int -> Q_1 = one_one_int))) # label(fact_1624_self__quotient) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1621 (all P_2 all P_1 all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P_1)) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(P_2))))) # label(fact_1625_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1622 (all P_2 all P_1 all X_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P_1) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) & hBOOL(P_2)))) # label(fact_1626_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1623 (all X_23 all Y_14 ((all E (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),E)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_23),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Y_14),E))))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_23),Y_14)))) # label(fact_1628_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1624 (all X_23 all Y_14 ((all E (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),E)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_23),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Y_14),E))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_23),Y_14)))) # label(fact_1629_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1625 (all T_8 exists Z all X_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_2),Z)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,T_8),X_2)))) # label(fact_1630_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1626 (all T_8 exists Z all X_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_2),Z)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,T_8),X_2)))) # label(fact_1631_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1627 (all T_8 exists Z all X_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Z)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,T_8),X_2)))) # label(fact_1632_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1628 (all T_8 exists Z all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Z)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_8),X_2)))) # label(fact_1633_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1629 (all T_8 exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T_8),X_2)))) # label(fact_1634_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1630 (all T_7 exists Z all X_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z),X_2)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,T_7),X_2)))) # label(fact_1635_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1631 (all T_7 exists Z all X_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Z),X_2)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,T_7),X_2)))) # label(fact_1636_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1632 (all T_7 exists Z all X_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),X_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,T_7),X_2)))) # label(fact_1637_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1633 (all T_7 exists Z all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z),X_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_7),X_2)))) # label(fact_1638_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1634 (all T_7 exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T_7),X_2)))) # label(fact_1639_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1635 (all T_6 exists Z all X_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_2),Z)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_2),T_6)))) # label(fact_1640_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1636 (all T_6 exists Z all X_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,X_2),Z)) -> hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_2),T_6)))) # label(fact_1641_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1637 (all T_6 exists Z all X_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),T_6)))) # label(fact_1642_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1638 (all T_6 exists Z all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Z)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),T_6)))) # label(fact_1643_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1639 (all T_6 exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),T_6)))) # label(fact_1644_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1640 (all T_5 exists Z all X_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z),X_2)) -> -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_2),T_5)))) # label(fact_1645_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1641 (all T_5 exists Z all X_2 (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,Z),X_2)) -> -hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,X_2),T_5)))) # label(fact_1646_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1642 (all T_5 exists Z all X_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),X_2)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),T_5)))) # label(fact_1647_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1643 (all T_5 exists Z all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z),X_2)) -> -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),T_5)))) # label(fact_1648_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1644 (all T_5 exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),X_2)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),T_5)))) # label(fact_1649_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1645 (all P_1 all P1 all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> ((all X_2 all K (hBOOL(hAPP_int_bool(P1,X_2)) <-> hBOOL(hAPP_int_bool(P1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D)))))) -> ((exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z)) -> (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P1,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P1,X1))) -> (exists X1 hBOOL(hAPP_int_bool(P_1,X1)))))))) # label(fact_1650_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1646 (all P_1 all P_2 all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> ((all X_2 all K (hBOOL(hAPP_int_bool(P_2,X_2)) <-> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D)))))) -> ((exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),X_2)) -> (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_2,X_2))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_2,X1))) -> (exists X1 hBOOL(hAPP_int_bool(P_1,X1)))))))) # label(fact_1651_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1647 (all Y all X ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(nat_tsub(X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(nat_tsub(X),Y) = zero_zero_int))) # label(fact_1652_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1648 (all N_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int)) -> hAPP_int_int(zfact,N_1) = one_one_int) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int)) -> hAPP_int_int(zfact,N_1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,N_1),hAPP_int_int(zfact,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,N_1),one_one_int)))))) # label(fact_1653_zfact_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1649 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim791455193or_rat(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,V)),one_one_rat))))) # label(fact_1654_floor__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1650 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1246769320r_real(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,V)),one_one_real))))) # label(fact_1655_floor__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1651 (all X_22 all Y_13 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim791455193or_rat(X_22)),archim791455193or_rat(Y_13))) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_22),Y_13)))) # label(fact_1658_floor__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1652 (all X_22 all Y_13 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1246769320r_real(X_22)),archim1246769320r_real(Y_13))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_22),Y_13)))) # label(fact_1659_floor__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1653 (all X_21 all Y_12 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_21),Y_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim791455193or_rat(X_21)),archim791455193or_rat(Y_12))))) # label(fact_1660_floor__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1654 (all X_21 all Y_12 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_21),Y_12)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1246769320r_real(X_21)),archim1246769320r_real(Y_12))))) # label(fact_1661_floor__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1655 (all V_8 archim791455193or_rat(hAPP_int_rat(number_number_of_rat,V_8)) = hAPP_int_int(number_number_of_int,V_8)) # label(fact_1664_floor__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1656 (all V_8 archim1246769320r_real(hAPP_int_real(number267125858f_real,V_8)) = hAPP_int_int(number_number_of_int,V_8)) # label(fact_1665_floor__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1657 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim791455193or_rat(X_1)),zero_zero_int)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),zero_zero_rat)))) # label(fact_1666_floor__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1658 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1246769320r_real(X_1)),zero_zero_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)))) # label(fact_1667_floor__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1659 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),archim791455193or_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),X_1)))) # label(fact_1668_zero__le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1660 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)))) # label(fact_1669_zero__le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1661 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),archim791455193or_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,one_one_rat),X_1)))) # label(fact_1670_zero__less__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1662 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X_1)))) # label(fact_1671_zero__less__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1663 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim791455193or_rat(X_1)),zero_zero_int)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),one_one_rat)))) # label(fact_1672_floor__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1664 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1246769320r_real(X_1)),zero_zero_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)))) # label(fact_1673_floor__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1665 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim791455193or_rat(X_1)),one_one_int)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),one_one_rat)))) # label(fact_1674_floor__less__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1666 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1246769320r_real(X_1)),one_one_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)))) # label(fact_1675_floor__less__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1667 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),archim791455193or_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,one_one_rat),X_1)))) # label(fact_1676_one__le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1668 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X_1)))) # label(fact_1677_one__le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1669 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim791455193or_rat(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),hAPP_int_rat(number_number_of_rat,V))))) # label(fact_1678_floor__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1670 (all X_1 all V (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1246769320r_real(X_1)),hAPP_int_int(number_number_of_int,V))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_int_real(number267125858f_real,V))))) # label(fact_1679_floor__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1671 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,V)),archim791455193or_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),X_1)))) # label(fact_1680_number__of__le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1672 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,V)),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,V)),X_1)))) # label(fact_1681_number__of__le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1673 (all X_20 archim791455193or_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_20),one_one_rat)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim791455193or_rat(X_20)),one_one_int)) # label(fact_1682_floor__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1674 (all X_20 archim1246769320r_real(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_20),one_one_real)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim1246769320r_real(X_20)),one_one_int)) # label(fact_1683_floor__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1675 (all X_19 all V_7 archim791455193or_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_19),hAPP_int_rat(number_number_of_rat,V_7))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim791455193or_rat(X_19)),hAPP_int_int(number_number_of_int,V_7))) # label(fact_1684_floor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1676 (all X_19 all V_7 archim1246769320r_real(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_19),hAPP_int_real(number267125858f_real,V_7))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim1246769320r_real(X_19)),hAPP_int_int(number_number_of_int,V_7))) # label(fact_1685_floor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1677 (all X_18 archim791455193or_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_18),one_one_rat)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim791455193or_rat(X_18)),one_one_int)) # label(fact_1686_floor__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1678 (all X_18 archim1246769320r_real(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_18),one_one_real)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim1246769320r_real(X_18)),one_one_int)) # label(fact_1687_floor__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1679 (all X_17 all V_6 archim791455193or_rat(hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_17),hAPP_int_rat(number_number_of_rat,V_6))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim791455193or_rat(X_17)),hAPP_int_int(number_number_of_int,V_6))) # label(fact_1688_floor__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1680 (all X_17 all V_6 archim1246769320r_real(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_17),hAPP_int_real(number267125858f_real,V_6))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim1246769320r_real(X_17)),hAPP_int_int(number_number_of_int,V_6))) # label(fact_1689_floor__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1681 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(nat_tsub(X),Y)))))) # label(fact_1690_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1682 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) -> hAPP_int_int(nat_tsub(X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y))) # label(fact_1691_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1683 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,V)),archim791455193or_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,V)),one_one_rat)),X_1)))) # label(fact_1692_number__of__less__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1684 (all V all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,V)),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,V)),one_one_real)),X_1)))) # label(fact_1693_number__of__less__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1685 (all B_1 all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,archim1246769320r_real(A_2)),archim1246769320r_real(B_1))),archim1246769320r_real(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_2),B_1))))))) # label(fact_1694_le__mult__floor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1686 (all B_1 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_int,zero_zero_int),B_1)) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),posDivAlg(A_2,B_1)))))) # label(fact_1695_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1687 (all Z_1 all X all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z_1))),one_one_int)),D_3)))))) # label(fact_1696_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1688 (all X all Z_1 all D_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z_1))),one_one_int)),D_3))),Z_1)))) # label(fact_1697_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1689 (all Aa (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Aa),ring_1_Ints_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),Aa)),Aa)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),zero_zero_real))))) # label(fact_1698_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1690 (all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Aa)),Aa)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int))))) # label(fact_1699_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1691 (all Aa (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Aa),ring_1_Ints_rat)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,one_one_rat),Aa)),Aa)),zero_zero_rat)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),zero_zero_rat))))) # label(fact_1700_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1692 (all Aa all Ba all Qa all R_2 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(Aa,Ba),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Qa),R_2))) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(hAPP_int_int(uminus_uminus_int,Aa),Ba),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,R_2),zero_zero_int)),hAPP_int_int(uminus_uminus_int,Qa)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(uminus_uminus_int,Qa)),one_one_int))),hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,R_2),zero_zero_int)),zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Ba),R_2))))))) # label(fact_1701_zminus1__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1693 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Ba)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(d22set,Aa)))))) # label(fact_1702_d22set__mem) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1694 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),archim1419379755ng_rat(X_1))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,min)),X_1)))) # label(fact_1703_zero__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1695 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),X_1)))) # label(fact_1704_zero__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1696 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_1)),zero_zero_int)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_int_real(number267125858f_real,min))))) # label(fact_1705_ceiling__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1697 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1419379755ng_rat(X_1)),zero_zero_int)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),hAPP_int_rat(number_number_of_rat,min))))) # label(fact_1706_ceiling__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1698 (all P_1 all N all K_1 (hBOOL(hAPP_int_bool(P_1,hAPP_int_int(div_mod_int(N),K_1))) <-> (K_1 = zero_zero_int -> hBOOL(hAPP_int_bool(P_1,N))) & (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) -> (all I_2 all J_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),J_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J_1),K_1)) & N = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_2)),J_1) -> hBOOL(hAPP_int_bool(P_1,J_1))))) & (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),zero_zero_int)) -> (all I_2 all J_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),J_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J_1),zero_zero_int)) & N = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_2)),J_1) -> hBOOL(hAPP_int_bool(P_1,J_1))))))) # label(fact_1707_split__zmod) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1699 (all X_1 all Y_2 all Z_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),Z_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_2),Z_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2))))) # label(fact_1708_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1700 (all X_1 all Y_2 all Z_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z_2),X_1)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z_2),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2))))) # label(fact_1709_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1701 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),Y_2)),zero_zero_real)))) # label(fact_1710_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1702 (all K_2 all L_2 (hAPP_int_int(div_mod_int(K_2),hAPP_int_int(uminus_uminus_int,L_2)) != zero_zero_int -> hAPP_int_int(div_mod_int(K_2),L_2) != zero_zero_int)) # label(fact_1711_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1703 (all K_2 all L_2 (hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,K_2)),L_2) != zero_zero_int -> hAPP_int_int(div_mod_int(K_2),L_2) != zero_zero_int)) # label(fact_1712_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1704 (all Aa all Ba all C (C != zero_zero_real -> (hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Aa) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C),Ba) <-> Aa = Ba))) # label(fact_1713_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1705 (all Aa all Ba all C (C != zero_zero_real -> (hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),C) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),C) <-> Aa = Ba))) # label(fact_1714_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1706 (all X_1 all Y_2 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),X_1)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_2),Y_2)) = zero_zero_real <-> X_1 = zero_zero_real & Y_2 = zero_zero_real)) # label(fact_1715_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1707 (all X all Y all Z_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z_1),X)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z_1),Y)))))) # label(fact_1716_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1708 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y)))))) # label(fact_1717_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1709 (all X_1 all Y_2 all Z_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),Z_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_2),Z_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2))))) # label(fact_1718_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1710 (all A_114 all B_85 all A_113 (hAPP_int_int(div_mod_int(A_114),B_85) = hAPP_int_int(div_mod_int(A_113),B_85) -> hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,A_114)),B_85) = hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,A_113)),B_85))) # label(fact_1720_mod__minus__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1711 (all A_112 all B_84 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(div_mo231679042de_int(A_112),B_84)),B_84) = hAPP_Q1762011733de_int(div_mo231679042de_int(A_112),B_84)) # label(fact_1721_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1712 (all A_112 all B_84 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(div_mo1740067990umeral(A_112),B_84)),B_84) = hAPP_C498520661umeral(div_mo1740067990umeral(A_112),B_84)) # label(fact_1722_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1713 (all A_112 all B_84 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(div_mod_nat(A_112),B_84)),B_84) = hAPP_nat_nat(div_mod_nat(A_112),B_84)) # label(fact_1723_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1714 (all A_112 all B_84 hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(A_112),B_84)),B_84) = hAPP_int_int(div_mod_int(A_112),B_84)) # label(fact_1724_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1715 (all X all M_1 hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,hAPP_int_int(div_mod_int(X),M_1))),M_1) = hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,X)),M_1)) # label(fact_1725_zminus__zmod) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1716 (all A_2 all B_1 hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,A_2)),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(div_mod_int(A_2),B_1))) # label(fact_1726_zmod__zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1717 (all A_111 all B_83 hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,A_111)),B_83) = hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,hAPP_int_int(div_mod_int(A_111),B_83))),B_83)) # label(fact_1727_mod__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1718 (all A_2 all B_1 hAPP_int_int(div_mod_int(A_2),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,A_2)),B_1))) # label(fact_1728_zmod__zminus2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1719 (all W_7 hAPP_rat_rat(uminus_uminus_rat,hAPP_int_rat(number_number_of_rat,W_7)) = hAPP_int_rat(number_number_of_rat,hAPP_int_int(uminus_uminus_int,W_7))) # label(fact_1729_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1720 (all W_7 hAPP_complex_complex(uminus473333897omplex,hAPP_int_complex(number528085621omplex,W_7)) = hAPP_int_complex(number528085621omplex,hAPP_int_int(uminus_uminus_int,W_7))) # label(fact_1730_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1721 (all W_7 hAPP_real_real(uminus_uminus_real,hAPP_int_real(number267125858f_real,W_7)) = hAPP_int_real(number267125858f_real,hAPP_int_int(uminus_uminus_int,W_7))) # label(fact_1731_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1722 (all W_7 hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,W_7)) = hAPP_int_int(number_number_of_int,hAPP_int_int(uminus_uminus_int,W_7))) # label(fact_1732_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1723 (all W_6 hAPP_int_rat(number_number_of_rat,hAPP_int_int(uminus_uminus_int,W_6)) = hAPP_rat_rat(uminus_uminus_rat,hAPP_int_rat(number_number_of_rat,W_6))) # label(fact_1733_number__of__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1724 (all W_6 hAPP_int_complex(number528085621omplex,hAPP_int_int(uminus_uminus_int,W_6)) = hAPP_complex_complex(uminus473333897omplex,hAPP_int_complex(number528085621omplex,W_6))) # label(fact_1734_number__of__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1725 (all W_6 hAPP_int_real(number267125858f_real,hAPP_int_int(uminus_uminus_int,W_6)) = hAPP_real_real(uminus_uminus_real,hAPP_int_real(number267125858f_real,W_6))) # label(fact_1735_number__of__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1726 (all W_6 hAPP_int_int(number_number_of_int,hAPP_int_int(uminus_uminus_int,W_6)) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,W_6))) # label(fact_1736_number__of__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1727 (all K_2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,min),K_2) = hAPP_int_int(uminus_uminus_int,K_2)) # label(fact_1738_mult__Min) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1728 (all W hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),W))) # label(fact_1739_real__le__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1729 (all Z_1 all W (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_1),W)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),Z_1)))) # label(fact_1740_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1730 (all Z_1 all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Z_1),X)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Z_1),Y))))) # label(fact_1741_real__add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1731 (all K_2 all I all J_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I),J_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,J_2),K_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I),K_2))))) # label(fact_1742_real__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1732 (all Z_1 all W (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z_1),W)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),Z_1)) -> Z_1 = W))) # label(fact_1743_real__le__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1733 (all A_110 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,A_110)),hAPP_rat_rat(abs_abs_rat,A_110)))) # label(fact_1744_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1734 (all A_110 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,A_110)),hAPP_real_real(abs_abs_real,A_110)))) # label(fact_1745_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1735 (all A_110 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,A_110)),hAPP_int_int(abs_abs_int,A_110)))) # label(fact_1746_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1736 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,Aa)),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),Ba)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),Ba)))) # label(fact_1747_abs__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1737 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,Aa)),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,Aa)),Ba)))) # label(fact_1748_abs__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1738 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,Aa)),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,hAPP_int_int(uminus_uminus_int,Aa)),Ba)))) # label(fact_1749_abs__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1739 (all A_109 all B_82 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_109),B_82)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,A_109)),B_82)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,A_109)),B_82))))) # label(fact_1750_abs__leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1740 (all A_109 all B_82 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_109),B_82)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,A_109)),B_82)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,A_109)),B_82))))) # label(fact_1751_abs__leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1741 (all A_109 all B_82 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_109),B_82)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,A_109)),B_82)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,A_109)),B_82))))) # label(fact_1752_abs__leI) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1742 (all A_108 all B_81 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,A_108)),B_81)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,A_108)),B_81)))) # label(fact_1753_abs__le__D2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1743 (all A_108 all B_81 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,A_108)),B_81)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,A_108)),B_81)))) # label(fact_1754_abs__le__D2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1744 (all A_108 all B_81 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,A_108)),B_81)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,A_108)),B_81)))) # label(fact_1755_abs__le__D2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1745 (all Aa (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Aa),ring_1_Ints_real)) -> hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_real_real(uminus_uminus_real,Aa)),ring_1_Ints_real)))) # label(fact_1756_Ints__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1746 (all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(uminus_uminus_int,Aa)),ring_1_Ints_int)))) # label(fact_1757_Ints__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1747 (all Aa (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Aa),ring_1_Ints_rat)) -> hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),ring_1_Ints_rat)))) # label(fact_1758_Ints__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1748 (all Aa (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Aa),ring_1_Ints_complex)) -> hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,hAPP_complex_complex(uminus473333897omplex,Aa)),ring_1_Ints_complex)))) # label(fact_1759_Ints__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1749 (all Z1 all Z2 all W hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Z1),Z2)),W) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z1),W)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z2),W))) # label(fact_1760_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1750 (all Z1 all Z2 all Z3 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z1),Z2)),Z3) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z2),Z3))) # label(fact_1761_real__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1751 (all Aa all Ba (hAPP_rat_rat(uminus_uminus_rat,Aa) = hAPP_rat_rat(uminus_uminus_rat,Ba) <-> Aa = Ba)) # label(fact_1762_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1752 (all Aa all Ba (hAPP_complex_complex(uminus473333897omplex,Aa) = hAPP_complex_complex(uminus473333897omplex,Ba) <-> Aa = Ba)) # label(fact_1763_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1753 (all Aa all Ba (hAPP_real_real(uminus_uminus_real,Aa) = hAPP_real_real(uminus_uminus_real,Ba) <-> Aa = Ba)) # label(fact_1764_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1754 (all Aa all Ba (hAPP_int_int(uminus_uminus_int,Aa) = hAPP_int_int(uminus_uminus_int,Ba) <-> Aa = Ba)) # label(fact_1765_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1755 (all Aa all Ba (hAPP_rat_rat(uminus_uminus_rat,Aa) = Ba <-> hAPP_rat_rat(uminus_uminus_rat,Ba) = Aa)) # label(fact_1766_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1756 (all Aa all Ba (hAPP_complex_complex(uminus473333897omplex,Aa) = Ba <-> hAPP_complex_complex(uminus473333897omplex,Ba) = Aa)) # label(fact_1767_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1757 (all Aa all Ba (hAPP_real_real(uminus_uminus_real,Aa) = Ba <-> hAPP_real_real(uminus_uminus_real,Ba) = Aa)) # label(fact_1768_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1758 (all Aa all Ba (hAPP_int_int(uminus_uminus_int,Aa) = Ba <-> hAPP_int_int(uminus_uminus_int,Ba) = Aa)) # label(fact_1769_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1759 (all Aa all Ba (Aa = hAPP_rat_rat(uminus_uminus_rat,Ba) <-> Ba = hAPP_rat_rat(uminus_uminus_rat,Aa))) # label(fact_1770_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1760 (all Aa all Ba (Aa = hAPP_complex_complex(uminus473333897omplex,Ba) <-> Ba = hAPP_complex_complex(uminus473333897omplex,Aa))) # label(fact_1771_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1761 (all Aa all Ba (Aa = hAPP_real_real(uminus_uminus_real,Ba) <-> Ba = hAPP_real_real(uminus_uminus_real,Aa))) # label(fact_1772_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1762 (all Aa all Ba (Aa = hAPP_int_int(uminus_uminus_int,Ba) <-> Ba = hAPP_int_int(uminus_uminus_int,Aa))) # label(fact_1773_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1763 (all Z_1 all W hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z_1),W) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,W),Z_1)) # label(fact_1774_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1764 (all A_107 hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(uminus_uminus_rat,A_107)) = hAPP_rat_rat(abs_abs_rat,A_107)) # label(fact_1775_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1765 (all A_107 hAPP_real_real(abs_abs_real,hAPP_real_real(uminus_uminus_real,A_107)) = hAPP_real_real(abs_abs_real,A_107)) # label(fact_1776_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1766 (all A_107 hAPP_int_int(abs_abs_int,hAPP_int_int(uminus_uminus_int,A_107)) = hAPP_int_int(abs_abs_int,A_107)) # label(fact_1777_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1767 (all A_106 hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(abs_abs_rat,A_106)) = hAPP_rat_rat(abs_abs_rat,A_106)) # label(fact_1778_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1768 (all A_106 hAPP_real_real(abs_abs_real,hAPP_real_real(abs_abs_real,A_106)) = hAPP_real_real(abs_abs_real,A_106)) # label(fact_1779_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1769 (all A_106 hAPP_int_int(abs_abs_int,hAPP_int_int(abs_abs_int,A_106)) = hAPP_int_int(abs_abs_int,A_106)) # label(fact_1780_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1770 (all Z_1 hAPP_int_int(uminus_uminus_int,hAPP_int_int(uminus_uminus_int,Z_1)) = Z_1) # label(fact_1781_zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1771 (all A_105 hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(uminus_uminus_rat,A_105)) = A_105) # label(fact_1782_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1772 (all A_105 hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(uminus473333897omplex,A_105)) = A_105) # label(fact_1783_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1773 (all A_105 hAPP_real_real(uminus_uminus_real,hAPP_real_real(uminus_uminus_real,A_105)) = A_105) # label(fact_1784_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1774 (all A_105 hAPP_int_int(uminus_uminus_int,hAPP_int_int(uminus_uminus_int,A_105)) = A_105) # label(fact_1785_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1775 (all Z_1 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,one_one_real),Z_1) = Z_1) # label(fact_1786_real__mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1776 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,Aa)),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),Ba)))) # label(fact_1787_abs__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1777 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,Aa)),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,Aa)),Ba)))) # label(fact_1788_abs__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1778 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,Aa)),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,Aa)),Ba)))) # label(fact_1789_abs__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1779 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) | X_1 = Y_2)) # label(fact_1790_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1780 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)) & X_1 != Y_2)) # label(fact_1791_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1781 (all A_104 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(abs_abs_rat,A_104))),zero_zero_rat))) # label(fact_1792_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1782 (all A_104 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(abs_abs_real,A_104))),zero_zero_real))) # label(fact_1793_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1783 (all A_104 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,hAPP_int_int(abs_abs_int,A_104))),zero_zero_int))) # label(fact_1794_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1784 (all A_103 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_103),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,A_103) = hAPP_rat_rat(uminus_uminus_rat,A_103))) # label(fact_1795_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1785 (all A_103 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_103),zero_zero_real)) -> hAPP_real_real(abs_abs_real,A_103) = hAPP_real_real(uminus_uminus_real,A_103))) # label(fact_1796_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1786 (all A_103 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_103),zero_zero_int)) -> hAPP_int_int(abs_abs_int,A_103) = hAPP_int_int(uminus_uminus_int,A_103))) # label(fact_1797_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1787 (all A_102 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_102),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,A_102) = hAPP_rat_rat(uminus_uminus_rat,A_102))) # label(fact_1798_abs__of__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1788 (all A_102 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_102),zero_zero_real)) -> hAPP_real_real(abs_abs_real,A_102) = hAPP_real_real(uminus_uminus_real,A_102))) # label(fact_1799_abs__of__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1789 (all A_102 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_102),zero_zero_int)) -> hAPP_int_int(abs_abs_int,A_102) = hAPP_int_int(uminus_uminus_int,A_102))) # label(fact_1800_abs__of__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1790 (all A_101 ((hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_101),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,A_101) = hAPP_rat_rat(uminus_uminus_rat,A_101)) & (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,A_101),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,A_101) = A_101))) # label(fact_1801_abs__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1791 (all A_101 ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_101),zero_zero_real)) -> hAPP_real_real(abs_abs_real,A_101) = hAPP_real_real(uminus_uminus_real,A_101)) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_101),zero_zero_real)) -> hAPP_real_real(abs_abs_real,A_101) = A_101))) # label(fact_1802_abs__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1792 (all A_101 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_101),zero_zero_int)) -> hAPP_int_int(abs_abs_int,A_101) = hAPP_int_int(uminus_uminus_int,A_101)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_101),zero_zero_int)) -> hAPP_int_int(abs_abs_int,A_101) = A_101))) # label(fact_1803_abs__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1793 (all W_5 all Z_9 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(uminus_uminus_rat,hAPP_int_rat(number_number_of_rat,W_5))),Z_9) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,hAPP_int_int(uminus_uminus_int,W_5))),Z_9)) # label(fact_1807_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1794 (all W_5 all Z_9 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(uminus473333897omplex,hAPP_int_complex(number528085621omplex,W_5))),Z_9) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,hAPP_int_int(uminus_uminus_int,W_5))),Z_9)) # label(fact_1808_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1795 (all W_5 all Z_9 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,hAPP_int_real(number267125858f_real,W_5))),Z_9) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(uminus_uminus_int,W_5))),Z_9)) # label(fact_1809_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1796 (all W_5 all Z_9 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,W_5))),Z_9) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(uminus_uminus_int,W_5))),Z_9)) # label(fact_1810_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1797 (all Z_8 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(number_number_of_rat,min)),Z_8) = hAPP_rat_rat(uminus_uminus_rat,Z_8)) # label(fact_1811_mult__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1798 (all Z_8 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_int_complex(number528085621omplex,min)),Z_8) = hAPP_complex_complex(uminus473333897omplex,Z_8)) # label(fact_1812_mult__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1799 (all Z_8 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,min)),Z_8) = hAPP_real_real(uminus_uminus_real,Z_8)) # label(fact_1813_mult__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1800 (all Z_8 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,min)),Z_8) = hAPP_int_int(uminus_uminus_int,Z_8)) # label(fact_1814_mult__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1801 (all Z_7 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Z_7),hAPP_int_rat(number_number_of_rat,min)) = hAPP_rat_rat(uminus_uminus_rat,Z_7)) # label(fact_1815_mult__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1802 (all Z_7 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_7),hAPP_int_complex(number528085621omplex,min)) = hAPP_complex_complex(uminus473333897omplex,Z_7)) # label(fact_1816_mult__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1803 (all Z_7 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Z_7),hAPP_int_real(number267125858f_real,min)) = hAPP_real_real(uminus_uminus_real,Z_7)) # label(fact_1817_mult__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1804 (all Z_7 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_7),hAPP_int_int(number_number_of_int,min)) = hAPP_int_int(uminus_uminus_int,Z_7)) # label(fact_1818_mult__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1805 (all I ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),zero_zero_int)) -> hAPP_int_int(abs_abs_int,I) = hAPP_int_int(uminus_uminus_int,I)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),zero_zero_int)) -> hAPP_int_int(abs_abs_int,I) = I))) # label(fact_1827_zabs__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1806 (all A_2 hAPP_int_int(div_mod_int(A_2),hAPP_int_int(number_number_of_int,min)) = zero_zero_int) # label(fact_1828_zmod__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1807 (all A_2 all B_1 ((hAPP_int_int(div_mod_int(A_2),B_1) = zero_zero_int -> hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,A_2)),B_1) = zero_zero_int) & (hAPP_int_int(div_mod_int(A_2),B_1) != zero_zero_int -> hAPP_int_int(div_mod_int(hAPP_int_int(uminus_uminus_int,A_2)),B_1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_1),hAPP_int_int(div_mod_int(A_2),B_1))))) # label(fact_1829_zmod__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1808 (all A_2 all B_1 ((hAPP_int_int(div_mod_int(A_2),B_1) = zero_zero_int -> hAPP_int_int(div_mod_int(A_2),hAPP_int_int(uminus_uminus_int,B_1)) = zero_zero_int) & (hAPP_int_int(div_mod_int(A_2),B_1) != zero_zero_int -> hAPP_int_int(div_mod_int(A_2),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(div_mod_int(A_2),B_1)),B_1)))) # label(fact_1830_zmod__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1809 (all Z_2 (hAPP_int_int(abs_abs_int,Z_2) = one_one_int <-> Z_2 = one_one_int | Z_2 = hAPP_int_int(number_number_of_int,min))) # label(fact_1831_abs__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1810 (all A_100 hAPP_Q1762011733de_int(div_mo231679042de_int(zero_z891286103de_int),A_100) = zero_z891286103de_int) # label(fact_1832_mod__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1811 (all A_100 hAPP_C498520661umeral(div_mo1740067990umeral(zero_z126310315umeral),A_100) = zero_z126310315umeral) # label(fact_1833_mod__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1812 (all A_100 hAPP_nat_nat(div_mod_nat(zero_zero_nat),A_100) = zero_zero_nat) # label(fact_1834_mod__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1813 (all A_100 hAPP_int_int(div_mod_int(zero_zero_int),A_100) = zero_zero_int) # label(fact_1835_mod__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1814 (all A_99 hAPP_Q1762011733de_int(div_mo231679042de_int(A_99),zero_z891286103de_int) = A_99) # label(fact_1836_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1815 (all A_99 hAPP_C498520661umeral(div_mo1740067990umeral(A_99),zero_z126310315umeral) = A_99) # label(fact_1837_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1816 (all A_99 hAPP_nat_nat(div_mod_nat(A_99),zero_zero_nat) = A_99) # label(fact_1838_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1817 (all A_99 hAPP_int_int(div_mod_int(A_99),zero_zero_int) = A_99) # label(fact_1839_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1818 (all A_98 hAPP_Q1762011733de_int(div_mo231679042de_int(A_98),A_98) = zero_z891286103de_int) # label(fact_1840_mod__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1819 (all A_98 hAPP_C498520661umeral(div_mo1740067990umeral(A_98),A_98) = zero_z126310315umeral) # label(fact_1841_mod__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1820 (all A_98 hAPP_nat_nat(div_mod_nat(A_98),A_98) = zero_zero_nat) # label(fact_1842_mod__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1821 (all A_98 hAPP_int_int(div_mod_int(A_98),A_98) = zero_zero_int) # label(fact_1843_mod__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1822 (all Aa (hAPP_rat_rat(abs_abs_rat,Aa) = zero_zero_rat <-> Aa = zero_zero_rat)) # label(fact_1844_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1823 (all Aa (hAPP_real_real(abs_abs_real,Aa) = zero_zero_real <-> Aa = zero_zero_real)) # label(fact_1845_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1824 (all Aa (hAPP_int_int(abs_abs_int,Aa) = zero_zero_int <-> Aa = zero_zero_int)) # label(fact_1846_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1825 (all A_97 all B_80 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,A_97)),B_80)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_97),B_80)))) # label(fact_1850_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1826 (all A_97 all B_80 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,A_97)),B_80)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_97),B_80)))) # label(fact_1851_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1827 (all A_97 all B_80 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,A_97)),B_80)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_97),B_80)))) # label(fact_1852_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1828 (all A_96 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_96),hAPP_rat_rat(abs_abs_rat,A_96)))) # label(fact_1853_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1829 (all A_96 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_96),hAPP_real_real(abs_abs_real,A_96)))) # label(fact_1854_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1830 (all A_96 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_96),hAPP_int_int(abs_abs_int,A_96)))) # label(fact_1855_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1831 (all B_79 all B_78 all A_95 all C_35 all A_94 (hAPP_Q1762011733de_int(div_mo231679042de_int(A_95),C_35) = hAPP_Q1762011733de_int(div_mo231679042de_int(A_94),C_35) -> (hAPP_Q1762011733de_int(div_mo231679042de_int(B_79),C_35) = hAPP_Q1762011733de_int(div_mo231679042de_int(B_78),C_35) -> hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_95),B_79)),C_35) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_94),B_78)),C_35)))) # label(fact_1856_mod__mult__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1832 (all B_79 all B_78 all A_95 all C_35 all A_94 (hAPP_C498520661umeral(div_mo1740067990umeral(A_95),C_35) = hAPP_C498520661umeral(div_mo1740067990umeral(A_94),C_35) -> (hAPP_C498520661umeral(div_mo1740067990umeral(B_79),C_35) = hAPP_C498520661umeral(div_mo1740067990umeral(B_78),C_35) -> hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_95),B_79)),C_35) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_94),B_78)),C_35)))) # label(fact_1857_mod__mult__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1833 (all B_79 all B_78 all A_95 all C_35 all A_94 (hAPP_nat_nat(div_mod_nat(A_95),C_35) = hAPP_nat_nat(div_mod_nat(A_94),C_35) -> (hAPP_nat_nat(div_mod_nat(B_79),C_35) = hAPP_nat_nat(div_mod_nat(B_78),C_35) -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_95),B_79)),C_35) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_94),B_78)),C_35)))) # label(fact_1858_mod__mult__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1834 (all B_79 all B_78 all A_95 all C_35 all A_94 (hAPP_int_int(div_mod_int(A_95),C_35) = hAPP_int_int(div_mod_int(A_94),C_35) -> (hAPP_int_int(div_mod_int(B_79),C_35) = hAPP_int_int(div_mod_int(B_78),C_35) -> hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_95),B_79)),C_35) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_94),B_78)),C_35)))) # label(fact_1859_mod__mult__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1835 (all A_93 all C_34 all B_77 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_93),C_34)),B_77)),C_34) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_93),B_77)),C_34)) # label(fact_1860_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1836 (all A_93 all C_34 all B_77 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_93),C_34)),B_77)),C_34) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_93),B_77)),C_34)) # label(fact_1861_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1837 (all A_93 all C_34 all B_77 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(div_mod_nat(A_93),C_34)),B_77)),C_34) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_93),B_77)),C_34)) # label(fact_1862_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1838 (all A_93 all C_34 all B_77 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(div_mod_int(A_93),C_34)),B_77)),C_34) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_93),B_77)),C_34)) # label(fact_1863_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1839 (all A_92 all C_33 all B_76 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_92),C_33)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_76),C_33)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_92),B_76)),C_33)) # label(fact_1864_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1840 (all A_92 all C_33 all B_76 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_92),C_33)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_76),C_33)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_92),B_76)),C_33)) # label(fact_1865_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1841 (all A_92 all C_33 all B_76 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_92),C_33)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_76),C_33)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(div_mod_nat(A_92),B_76)),C_33)) # label(fact_1866_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1842 (all A_92 all C_33 all B_76 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_92),C_33)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_76),C_33)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(div_mod_int(A_92),B_76)),C_33)) # label(fact_1867_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1843 (all C_32 all A_91 all B_75 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_32),A_91)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_32),B_75)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_32),hAPP_Q1762011733de_int(div_mo231679042de_int(A_91),B_75))) # label(fact_1868_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1844 (all C_32 all A_91 all B_75 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_32),A_91)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_32),B_75)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_32),hAPP_C498520661umeral(div_mo1740067990umeral(A_91),B_75))) # label(fact_1869_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1845 (all C_32 all A_91 all B_75 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_32),A_91)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_32),B_75)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_32),hAPP_nat_nat(div_mod_nat(A_91),B_75))) # label(fact_1870_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1846 (all C_32 all A_91 all B_75 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_32),A_91)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_32),B_75)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_32),hAPP_int_int(div_mod_int(A_91),B_75))) # label(fact_1871_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1847 (all A_90 all B_74 all C_31 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_90),B_74)),C_31) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_90),C_31)),hAPP_Q1762011733de_int(div_mo231679042de_int(B_74),C_31))),C_31)) # label(fact_1872_mod__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1848 (all A_90 all B_74 all C_31 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_90),B_74)),C_31) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_90),C_31)),hAPP_C498520661umeral(div_mo1740067990umeral(B_74),C_31))),C_31)) # label(fact_1873_mod__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1849 (all A_90 all B_74 all C_31 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_90),B_74)),C_31) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(div_mod_nat(A_90),C_31)),hAPP_nat_nat(div_mod_nat(B_74),C_31))),C_31)) # label(fact_1874_mod__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1850 (all A_90 all B_74 all C_31 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_90),B_74)),C_31) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(div_mod_int(A_90),C_31)),hAPP_int_int(div_mod_int(B_74),C_31))),C_31)) # label(fact_1875_mod__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1851 (all A_89 all B_73 all C_30 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_89),B_73)),C_30) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_89),C_30)),B_73)),C_30)) # label(fact_1876_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1852 (all A_89 all B_73 all C_30 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_89),B_73)),C_30) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_89),C_30)),B_73)),C_30)) # label(fact_1877_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1853 (all A_89 all B_73 all C_30 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_89),B_73)),C_30) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(div_mod_nat(A_89),C_30)),B_73)),C_30)) # label(fact_1878_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1854 (all A_89 all B_73 all C_30 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_89),B_73)),C_30) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(div_mod_int(A_89),C_30)),B_73)),C_30)) # label(fact_1879_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1855 (all A_88 all B_72 all C_29 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_88),B_72)),C_29) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_88),hAPP_Q1762011733de_int(div_mo231679042de_int(B_72),C_29))),C_29)) # label(fact_1880_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1856 (all A_88 all B_72 all C_29 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_88),B_72)),C_29) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_88),hAPP_C498520661umeral(div_mo1740067990umeral(B_72),C_29))),C_29)) # label(fact_1881_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1857 (all A_88 all B_72 all C_29 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_88),B_72)),C_29) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_88),hAPP_nat_nat(div_mod_nat(B_72),C_29))),C_29)) # label(fact_1882_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1858 (all A_88 all B_72 all C_29 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_88),B_72)),C_29) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_88),hAPP_int_int(div_mod_int(B_72),C_29))),C_29)) # label(fact_1883_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1859 (all B_71 all B_70 all A_87 all C_28 all A_86 (hAPP_Q1762011733de_int(div_mo231679042de_int(A_87),C_28) = hAPP_Q1762011733de_int(div_mo231679042de_int(A_86),C_28) -> (hAPP_Q1762011733de_int(div_mo231679042de_int(B_71),C_28) = hAPP_Q1762011733de_int(div_mo231679042de_int(B_70),C_28) -> hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_87),B_71)),C_28) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_86),B_70)),C_28)))) # label(fact_1884_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1860 (all B_71 all B_70 all A_87 all C_28 all A_86 (hAPP_C498520661umeral(div_mo1740067990umeral(A_87),C_28) = hAPP_C498520661umeral(div_mo1740067990umeral(A_86),C_28) -> (hAPP_C498520661umeral(div_mo1740067990umeral(B_71),C_28) = hAPP_C498520661umeral(div_mo1740067990umeral(B_70),C_28) -> hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_87),B_71)),C_28) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_86),B_70)),C_28)))) # label(fact_1885_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.72 1861 (all B_71 all B_70 all A_87 all C_28 all A_86 (hAPP_nat_nat(div_mod_nat(A_87),C_28) = hAPP_nat_nat(div_mod_nat(A_86),C_28) -> (hAPP_nat_nat(div_mod_nat(B_71),C_28) = hAPP_nat_nat(div_mod_nat(B_70),C_28) -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_87),B_71)),C_28) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_86),B_70)),C_28)))) # label(fact_1886_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1862 (all B_71 all B_70 all A_87 all C_28 all A_86 (hAPP_int_int(div_mod_int(A_87),C_28) = hAPP_int_int(div_mod_int(A_86),C_28) -> (hAPP_int_int(div_mod_int(B_71),C_28) = hAPP_int_int(div_mod_int(B_70),C_28) -> hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_87),B_71)),C_28) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_86),B_70)),C_28)))) # label(fact_1887_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1863 (all A_85 all C_27 all B_69 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_85),C_27)),B_69)),C_27) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_85),B_69)),C_27)) # label(fact_1888_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1864 (all A_85 all C_27 all B_69 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_85),C_27)),B_69)),C_27) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_85),B_69)),C_27)) # label(fact_1889_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1865 (all A_85 all C_27 all B_69 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(div_mod_nat(A_85),C_27)),B_69)),C_27) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_85),B_69)),C_27)) # label(fact_1890_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1866 (all A_85 all C_27 all B_69 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(div_mod_int(A_85),C_27)),B_69)),C_27) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_85),B_69)),C_27)) # label(fact_1891_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1867 (all A_84 all B_68 all C_26 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_84),hAPP_Q1762011733de_int(div_mo231679042de_int(B_68),C_26))),C_26) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_84),B_68)),C_26)) # label(fact_1892_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1868 (all A_84 all B_68 all C_26 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_84),hAPP_C498520661umeral(div_mo1740067990umeral(B_68),C_26))),C_26) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_84),B_68)),C_26)) # label(fact_1893_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1869 (all A_84 all B_68 all C_26 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_84),hAPP_nat_nat(div_mod_nat(B_68),C_26))),C_26) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_84),B_68)),C_26)) # label(fact_1894_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1870 (all A_84 all B_68 all C_26 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_84),hAPP_int_int(div_mod_int(B_68),C_26))),C_26) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_84),B_68)),C_26)) # label(fact_1895_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1871 (all A_83 all B_67 all C_25 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_83),B_67)),C_25) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_83),C_25)),hAPP_Q1762011733de_int(div_mo231679042de_int(B_67),C_25))),C_25)) # label(fact_1896_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1872 (all A_83 all B_67 all C_25 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_83),B_67)),C_25) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_83),C_25)),hAPP_C498520661umeral(div_mo1740067990umeral(B_67),C_25))),C_25)) # label(fact_1897_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1873 (all A_83 all B_67 all C_25 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_83),B_67)),C_25) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(div_mod_nat(A_83),C_25)),hAPP_nat_nat(div_mod_nat(B_67),C_25))),C_25)) # label(fact_1898_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1874 (all A_83 all B_67 all C_25 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_67)),C_25) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(div_mod_int(A_83),C_25)),hAPP_int_int(div_mod_int(B_67),C_25))),C_25)) # label(fact_1899_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1875 (all A_82 all B_66 all C_24 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_82),B_66)),C_24) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_82),C_24)),B_66)),C_24)) # label(fact_1900_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1876 (all A_82 all B_66 all C_24 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_82),B_66)),C_24) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_82),C_24)),B_66)),C_24)) # label(fact_1901_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1877 (all A_82 all B_66 all C_24 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_82),B_66)),C_24) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(div_mod_nat(A_82),C_24)),B_66)),C_24)) # label(fact_1902_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1878 (all A_82 all B_66 all C_24 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_82),B_66)),C_24) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(div_mod_int(A_82),C_24)),B_66)),C_24)) # label(fact_1903_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1879 (all A_81 all B_65 all C_23 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_81),B_65)),C_23) = hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_81),hAPP_Q1762011733de_int(div_mo231679042de_int(B_65),C_23))),C_23)) # label(fact_1904_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1880 (all A_81 all B_65 all C_23 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_81),B_65)),C_23) = hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_81),hAPP_C498520661umeral(div_mo1740067990umeral(B_65),C_23))),C_23)) # label(fact_1905_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1881 (all A_81 all B_65 all C_23 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_81),B_65)),C_23) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_81),hAPP_nat_nat(div_mod_nat(B_65),C_23))),C_23)) # label(fact_1906_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1882 (all A_81 all B_65 all C_23 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_81),B_65)),C_23) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_81),hAPP_int_int(div_mod_int(B_65),C_23))),C_23)) # label(fact_1907_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1883 (all B_64 all A_80 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_64),A_80)),B_64) = hAPP_Q1762011733de_int(div_mo231679042de_int(A_80),B_64)) # label(fact_1908_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1884 (all B_64 all A_80 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,B_64),A_80)),B_64) = hAPP_C498520661umeral(div_mo1740067990umeral(A_80),B_64)) # label(fact_1909_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1885 (all B_64 all A_80 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_64),A_80)),B_64) = hAPP_nat_nat(div_mod_nat(A_80),B_64)) # label(fact_1910_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1886 (all B_64 all A_80 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_64),A_80)),B_64) = hAPP_int_int(div_mod_int(A_80),B_64)) # label(fact_1911_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1887 (all A_79 all B_63 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_79),B_63)),B_63) = hAPP_Q1762011733de_int(div_mo231679042de_int(A_79),B_63)) # label(fact_1912_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1888 (all A_79 all B_63 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_79),B_63)),B_63) = hAPP_C498520661umeral(div_mo1740067990umeral(A_79),B_63)) # label(fact_1913_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1889 (all A_79 all B_63 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_79),B_63)),B_63) = hAPP_nat_nat(div_mod_nat(A_79),B_63)) # label(fact_1914_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1890 (all A_79 all B_63 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_79),B_63)),B_63) = hAPP_int_int(div_mod_int(A_79),B_63)) # label(fact_1915_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1891 (all A_78 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(abs_abs_rat,A_78)),hAPP_rat_rat(abs_abs_rat,A_78)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_78),A_78)) # label(fact_1916_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1892 (all A_78 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(abs_abs_real,A_78)),hAPP_real_real(abs_abs_real,A_78)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_78),A_78)) # label(fact_1917_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1893 (all A_78 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,A_78)),hAPP_int_int(abs_abs_int,A_78)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_78),A_78)) # label(fact_1918_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1894 (all A_77 all B_62 hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_77),B_62)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(abs_abs_rat,A_77)),hAPP_rat_rat(abs_abs_rat,B_62))) # label(fact_1919_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1895 (all A_77 all B_62 hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_77),B_62)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(abs_abs_real,A_77)),hAPP_real_real(abs_abs_real,B_62))) # label(fact_1920_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1896 (all A_77 all B_62 hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_77),B_62)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,A_77)),hAPP_int_int(abs_abs_int,B_62))) # label(fact_1921_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1897 (all A_76 all B_61 hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(abs_abs_rat,A_76)),hAPP_rat_rat(abs_abs_rat,B_61))) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(abs_abs_rat,A_76)),hAPP_rat_rat(abs_abs_rat,B_61))) # label(fact_1922_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1898 (all A_76 all B_61 hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(abs_abs_real,A_76)),hAPP_real_real(abs_abs_real,B_61))) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(abs_abs_real,A_76)),hAPP_real_real(abs_abs_real,B_61))) # label(fact_1923_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1899 (all A_76 all B_61 hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,A_76)),hAPP_int_int(abs_abs_int,B_61))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,A_76)),hAPP_int_int(abs_abs_int,B_61))) # label(fact_1924_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1900 (all B_60 all B_59 all A_75 all C_22 all A_74 (hAPP_int_int(div_mod_int(A_75),C_22) = hAPP_int_int(div_mod_int(A_74),C_22) -> (hAPP_int_int(div_mod_int(B_60),C_22) = hAPP_int_int(div_mod_int(B_59),C_22) -> hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_75),B_60)),C_22) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_74),B_59)),C_22)))) # label(fact_1925_mod__diff__cong) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1901 (all A_73 all B_58 all C_21 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_73),B_58)),C_21) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(div_mod_int(A_73),C_21)),hAPP_int_int(div_mod_int(B_58),C_21))),C_21)) # label(fact_1926_mod__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1902 (all A_72 all B_57 all C_20 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_72),B_57)),C_20) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(div_mod_int(A_72),C_20)),B_57)),C_20)) # label(fact_1927_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1903 (all A_71 all B_56 all C_19 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_71),B_56)),C_19) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_71),hAPP_int_int(div_mod_int(B_56),C_19))),C_19)) # label(fact_1928_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1904 (all A_70 all B_55 hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_70),B_55)) = hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,B_55),A_70))) # label(fact_1932_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1905 (all A_70 all B_55 hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_70),B_55)) = hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_55),A_70))) # label(fact_1933_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1906 (all A_70 all B_55 hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_70),B_55)) = hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_55),A_70))) # label(fact_1934_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1907 (all X_16 archim1246769320r_real(hAPP_real_real(uminus_uminus_real,X_16)) = hAPP_int_int(uminus_uminus_int,archim856651990g_real(X_16))) # label(fact_1935_floor__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1908 (all X_16 archim791455193or_rat(hAPP_rat_rat(uminus_uminus_rat,X_16)) = hAPP_int_int(uminus_uminus_int,archim1419379755ng_rat(X_16))) # label(fact_1936_floor__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1909 (all X_15 archim856651990g_real(hAPP_real_real(uminus_uminus_real,X_15)) = hAPP_int_int(uminus_uminus_int,archim1246769320r_real(X_15))) # label(fact_1937_ceiling__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1910 (all X_15 archim1419379755ng_rat(hAPP_rat_rat(uminus_uminus_rat,X_15)) = hAPP_int_int(uminus_uminus_int,archim791455193or_rat(X_15))) # label(fact_1938_ceiling__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1911 (all X_14 archim856651990g_real(X_14) = hAPP_int_int(uminus_uminus_int,archim1246769320r_real(hAPP_real_real(uminus_uminus_real,X_14)))) # label(fact_1939_ceiling__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1912 (all X_14 archim1419379755ng_rat(X_14) = hAPP_int_int(uminus_uminus_int,archim791455193or_rat(hAPP_rat_rat(uminus_uminus_rat,X_14)))) # label(fact_1940_ceiling__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1913 (all Aa (hAPP_rat_rat(uminus_uminus_rat,Aa) = Aa <-> Aa = zero_zero_rat)) # label(fact_1941_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1914 (all Aa (hAPP_real_real(uminus_uminus_real,Aa) = Aa <-> Aa = zero_zero_real)) # label(fact_1942_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1915 (all Aa (hAPP_int_int(uminus_uminus_int,Aa) = Aa <-> Aa = zero_zero_int)) # label(fact_1943_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1916 (all Aa (hAPP_rat_rat(uminus_uminus_rat,Aa) = zero_zero_rat <-> Aa = zero_zero_rat)) # label(fact_1944_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1917 (all Aa (hAPP_complex_complex(uminus473333897omplex,Aa) = zero_zero_complex <-> Aa = zero_zero_complex)) # label(fact_1945_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1918 (all Aa (hAPP_real_real(uminus_uminus_real,Aa) = zero_zero_real <-> Aa = zero_zero_real)) # label(fact_1946_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1919 (all Aa (hAPP_int_int(uminus_uminus_int,Aa) = zero_zero_int <-> Aa = zero_zero_int)) # label(fact_1947_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1920 (all Aa (Aa = hAPP_rat_rat(uminus_uminus_rat,Aa) <-> Aa = zero_zero_rat)) # label(fact_1948_equal__neg__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1921 (all Aa (Aa = hAPP_real_real(uminus_uminus_real,Aa) <-> Aa = zero_zero_real)) # label(fact_1949_equal__neg__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1922 (all Aa (Aa = hAPP_int_int(uminus_uminus_int,Aa) <-> Aa = zero_zero_int)) # label(fact_1950_equal__neg__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1923 (all Aa (zero_zero_rat = hAPP_rat_rat(uminus_uminus_rat,Aa) <-> zero_zero_rat = Aa)) # label(fact_1951_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1924 (all Aa (zero_zero_complex = hAPP_complex_complex(uminus473333897omplex,Aa) <-> zero_zero_complex = Aa)) # label(fact_1952_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1925 (all Aa (zero_zero_real = hAPP_real_real(uminus_uminus_real,Aa) <-> zero_zero_real = Aa)) # label(fact_1953_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1926 (all Aa (zero_zero_int = hAPP_int_int(uminus_uminus_int,Aa) <-> zero_zero_int = Aa)) # label(fact_1954_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1927 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(uminus407446779t_bool,Y_2)),X_1)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(uminus407446779t_bool,X_1)),Y_2)))) # label(fact_1959_compl__le__swap2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1928 (all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(uminus1024588959t_bool,Y_2)),X_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(uminus1024588959t_bool,X_1)),Y_2)))) # label(fact_1960_compl__le__swap2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1929 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),hAPP_f1805168059t_bool(uminus407446779t_bool,X_1))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),hAPP_f1805168059t_bool(uminus407446779t_bool,Y_2))))) # label(fact_1961_compl__le__swap1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1930 (all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),hAPP_f800510211t_bool(uminus1024588959t_bool,X_1))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),hAPP_f800510211t_bool(uminus1024588959t_bool,Y_2))))) # label(fact_1962_compl__le__swap1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1931 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_2)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(uminus407446779t_bool,Y_2)),hAPP_f1805168059t_bool(uminus407446779t_bool,X_1))))) # label(fact_1963_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1932 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(uminus1024588959t_bool,Y_2)),hAPP_f800510211t_bool(uminus1024588959t_bool,X_1))))) # label(fact_1964_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1933 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(uminus407446779t_bool,X_1)),hAPP_f1805168059t_bool(uminus407446779t_bool,Y_2))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_2),X_1)))) # label(fact_1965_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1934 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(uminus1024588959t_bool,X_1)),hAPP_f800510211t_bool(uminus1024588959t_bool,Y_2))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_1)))) # label(fact_1966_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1935 (all A_69 all B_54 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_69),B_54)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,B_54)),hAPP_rat_rat(uminus_uminus_rat,A_69))))) # label(fact_1967_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1936 (all A_69 all B_54 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_69),B_54)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,B_54)),hAPP_real_real(uminus_uminus_real,A_69))))) # label(fact_1968_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1937 (all A_69 all B_54 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_69),B_54)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,B_54)),hAPP_int_int(uminus_uminus_int,A_69))))) # label(fact_1969_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1938 (all Ba all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,Ba)),hAPP_rat_rat(uminus_uminus_rat,Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),Ba)))) # label(fact_1970_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1939 (all Ba all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,Ba)),hAPP_real_real(uminus_uminus_real,Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)))) # label(fact_1971_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1940 (all Ba all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,Ba)),hAPP_int_int(uminus_uminus_int,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba)))) # label(fact_1972_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1941 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,Ba)),Aa)))) # label(fact_1973_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1942 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,Aa)),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,Ba)),Aa)))) # label(fact_1974_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1943 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,Aa)),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,Ba)),Aa)))) # label(fact_1975_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1944 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),hAPP_rat_rat(uminus_uminus_rat,Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Ba),hAPP_rat_rat(uminus_uminus_rat,Aa))))) # label(fact_1976_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1945 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),hAPP_real_real(uminus_uminus_real,Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Ba),hAPP_real_real(uminus_uminus_real,Aa))))) # label(fact_1977_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1946 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),hAPP_int_int(uminus_uminus_int,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),hAPP_int_int(uminus_uminus_int,Aa))))) # label(fact_1978_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1947 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,hAPP_f1805168059t_bool(uminus407446779t_bool,Y_2)),X_1)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,hAPP_f1805168059t_bool(uminus407446779t_bool,X_1)),Y_2)))) # label(fact_1979_compl__less__swap2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1948 (all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(uminus1024588959t_bool,Y_2)),X_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(uminus1024588959t_bool,X_1)),Y_2)))) # label(fact_1980_compl__less__swap2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1949 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),hAPP_f1805168059t_bool(uminus407446779t_bool,X_1))) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,X_1),hAPP_f1805168059t_bool(uminus407446779t_bool,Y_2))))) # label(fact_1981_compl__less__swap1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1950 (all Y_2 all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),hAPP_f800510211t_bool(uminus1024588959t_bool,X_1))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),hAPP_f800510211t_bool(uminus1024588959t_bool,Y_2))))) # label(fact_1982_compl__less__swap1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1951 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,hAPP_f1805168059t_bool(uminus407446779t_bool,X_1)),hAPP_f1805168059t_bool(uminus407446779t_bool,Y_2))) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,Y_2),X_1)))) # label(fact_1983_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1952 (all X_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(uminus1024588959t_bool,X_1)),hAPP_f800510211t_bool(uminus1024588959t_bool,Y_2))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_1)))) # label(fact_1984_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1953 (all Ba all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(uminus_uminus_rat,Ba)),hAPP_rat_rat(uminus_uminus_rat,Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),Ba)))) # label(fact_1985_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1954 (all Ba all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,Ba)),hAPP_real_real(uminus_uminus_real,Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)))) # label(fact_1986_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1955 (all Ba all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,Ba)),hAPP_int_int(uminus_uminus_int,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)))) # label(fact_1987_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1956 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),Ba)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(uminus_uminus_rat,Ba)),Aa)))) # label(fact_1988_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1957 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,Aa)),Ba)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,Ba)),Aa)))) # label(fact_1989_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1958 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,Aa)),Ba)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,Ba)),Aa)))) # label(fact_1990_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1959 (all Aa all Ba (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),hAPP_rat_rat(uminus_uminus_rat,Ba))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Ba),hAPP_rat_rat(uminus_uminus_rat,Aa))))) # label(fact_1991_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1960 (all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),hAPP_real_real(uminus_uminus_real,Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),hAPP_real_real(uminus_uminus_real,Aa))))) # label(fact_1992_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1961 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(uminus_uminus_int,Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),hAPP_int_int(uminus_uminus_int,Aa))))) # label(fact_1993_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1962 (all Aa all Ba (hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),Aa) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Ba),Ba) <-> Aa = Ba | Aa = hAPP_rat_rat(uminus_uminus_rat,Ba))) # label(fact_1994_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1963 (all Aa all Ba (hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Aa),Aa) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Ba),Ba) <-> Aa = Ba | Aa = hAPP_complex_complex(uminus473333897omplex,Ba))) # label(fact_1995_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1964 (all Aa all Ba (hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),Aa) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Ba),Ba) <-> Aa = Ba | Aa = hAPP_real_real(uminus_uminus_real,Ba))) # label(fact_1996_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1965 (all Aa all Ba (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),Aa) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),Ba) <-> Aa = Ba | Aa = hAPP_int_int(uminus_uminus_int,Ba))) # label(fact_1997_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1966 (all A_68 all B_53 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(uminus_uminus_rat,A_68)),hAPP_rat_rat(uminus_uminus_rat,B_53)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_68),B_53)) # label(fact_1998_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1967 (all A_68 all B_53 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(uminus473333897omplex,A_68)),hAPP_complex_complex(uminus473333897omplex,B_53)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_68),B_53)) # label(fact_1999_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1968 (all A_68 all B_53 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,A_68)),hAPP_real_real(uminus_uminus_real,B_53)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_68),B_53)) # label(fact_2000_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1969 (all A_68 all B_53 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(uminus_uminus_int,A_68)),hAPP_int_int(uminus_uminus_int,B_53)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_68),B_53)) # label(fact_2001_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1970 (all A_67 all B_52 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(uminus_uminus_rat,A_67)),B_52) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_67),hAPP_rat_rat(uminus_uminus_rat,B_52))) # label(fact_2002_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1971 (all A_67 all B_52 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(uminus473333897omplex,A_67)),B_52) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_67),hAPP_complex_complex(uminus473333897omplex,B_52))) # label(fact_2003_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1972 (all A_67 all B_52 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,A_67)),B_52) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_67),hAPP_real_real(uminus_uminus_real,B_52))) # label(fact_2004_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1973 (all A_67 all B_52 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(uminus_uminus_int,A_67)),B_52) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_67),hAPP_int_int(uminus_uminus_int,B_52))) # label(fact_2005_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1974 (all X_13 all Y_11 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(uminus473333897omplex,X_13)),Y_11) = hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_13),Y_11))) # label(fact_2006_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1975 (all X_13 all Y_11 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,X_13)),Y_11) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_13),Y_11))) # label(fact_2007_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1976 (all A_66 all B_51 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(uminus473333897omplex,A_66)),B_51) = hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_66),B_51))) # label(fact_2008_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1977 (all A_66 all B_51 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,A_66)),B_51) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_66),B_51))) # label(fact_2009_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1978 (all Xa_3 all X_12 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_3),hAPP_complex_complex(uminus473333897omplex,X_12)) = hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Xa_3),X_12))) # label(fact_2010_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1979 (all Xa_3 all X_12 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_3),hAPP_real_real(uminus_uminus_real,X_12)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Xa_3),X_12))) # label(fact_2011_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1980 (all A_65 all B_50 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_65),hAPP_complex_complex(uminus473333897omplex,B_50)) = hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_65),B_50))) # label(fact_2012_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1981 (all A_65 all B_50 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_65),hAPP_real_real(uminus_uminus_real,B_50)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_65),B_50))) # label(fact_2013_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1982 (all A_64 all B_49 hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_64),B_49)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(uminus_uminus_rat,A_64)),B_49)) # label(fact_2014_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1983 (all A_64 all B_49 hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_64),B_49)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(uminus473333897omplex,A_64)),B_49)) # label(fact_2015_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1984 (all A_64 all B_49 hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_64),B_49)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,A_64)),B_49)) # label(fact_2016_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1985 (all A_64 all B_49 hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_64),B_49)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(uminus_uminus_int,A_64)),B_49)) # label(fact_2017_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1986 (all A_63 all B_48 hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_63),B_48)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_63),hAPP_rat_rat(uminus_uminus_rat,B_48))) # label(fact_2018_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1987 (all A_63 all B_48 hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_63),B_48)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_63),hAPP_complex_complex(uminus473333897omplex,B_48))) # label(fact_2019_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1988 (all A_63 all B_48 hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_63),B_48)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_63),hAPP_real_real(uminus_uminus_real,B_48))) # label(fact_2020_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1989 (all A_63 all B_48 hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_63),B_48)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_63),hAPP_int_int(uminus_uminus_int,B_48))) # label(fact_2021_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1990 (all A_62 all B_47 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(uminus_uminus_rat,A_62)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_62),B_47)) = B_47) # label(fact_2022_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1991 (all A_62 all B_47 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(uminus473333897omplex,A_62)),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_62),B_47)) = B_47) # label(fact_2023_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1992 (all A_62 all B_47 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(uminus_uminus_real,A_62)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_62),B_47)) = B_47) # label(fact_2024_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1993 (all A_62 all B_47 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,A_62)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_62),B_47)) = B_47) # label(fact_2025_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1994 (all A_61 all B_46 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_61),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(uminus_uminus_rat,A_61)),B_46)) = B_46) # label(fact_2026_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1995 (all A_61 all B_46 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_61),hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(uminus473333897omplex,A_61)),B_46)) = B_46) # label(fact_2027_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1996 (all A_61 all B_46 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_61),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(uminus_uminus_real,A_61)),B_46)) = B_46) # label(fact_2028_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1997 (all A_61 all B_46 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_61),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,A_61)),B_46)) = B_46) # label(fact_2029_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1998 (all A_60 all B_45 hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_60),B_45)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(uminus_uminus_rat,B_45)),hAPP_rat_rat(uminus_uminus_rat,A_60))) # label(fact_2030_minus__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 1999 (all A_60 all B_45 hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_60),B_45)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(uminus473333897omplex,B_45)),hAPP_complex_complex(uminus473333897omplex,A_60))) # label(fact_2031_minus__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2000 (all A_60 all B_45 hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_60),B_45)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(uminus_uminus_real,B_45)),hAPP_real_real(uminus_uminus_real,A_60))) # label(fact_2032_minus__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2001 (all A_60 all B_45 hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_60),B_45)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,B_45)),hAPP_int_int(uminus_uminus_int,A_60))) # label(fact_2033_minus__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2002 (all A_59 all B_44 hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_59),B_44)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(uminus_uminus_rat,A_59)),hAPP_rat_rat(uminus_uminus_rat,B_44))) # label(fact_2034_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2003 (all A_59 all B_44 hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_59),B_44)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(uminus473333897omplex,A_59)),hAPP_complex_complex(uminus473333897omplex,B_44))) # label(fact_2035_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2004 (all A_59 all B_44 hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_59),B_44)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(uminus_uminus_real,A_59)),hAPP_real_real(uminus_uminus_real,B_44))) # label(fact_2036_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2005 (all A_59 all B_44 hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_59),B_44)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,A_59)),hAPP_int_int(uminus_uminus_int,B_44))) # label(fact_2037_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2006 (all A_2 hAPP_int_int(div_mod_int(A_2),A_2) = zero_zero_int) # label(fact_2038_zmod__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2007 (all B_1 hAPP_int_int(div_mod_int(zero_zero_int),B_1) = zero_zero_int) # label(fact_2039_zmod__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2008 (all A_58 all B_43 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(uminus_uminus_rat,A_58)),hAPP_rat_rat(uminus_uminus_rat,B_43)) = hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_58),B_43))) # label(fact_2040_minus__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2009 (all A_58 all B_43 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(uminus473333897omplex,A_58)),hAPP_complex_complex(uminus473333897omplex,B_43)) = hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_58),B_43))) # label(fact_2041_minus__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2010 (all A_58 all B_43 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(uminus_uminus_real,A_58)),hAPP_real_real(uminus_uminus_real,B_43)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_58),B_43))) # label(fact_2042_minus__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2011 (all A_58 all B_43 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(uminus_uminus_int,A_58)),hAPP_int_int(uminus_uminus_int,B_43)) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_58),B_43))) # label(fact_2043_minus__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2012 (all A_57 all B_42 hAPP_rat_rat(uminus_uminus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_57),B_42)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,B_42),A_57)) # label(fact_2044_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2013 (all A_57 all B_42 hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_57),B_42)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,B_42),A_57)) # label(fact_2045_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2014 (all A_57 all B_42 hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_57),B_42)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_42),A_57)) # label(fact_2046_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2015 (all A_57 all B_42 hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_57),B_42)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_42),A_57)) # label(fact_2047_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2016 (all A_2 all B_1 all C_1 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(div_mod_int(B_1),C_1))),C_1) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)),C_1)) # label(fact_2048_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2017 (all A_2 all B_1 all C_1 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)),C_1) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(div_mod_int(B_1),C_1))),C_1)) # label(fact_2049_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2018 (all X all M_1 all Y hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(div_mod_int(X),M_1)),Y)),M_1) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)),M_1)) # label(fact_2051_zdiff__zmod__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2019 (all X all Y all M_1 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),hAPP_int_int(div_mod_int(Y),M_1))),M_1) = hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)),M_1)) # label(fact_2052_zdiff__zmod__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2020 (all Z_1 all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(uminus_uminus_int,Z_1)),W) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),W))) # label(fact_2053_zmult__zminus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2021 (all W hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,W)) = hAPP_int_int(number_number_of_int,hAPP_int_int(uminus_uminus_int,W))) # label(fact_2055_minus__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2022 (all Z_1 all W hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),W)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,Z_1)),hAPP_int_int(uminus_uminus_int,W))) # label(fact_2057_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2023 (all X_11 ((hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_11)),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,hAPP_int_rat(number_number_of_rat,X_11)) = hAPP_rat_rat(uminus_uminus_rat,hAPP_int_rat(number_number_of_rat,X_11))) & (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_11)),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,hAPP_int_rat(number_number_of_rat,X_11)) = hAPP_int_rat(number_number_of_rat,X_11)))) # label(fact_2058_abs__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2024 (all X_11 ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,X_11)),zero_zero_real)) -> hAPP_real_real(abs_abs_real,hAPP_int_real(number267125858f_real,X_11)) = hAPP_real_real(uminus_uminus_real,hAPP_int_real(number267125858f_real,X_11))) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,X_11)),zero_zero_real)) -> hAPP_real_real(abs_abs_real,hAPP_int_real(number267125858f_real,X_11)) = hAPP_int_real(number267125858f_real,X_11)))) # label(fact_2059_abs__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2025 (all X_11 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,X_11)),zero_zero_int)) -> hAPP_int_int(abs_abs_int,hAPP_int_int(number_number_of_int,X_11)) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,X_11))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,X_11)),zero_zero_int)) -> hAPP_int_int(abs_abs_int,hAPP_int_int(number_number_of_int,X_11)) = hAPP_int_int(number_number_of_int,X_11)))) # label(fact_2060_abs__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2026 (all Ba all Aa (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Aa),ring_1_Ints_real)) -> (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Ba),ring_1_Ints_real)) -> hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Aa),Ba)),ring_1_Ints_real))))) # label(fact_2065_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2027 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),ring_1_Ints_int)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),Ba)),ring_1_Ints_int))))) # label(fact_2066_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2028 (all Ba all Aa (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Aa),ring_1_Ints_rat)) -> (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Ba),ring_1_Ints_rat)) -> hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Aa),Ba)),ring_1_Ints_rat))))) # label(fact_2067_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2029 (all Ba all Aa (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Aa),ring_1_Ints_complex)) -> (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Ba),ring_1_Ints_complex)) -> hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Aa),Ba)),ring_1_Ints_complex))))) # label(fact_2068_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2030 (all Ba all Aa (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Aa),ring_1_Ints_real)) -> (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Ba),ring_1_Ints_real)) -> hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Ba)),ring_1_Ints_real))))) # label(fact_2069_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2031 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),ring_1_Ints_int)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba)),ring_1_Ints_int))))) # label(fact_2070_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2032 (all Ba all Aa (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Aa),ring_1_Ints_rat)) -> (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Ba),ring_1_Ints_rat)) -> hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Ba)),ring_1_Ints_rat))))) # label(fact_2071_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2033 (all Ba all Aa (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Aa),ring_1_Ints_complex)) -> (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Ba),ring_1_Ints_complex)) -> hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Aa),Ba)),ring_1_Ints_complex))))) # label(fact_2072_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2034 (all W_1 hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_int_real(number267125858f_real,W_1)),ring_1_Ints_real))) # label(fact_2073_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2035 (all W_1 hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(number_number_of_int,W_1)),ring_1_Ints_int))) # label(fact_2074_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2036 (all W_1 hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,hAPP_int_rat(number_number_of_rat,W_1)),ring_1_Ints_rat))) # label(fact_2075_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2037 (all W_1 hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,hAPP_int_complex(number528085621omplex,W_1)),ring_1_Ints_complex))) # label(fact_2076_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2038 (all Ba all Aa (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Aa),ring_1_Ints_real)) -> (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Ba),ring_1_Ints_real)) -> hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),Ba)),ring_1_Ints_real))))) # label(fact_2081_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2039 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),ring_1_Ints_int)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),ring_1_Ints_int))))) # label(fact_2082_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2040 (all Ba all Aa (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Aa),ring_1_Ints_rat)) -> (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Ba),ring_1_Ints_rat)) -> hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),Ba)),ring_1_Ints_rat))))) # label(fact_2083_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2041 (all Ba all Aa (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Aa),ring_1_Ints_complex)) -> (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Ba),ring_1_Ints_complex)) -> hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Aa),Ba)),ring_1_Ints_complex))))) # label(fact_2084_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2042 (all B_41 all A_56 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_41),A_56)),B_41) = zero_z891286103de_int) # label(fact_2085_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2043 (all B_41 all A_56 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_41),A_56)),B_41) = zero_z126310315umeral) # label(fact_2086_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2044 (all B_41 all A_56 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_41),A_56)),B_41) = zero_zero_nat) # label(fact_2087_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2045 (all B_41 all A_56 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_41),A_56)),B_41) = zero_zero_int) # label(fact_2088_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2046 (all A_55 all B_40 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_55),B_40)),B_40) = zero_z891286103de_int) # label(fact_2089_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2047 (all A_55 all B_40 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_55),B_40)),B_40) = zero_z126310315umeral) # label(fact_2090_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2048 (all A_55 all B_40 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_55),B_40)),B_40) = zero_zero_nat) # label(fact_2091_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2049 (all A_55 all B_40 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_55),B_40)),B_40) = zero_zero_int) # label(fact_2092_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2050 (all A_54 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_54)) -> hAPP_rat_rat(abs_abs_rat,A_54) = A_54)) # label(fact_2093_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2051 (all A_54 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_54)) -> hAPP_real_real(abs_abs_real,A_54) = A_54)) # label(fact_2094_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2052 (all A_54 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_54)) -> hAPP_int_int(abs_abs_int,A_54) = A_54)) # label(fact_2095_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2053 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,Aa)),zero_zero_rat)) <-> Aa = zero_zero_rat)) # label(fact_2096_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2054 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,Aa)),zero_zero_real)) <-> Aa = zero_zero_real)) # label(fact_2097_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2055 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,Aa)),zero_zero_int)) <-> Aa = zero_zero_int)) # label(fact_2098_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2056 (all A_53 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(abs_abs_rat,A_53)))) # label(fact_2099_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2057 (all A_53 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(abs_abs_real,A_53)))) # label(fact_2100_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2058 (all A_53 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(abs_abs_int,A_53)))) # label(fact_2101_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2059 (all A_52 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_52)) -> hAPP_rat_rat(abs_abs_rat,A_52) = A_52)) # label(fact_2102_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2060 (all A_52 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_52)) -> hAPP_real_real(abs_abs_real,A_52) = A_52)) # label(fact_2103_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2061 (all A_52 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_52)) -> hAPP_int_int(abs_abs_int,A_52) = A_52)) # label(fact_2104_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2062 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(abs_abs_rat,Aa))) <-> Aa != zero_zero_rat)) # label(fact_2105_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2063 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(abs_abs_real,Aa))) <-> Aa != zero_zero_real)) # label(fact_2106_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2064 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(abs_abs_int,Aa))) <-> Aa != zero_zero_int)) # label(fact_2107_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2065 (all A_51 -hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,A_51)),zero_zero_rat))) # label(fact_2108_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2066 (all A_51 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,A_51)),zero_zero_real))) # label(fact_2109_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2067 (all A_51 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,A_51)),zero_zero_int))) # label(fact_2110_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2068 (all A_50 hAPP_Q1762011733de_int(div_mo231679042de_int(A_50),one_on1684967323de_int) = zero_z891286103de_int) # label(fact_2111_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2069 (all A_50 hAPP_C498520661umeral(div_mo1740067990umeral(A_50),one_on1645066479umeral) = zero_z126310315umeral) # label(fact_2112_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2070 (all A_50 hAPP_nat_nat(div_mod_nat(A_50),one_one_nat) = zero_zero_nat) # label(fact_2113_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2071 (all A_50 hAPP_int_int(div_mod_int(A_50),one_one_int) = zero_zero_int) # label(fact_2114_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2072 (all B_39 all D_6 all A_49 all C_18 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,A_49)),C_18)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,B_39)),D_6)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(abs_abs_rat,A_49)),hAPP_rat_rat(abs_abs_rat,B_39))),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,C_18),D_6)))))) # label(fact_2115_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2073 (all B_39 all D_6 all A_49 all C_18 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,A_49)),C_18)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,B_39)),D_6)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(abs_abs_real,A_49)),hAPP_real_real(abs_abs_real,B_39))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_18),D_6)))))) # label(fact_2116_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2074 (all B_39 all D_6 all A_49 all C_18 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,A_49)),C_18)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,B_39)),D_6)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,A_49)),hAPP_int_int(abs_abs_int,B_39))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_18),D_6)))))) # label(fact_2117_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2075 (all A_48 all C_17 all B_38 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_48),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_17),B_38))),B_38) = hAPP_Q1762011733de_int(div_mo231679042de_int(A_48),B_38)) # label(fact_2118_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2076 (all A_48 all C_17 all B_38 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_48),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_17),B_38))),B_38) = hAPP_C498520661umeral(div_mo1740067990umeral(A_48),B_38)) # label(fact_2119_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2077 (all A_48 all C_17 all B_38 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_48),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_17),B_38))),B_38) = hAPP_nat_nat(div_mod_nat(A_48),B_38)) # label(fact_2120_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2078 (all A_48 all C_17 all B_38 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_48),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_17),B_38))),B_38) = hAPP_int_int(div_mod_int(A_48),B_38)) # label(fact_2121_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2079 (all A_47 all B_37 all C_16 hAPP_Q1762011733de_int(div_mo231679042de_int(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_47),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_37),C_16))),B_37) = hAPP_Q1762011733de_int(div_mo231679042de_int(A_47),B_37)) # label(fact_2122_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2080 (all A_47 all B_37 all C_16 hAPP_C498520661umeral(div_mo1740067990umeral(hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_47),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_37),C_16))),B_37) = hAPP_C498520661umeral(div_mo1740067990umeral(A_47),B_37)) # label(fact_2123_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2081 (all A_47 all B_37 all C_16 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_47),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_37),C_16))),B_37) = hAPP_nat_nat(div_mod_nat(A_47),B_37)) # label(fact_2124_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2082 (all A_47 all B_37 all C_16 hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_47),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_37),C_16))),B_37) = hAPP_int_int(div_mod_int(A_47),B_37)) # label(fact_2125_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2083 (all A_46 all B_36 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_46),B_36))),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(abs_abs_rat,A_46)),hAPP_rat_rat(abs_abs_rat,B_36))))) # label(fact_2126_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2084 (all A_46 all B_36 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_46),B_36))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(abs_abs_real,A_46)),hAPP_real_real(abs_abs_real,B_36))))) # label(fact_2127_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2085 (all A_46 all B_36 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_46),B_36))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,A_46)),hAPP_int_int(abs_abs_int,B_36))))) # label(fact_2128_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2086 (all A_45 all B_35 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(abs_abs_rat,A_45)),hAPP_rat_rat(abs_abs_rat,B_35)))),hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_45),B_35))))) # label(fact_2129_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2087 (all A_45 all B_35 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(abs_abs_real,A_45)),hAPP_real_real(abs_abs_real,B_35)))),hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_45),B_35))))) # label(fact_2130_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2088 (all A_45 all B_35 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(abs_abs_int,A_45)),hAPP_int_int(abs_abs_int,B_35)))),hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_45),B_35))))) # label(fact_2131_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2089 (all A_44 all B_34 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(abs_abs_rat,A_44)),hAPP_rat_rat(abs_abs_rat,B_34))),hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_44),B_34))))) # label(fact_2132_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2090 (all A_44 all B_34 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(abs_abs_real,A_44)),hAPP_real_real(abs_abs_real,B_34))),hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_44),B_34))))) # label(fact_2133_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2091 (all A_44 all B_34 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(abs_abs_int,A_44)),hAPP_int_int(abs_abs_int,B_34))),hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_44),B_34))))) # label(fact_2134_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2092 (all A_43 all B_33 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(abs_abs_rat,A_43)),hAPP_rat_rat(abs_abs_rat,B_33))),hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,B_33),A_43))))) # label(fact_2135_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2093 (all A_43 all B_33 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(abs_abs_real,A_43)),hAPP_real_real(abs_abs_real,B_33))),hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_33),A_43))))) # label(fact_2136_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2094 (all A_43 all B_33 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(abs_abs_int,A_43)),hAPP_int_int(abs_abs_int,B_33))),hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_33),A_43))))) # label(fact_2137_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2095 (all X_1 all Aa all R_2 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_1),Aa))),R_2)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Aa),R_2)),X_1)) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),R_2))))) # label(fact_2138_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2096 (all X_1 all Aa all R_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),Aa))),R_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Aa),R_2)),X_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),R_2))))) # label(fact_2139_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2097 (all X_1 all Aa all R_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Aa))),R_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),R_2)),X_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),R_2))))) # label(fact_2140_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2098 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(d22set,Aa))))) # label(fact_2141_d22set__le__swap) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2099 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),Aa)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Aa)))) # label(fact_2142_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2100 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,Aa)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)))) # label(fact_2143_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2101 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,Aa)),Aa)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)))) # label(fact_2144_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2102 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),zero_zero_rat)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),Aa)))) # label(fact_2145_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2103 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,Aa)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Aa)))) # label(fact_2146_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2104 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,Aa)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)))) # label(fact_2147_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2105 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),hAPP_rat_rat(uminus_uminus_rat,Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),zero_zero_rat)))) # label(fact_2148_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2106 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),hAPP_real_real(uminus_uminus_real,Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)))) # label(fact_2149_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2107 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),hAPP_int_int(uminus_uminus_int,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int)))) # label(fact_2150_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2108 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_rat_rat(uminus_uminus_rat,Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Aa),zero_zero_rat)))) # label(fact_2151_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2109 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(uminus_uminus_real,Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),zero_zero_real)))) # label(fact_2152_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2110 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(uminus_uminus_int,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int)))) # label(fact_2153_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2111 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(d22set,Aa))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa)))) # label(fact_2154_d22set__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2112 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),Aa)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),Aa)))) # label(fact_2155_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2113 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,Aa)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Aa)))) # label(fact_2156_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2114 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,Aa)),Aa)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa)))) # label(fact_2157_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2115 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(uminus_uminus_rat,Aa)),zero_zero_rat)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),Aa)))) # label(fact_2158_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2116 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,Aa)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Aa)))) # label(fact_2159_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2117 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,Aa)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa)))) # label(fact_2160_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2118 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),hAPP_rat_rat(uminus_uminus_rat,Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),zero_zero_rat)))) # label(fact_2161_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2119 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),hAPP_real_real(uminus_uminus_real,Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),zero_zero_real)))) # label(fact_2162_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2120 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(uminus_uminus_int,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int)))) # label(fact_2163_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2121 (all Aa (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_rat_rat(uminus_uminus_rat,Aa))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Aa),zero_zero_rat)))) # label(fact_2164_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2122 (all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(uminus_uminus_real,Aa))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),zero_zero_real)))) # label(fact_2165_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2123 (all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(uminus_uminus_int,Aa))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int)))) # label(fact_2166_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2124 (all A_42 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_42),hAPP_rat_rat(uminus_uminus_rat,A_42)) = zero_zero_rat) # label(fact_2167_right__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2125 (all A_42 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_42),hAPP_complex_complex(uminus473333897omplex,A_42)) = zero_zero_complex) # label(fact_2168_right__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2126 (all A_42 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_42),hAPP_real_real(uminus_uminus_real,A_42)) = zero_zero_real) # label(fact_2169_right__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2127 (all A_42 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_42),hAPP_int_int(uminus_uminus_int,A_42)) = zero_zero_int) # label(fact_2170_right__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2128 (all Aa all Ba (Aa = hAPP_rat_rat(uminus_uminus_rat,Ba) <-> hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Ba) = zero_zero_rat)) # label(fact_2171_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2129 (all Aa all Ba (Aa = hAPP_complex_complex(uminus473333897omplex,Ba) <-> hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Aa),Ba) = zero_zero_complex)) # label(fact_2172_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2130 (all Aa all Ba (Aa = hAPP_real_real(uminus_uminus_real,Ba) <-> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Ba) = zero_zero_real)) # label(fact_2173_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2131 (all Aa all Ba (Aa = hAPP_int_int(uminus_uminus_int,Ba) <-> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba) = zero_zero_int)) # label(fact_2174_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2132 (all A_41 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(uminus_uminus_rat,A_41)),A_41) = zero_zero_rat) # label(fact_2175_left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2133 (all A_41 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(uminus473333897omplex,A_41)),A_41) = zero_zero_complex) # label(fact_2176_left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2134 (all A_41 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(uminus_uminus_real,A_41)),A_41) = zero_zero_real) # label(fact_2177_left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2135 (all A_41 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,A_41)),A_41) = zero_zero_int) # label(fact_2178_left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2136 (all A_40 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(uminus_uminus_rat,A_40)),A_40) = zero_zero_rat) # label(fact_2179_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2137 (all A_40 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(uminus473333897omplex,A_40)),A_40) = zero_zero_complex) # label(fact_2180_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2138 (all A_40 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(uminus_uminus_real,A_40)),A_40) = zero_zero_real) # label(fact_2181_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2139 (all A_40 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,A_40)),A_40) = zero_zero_int) # label(fact_2182_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2140 (all X_1 all Y_2 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_1),Y_2) = zero_zero_rat <-> Y_2 = hAPP_rat_rat(uminus_uminus_rat,X_1))) # label(fact_2183_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2141 (all X_1 all Y_2 (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X_1),Y_2) = zero_zero_complex <-> Y_2 = hAPP_complex_complex(uminus473333897omplex,X_1))) # label(fact_2184_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2142 (all X_1 all Y_2 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2) = zero_zero_real <-> Y_2 = hAPP_real_real(uminus_uminus_real,X_1))) # label(fact_2185_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2143 (all X_1 all Y_2 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_1),Y_2) = zero_zero_int <-> Y_2 = hAPP_int_int(uminus_uminus_int,X_1))) # label(fact_2186_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2144 (all A_39 all B_32 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_39),B_32) = zero_zero_rat -> hAPP_rat_rat(uminus_uminus_rat,A_39) = B_32)) # label(fact_2187_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2145 (all A_39 all B_32 (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_39),B_32) = zero_zero_complex -> hAPP_complex_complex(uminus473333897omplex,A_39) = B_32)) # label(fact_2188_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2146 (all A_39 all B_32 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_39),B_32) = zero_zero_real -> hAPP_real_real(uminus_uminus_real,A_39) = B_32)) # label(fact_2189_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2147 (all A_39 all B_32 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_39),B_32) = zero_zero_int -> hAPP_int_int(uminus_uminus_int,A_39) = B_32)) # label(fact_2190_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2148 (all A_38 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,zero_zero_rat),A_38) = hAPP_rat_rat(uminus_uminus_rat,A_38)) # label(fact_2191_diff__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2149 (all A_38 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,zero_zero_complex),A_38) = hAPP_complex_complex(uminus473333897omplex,A_38)) # label(fact_2192_diff__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2150 (all A_38 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,zero_zero_real),A_38) = hAPP_real_real(uminus_uminus_real,A_38)) # label(fact_2193_diff__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2151 (all A_38 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,zero_zero_int),A_38) = hAPP_int_int(uminus_uminus_int,A_38)) # label(fact_2194_diff__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2152 (all X_1 (hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_1),X_1) = one_one_rat <-> X_1 = one_one_rat | X_1 = hAPP_rat_rat(uminus_uminus_rat,one_one_rat))) # label(fact_2195_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2153 (all X_1 (hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_1),X_1) = one_one_complex <-> X_1 = one_one_complex | X_1 = hAPP_complex_complex(uminus473333897omplex,one_one_complex))) # label(fact_2196_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2154 (all X_1 (hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),X_1) = one_one_real <-> X_1 = one_one_real | X_1 = hAPP_real_real(uminus_uminus_real,one_one_real))) # label(fact_2197_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2155 (all X_1 (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),X_1) = one_one_int <-> X_1 = one_one_int | X_1 = hAPP_int_int(uminus_uminus_int,one_one_int))) # label(fact_2198_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2156 (all X_10 hAPP_rat_rat(uminus_uminus_rat,X_10) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(uminus_uminus_rat,one_one_rat)),X_10)) # label(fact_2199_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2157 (all X_10 hAPP_complex_complex(uminus473333897omplex,X_10) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(uminus473333897omplex,one_one_complex)),X_10)) # label(fact_2200_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2158 (all X_10 hAPP_real_real(uminus_uminus_real,X_10) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,one_one_real)),X_10)) # label(fact_2201_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2159 (all X_10 hAPP_int_int(uminus_uminus_int,X_10) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(uminus_uminus_int,one_one_int)),X_10)) # label(fact_2202_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2160 (all A_37 all B_31 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_37),hAPP_rat_rat(uminus_uminus_rat,B_31)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_37),B_31)) # label(fact_2203_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2161 (all A_37 all B_31 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_37),hAPP_complex_complex(uminus473333897omplex,B_31)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_37),B_31)) # label(fact_2204_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2162 (all A_37 all B_31 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_37),hAPP_real_real(uminus_uminus_real,B_31)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_37),B_31)) # label(fact_2205_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2163 (all A_37 all B_31 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_37),hAPP_int_int(uminus_uminus_int,B_31)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_37),B_31)) # label(fact_2206_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2164 (all A_36 all B_30 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_36),B_30) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_36),hAPP_rat_rat(uminus_uminus_rat,B_30))) # label(fact_2207_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2165 (all A_36 all B_30 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_36),B_30) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_36),hAPP_complex_complex(uminus473333897omplex,B_30))) # label(fact_2208_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2166 (all A_36 all B_30 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_36),B_30) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_36),hAPP_real_real(uminus_uminus_real,B_30))) # label(fact_2209_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2167 (all A_36 all B_30 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_36),B_30) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_36),hAPP_int_int(uminus_uminus_int,B_30))) # label(fact_2210_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2168 (all A_35 all B_29 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_35),B_29) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_35),hAPP_rat_rat(uminus_uminus_rat,B_29))) # label(fact_2211_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2169 (all A_35 all B_29 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_35),B_29) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_35),hAPP_complex_complex(uminus473333897omplex,B_29))) # label(fact_2212_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2170 (all A_35 all B_29 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_35),B_29) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_35),hAPP_real_real(uminus_uminus_real,B_29))) # label(fact_2213_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2171 (all A_35 all B_29 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_35),B_29) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_35),hAPP_int_int(uminus_uminus_int,B_29))) # label(fact_2214_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2172 (all X_9 all Y_10 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X_9),Y_10) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X_9),hAPP_rat_rat(uminus_uminus_rat,Y_10))) # label(fact_2215_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2173 (all X_9 all Y_10 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_9),Y_10) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X_9),hAPP_complex_complex(uminus473333897omplex,Y_10))) # label(fact_2216_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2174 (all X_9 all Y_10 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_9),Y_10) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_9),hAPP_real_real(uminus_uminus_real,Y_10))) # label(fact_2217_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2175 (all X_9 all Y_10 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_9),Y_10) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_9),hAPP_int_int(uminus_uminus_int,Y_10))) # label(fact_2218_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2176 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(A_2),B_1)),B_1)))) # label(fact_2219_pos__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2177 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),hAPP_int_int(div_mod_int(A_2),B_1))))) # label(fact_2220_neg__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2178 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(X),Y)))))) # label(fact_2221_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2179 (all K_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(M_1),K_2)),M_1)))) # label(fact_2222_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2180 (all M all D (hAPP_int_int(div_mod_int(M),D) = zero_zero_int <-> (exists Q_3 M = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,D),Q_3)))) # label(fact_2223_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2181 (all M_1 all N_1 (hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1)) = one_one_int -> hAPP_int_int(abs_abs_int,M_1) = one_one_int)) # label(fact_2224_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2182 (all Z_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(uminus_uminus_int,Z_1)),Z_1) = zero_zero_int) # label(fact_2225_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2183 (all Z_1 all W hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),hAPP_int_int(uminus_uminus_int,W)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_1),W)) # label(fact_2227_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2184 (all Z_1 all W hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_1),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),hAPP_int_int(uminus_uminus_int,W))) # label(fact_2228_diff__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2185 (all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,min)),B_1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_1),one_one_int))) # label(fact_2229_zmod__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2186 (all B_28 all A_34 ((hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),A_34)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,A_34),zero_zero_rat))) & (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),B_28)) | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,B_28),zero_zero_rat))) -> hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_34),B_28)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(abs_abs_rat,A_34)),hAPP_rat_rat(abs_abs_rat,B_28)))) # label(fact_2230_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2187 (all B_28 all A_34 ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_34)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_34),zero_zero_real))) & (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_28)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_28),zero_zero_real))) -> hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_34),B_28)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(abs_abs_real,A_34)),hAPP_real_real(abs_abs_real,B_28)))) # label(fact_2231_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2188 (all B_28 all A_34 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_34)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_34),zero_zero_int))) & (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_28)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_28),zero_zero_int))) -> hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_34),B_28)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,A_34)),hAPP_int_int(abs_abs_int,B_28)))) # label(fact_2232_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.73 2189 (all Y_9 all X_8 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),X_8)) -> hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(abs_abs_rat,Y_9)),X_8) = hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_9),X_8)))) # label(fact_2233_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2190 (all Y_9 all X_8 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_8)) -> hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(abs_abs_real,Y_9)),X_8) = hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_9),X_8)))) # label(fact_2234_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2191 (all Y_9 all X_8 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_8)) -> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,Y_9)),X_8) = hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y_9),X_8)))) # label(fact_2235_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2192 (all A_33 all B_27 all C_15 all D_5 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_33),B_27)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,C_15),D_5)))),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_33),C_15))),hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,B_27),D_5)))))) # label(fact_2236_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2193 (all A_33 all B_27 all C_15 all D_5 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_33),B_27)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,C_15),D_5)))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_33),C_15))),hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_27),D_5)))))) # label(fact_2237_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2194 (all A_33 all B_27 all C_15 all D_5 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_33),B_27)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_15),D_5)))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_33),C_15))),hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_27),D_5)))))) # label(fact_2238_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2195 (all A_32 all B_26 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_rat_rat(abs_abs_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_32),B_26))),hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(abs_abs_rat,A_32)),hAPP_rat_rat(abs_abs_rat,B_26))))) # label(fact_2239_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2196 (all A_32 all B_26 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_32),B_26))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(abs_abs_real,A_32)),hAPP_real_real(abs_abs_real,B_26))))) # label(fact_2240_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2197 (all A_32 all B_26 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_32),B_26))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(abs_abs_int,A_32)),hAPP_int_int(abs_abs_int,B_26))))) # label(fact_2241_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2198 (all Aa (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Aa),ring_1_Ints_real)) -> (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Aa) = zero_zero_real <-> Aa = zero_zero_real))) # label(fact_2242_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2199 (all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int)) -> (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa) = zero_zero_int <-> Aa = zero_zero_int))) # label(fact_2243_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2200 (all Aa (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Aa),ring_1_Ints_rat)) -> (hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Aa),Aa) = zero_zero_rat <-> Aa = zero_zero_rat))) # label(fact_2244_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2201 (all Aa (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Aa),ring_1_Ints_complex)) -> (hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Aa),Aa) = zero_zero_complex <-> Aa = zero_zero_complex))) # label(fact_2245_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2202 (all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(abs_abs_int,Z_2)),one_one_int)) <-> Z_2 = zero_zero_int)) # label(fact_2246_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2203 (all B_1 all 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_int,B_1),A_2)) -> hAPP_int_int(div_mod_int(A_2),B_1) = A_2))) # label(fact_2247_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2204 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(A_2),B_1)),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),hAPP_int_int(div_mod_int(A_2),B_1))))) # label(fact_2248_neg__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2205 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(A_2),B_1)),zero_zero_int)))) # label(fact_2249_neg__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2206 (all B_1 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_int,A_2),B_1)) -> hAPP_int_int(div_mod_int(A_2),B_1) = A_2))) # label(fact_2250_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2207 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(A_2),B_1))) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(A_2),B_1)),B_1)))) # label(fact_2251_pos__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2208 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(A_2),B_1))))) # label(fact_2252_pos__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2209 (all B_1 posDivAlg(zero_zero_int,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),zero_zero_int)) # label(fact_2253_posDivAlg__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2210 (all V_5 all W_4 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_int_rat(number_number_of_rat,V_5)),hAPP_int_rat(number_number_of_rat,W_4)) = hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_5),hAPP_int_int(uminus_uminus_int,W_4)))) # label(fact_2254_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2211 (all V_5 all W_4 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_int_complex(number528085621omplex,V_5)),hAPP_int_complex(number528085621omplex,W_4)) = hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_5),hAPP_int_int(uminus_uminus_int,W_4)))) # label(fact_2255_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2212 (all V_5 all W_4 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(number267125858f_real,V_5)),hAPP_int_real(number267125858f_real,W_4)) = hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_5),hAPP_int_int(uminus_uminus_int,W_4)))) # label(fact_2256_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2213 (all V_5 all W_4 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(number_number_of_int,V_5)),hAPP_int_int(number_number_of_int,W_4)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_5),hAPP_int_int(uminus_uminus_int,W_4)))) # label(fact_2257_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2214 (all M_1 all N_1 (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1) = one_one_int -> M_1 = one_one_int | M_1 = hAPP_int_int(number_number_of_int,min))) # label(fact_2258_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2215 (all M all N (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),N) = one_one_int <-> M = one_one_int & N = one_one_int | M = hAPP_int_int(number_number_of_int,min) & N = hAPP_int_int(number_number_of_int,min))) # label(fact_2259_zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2216 (all V_2 all W hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,W)) = hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_2),hAPP_int_int(uminus_uminus_int,W)))) # label(fact_2260_minus__numeral__code_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2217 (all A_2 all B_1 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (B_1 != zero_zero_int -> hAPP_int_int(div_mod_int(A_2),B_1) = R_3))) # label(fact_2261_divmod__int__rel__mod) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2218 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(d22set,Aa))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Ba)))) # label(fact_2262_d22set__g__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2219 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1)),zero_zero_int)) -> hAPP_int_int(div_mod_int(A_2),B_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1)))) # label(fact_2263_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2220 (all V_4 all C_14 all W_3 hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,V_4)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,C_14),hAPP_int_rat(number_number_of_rat,W_3))) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(number_number_of_rat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_4),hAPP_int_int(uminus_uminus_int,W_3)))),C_14)) # label(fact_2264_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2221 (all V_4 all C_14 all W_3 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,V_4)),hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,C_14),hAPP_int_complex(number528085621omplex,W_3))) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_int_complex(number528085621omplex,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_4),hAPP_int_int(uminus_uminus_int,W_3)))),C_14)) # label(fact_2265_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2222 (all V_4 all C_14 all W_3 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,V_4)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C_14),hAPP_int_real(number267125858f_real,W_3))) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(number267125858f_real,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_4),hAPP_int_int(uminus_uminus_int,W_3)))),C_14)) # label(fact_2266_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2223 (all V_4 all C_14 all W_3 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_4)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_14),hAPP_int_int(number_number_of_int,W_3))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_4),hAPP_int_int(uminus_uminus_int,W_3)))),C_14)) # label(fact_2267_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2224 (all Aa (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Aa),ring_1_Ints_real)) -> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),Aa)),Aa) != zero_zero_real)) # label(fact_2268_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2225 (all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int)) -> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Aa)),Aa) != zero_zero_int)) # label(fact_2269_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2226 (all Aa (hBOOL(hAPP_f311463272l_bool(hAPP_r1889917837l_bool(member_rat,Aa),ring_1_Ints_rat)) -> hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,one_one_rat),Aa)),Aa) != zero_zero_rat)) # label(fact_2270_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2227 (all Aa (hBOOL(hAPP_f1734966846l_bool(hAPP_c769186317l_bool(member_complex,Aa),ring_1_Ints_complex)) -> hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,one_one_complex),Aa)),Aa) != zero_zero_complex)) # label(fact_2271_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2228 (all A_12 all B_10 all Q_5 all Y (A_12 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_10),Q_5)),Y) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),B_10))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_10),Y)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),zero_zero_int))) -> (B_10 != zero_zero_int -> hAPP_int_int(div_mod_int(A_12),B_10) = Y)))) # label(fact_2272_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2229 (all Q_1 all B_1 all R_3 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_3),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(div_mod_int(Q_1),C_1))),R_3)),zero_zero_int)))))) # label(fact_2273_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2230 (all Q_1 all B_1 all R_3 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),R_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_3),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),C_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(div_mod_int(Q_1),C_1))),R_3))))))) # label(fact_2274_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2231 (all Q_1 all B_1 all R_3 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(div_mod_int(Q_1),C_1))),R_3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),C_1))))))) # label(fact_2275_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2232 (all Q_1 all B_1 all R_3 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(div_mod_int(Q_1),C_1))),R_3))))))) # label(fact_2276_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2233 (all M_6 all D_4 (hAPP_int_int(div_mod_int(M_6),D_4) = zero_zero_int -> (exists Q_3 M_6 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,D_4),Q_3)))) # label(fact_2277_zmod__eq__0D) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2234 (all K_2 all L_2 ((L_2 = zero_zero_int -> pdivmod(K_2,L_2) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),hAPP_int_int(abs_abs_int,K_2))) & (L_2 != zero_zero_int -> pdivmod(K_2,L_2) = posDivAlg(hAPP_int_int(abs_abs_int,K_2),hAPP_int_int(abs_abs_int,L_2))))) # label(fact_2278_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2235 (all K_2 all L_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),L_2)) -> hAPP_int_int(z3mod(K_2),L_2) = hAPP_int_int(div_mod_int(K_2),L_2)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),L_2)) -> hAPP_int_int(z3mod(K_2),L_2) = hAPP_int_int(div_mod_int(K_2),hAPP_int_int(uminus_uminus_int,L_2))))) # label(fact_2279_z3mod__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2236 (all M_1 all N_1 all R_5 all S_4 all S_2 all T_3 all T_2 all R_3 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_3),zero_zero_int)) -> xzgcda(M_1,N_1,R_5,R_3,S_4,S_2,T_3,T_2) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,R_5),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,S_4),T_3))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_3),zero_zero_int)) -> xzgcda(M_1,N_1,R_5,R_3,S_4,S_2,T_3,T_2) = xzgcda(M_1,N_1,R_3,hAPP_int_int(div_mod_int(R_5),R_3),S_2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,S_4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,R_5),R_3)),S_2)),T_2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,T_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,R_5),R_3)),T_2)))))) # label(fact_2280_xzgcda_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2237 (all K_1 all F all N ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_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))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N)) & hAPP_nat_int(F,I_2) = K_1)))))) # label(fact_2281_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2238 (all K_1 all F all N ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_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))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N)) & hAPP_nat_int(F,I_2) = K_1)))))) # label(fact_2282_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2239 (all K_1 all F all N all M ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),N)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),one_one_nat))),hAPP_nat_int(F,I_2)))),one_one_int)))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,M)),K_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),hAPP_nat_int(F,N))) -> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),N)) & hAPP_nat_int(F,I_2) = K_1))))))) # label(fact_2283_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2240 (all B_1 negDivAlg(hAPP_int_int(number_number_of_int,min),B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_1),one_one_int))) # label(fact_2284_negDivAlg__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2241 (all C_1 all A_2 all B_1 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (B_1 != zero_zero_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),C_1)),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Q_1),C_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(div_mod_int(Q_1),C_1))),R_3)))))))) # label(fact_2285_zmult2__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2242 (all X_1 (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_1),X_1))) <-> X_1 = zero_zero_real)) # label(fact_2286_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2243 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(M_1),N_1)),N_1)))) # label(fact_2287_mod__le__divisor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2244 (all M all D (hAPP_nat_nat(div_mod_nat(M),D) = zero_zero_nat <-> (exists Q_3 M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,D),Q_3)))) # label(fact_2288_mod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2245 (all N_1 all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = zero_zero_nat) & (M_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1))))) # label(fact_2289_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2246 (all M_1 all N_1 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(div_mod_nat(M_1),N_1) = M_1) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(div_mod_nat(M_1),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1)))) # label(fact_2290_mod__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2247 (all M_1 all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(div_mod_nat(M_1),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1))) # label(fact_2291_mod__geq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2248 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(M_1),N_1)),N_1)))) # label(fact_2292_mod__less__divisor) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2249 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(div_mod_nat(M_1),N_1) = M_1)) # label(fact_2293_mod__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2250 (all Q_1 all R_3 all B_1 all C_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,R_3),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),hAPP_nat_nat(div_mod_nat(Q_1),C_1))),R_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),C_1)))))) # label(fact_2294_mod__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2251 (all P_1 all N all K_1 (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(div_mod_nat(N),K_1))) <-> (K_1 = zero_zero_nat -> hBOOL(hAPP_nat_bool(P_1,N))) & (K_1 != zero_zero_nat -> (all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_1)) -> (N = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_2)),J_1) -> hBOOL(hAPP_nat_bool(P_1,J_1)))))))) # label(fact_2295_split__mod) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2252 (all R_3 ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),zero_zero_real)) -> hAPP_real_real(abs_abs_real,R_3) = hAPP_real_real(uminus_uminus_real,R_3)) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),zero_zero_real)) -> hAPP_real_real(abs_abs_real,R_3) = R_3))) # label(fact_2296_real__abs__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2253 (all A_2 ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),zero_zero_real)) -> hAPP_real_real(abs_abs_real,A_2) = hAPP_real_real(uminus_uminus_real,A_2)) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),zero_zero_real)) -> hAPP_real_real(abs_abs_real,A_2) = A_2))) # label(fact_2297_abs__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2254 (all K_2 all N_1 all M_1 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1)),M_1)),N_1) = hAPP_nat_nat(div_mod_nat(M_1),N_1)) # label(fact_2298_mod__mult__self3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2255 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(div_mod_nat(M_1),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1))) # label(fact_2299_le__mod__geq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2256 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(M_1),N_1)),M_1))) # label(fact_2300_mod__less__eq__dividend) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2257 (all X all Y all L_2 all M_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(uminus_uminus_real,L_2)),hAPP_real_real(uminus_uminus_real,M_1))))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(uminus_uminus_real,L_2)))),hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Y),hAPP_real_real(uminus_uminus_real,M_1))))))) # label(fact_2301_abs__sum__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2258 (all X_1 all R_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X_1)),R_2)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,R_2)),X_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),R_2)))) # label(fact_2302_abs__le__interval__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2259 (all Z_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1))))) # label(fact_2303_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2260 (all Y all X all Z_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1))))) # label(fact_2304_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2261 (all R_3 all S_2 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,R_3),S_2) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,R_3),hAPP_real_real(uminus_uminus_real,S_2))) # label(fact_2305_real__diff__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2262 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(uminus_uminus_real,Y))) # label(fact_2306_minus__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2263 (all X all Y hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(uminus_uminus_real,Y))) = hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Y),hAPP_real_real(uminus_uminus_real,X)))) # label(fact_2307_abs__minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2264 (all X -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(abs_abs_real,X)),one_one_real)),X))) # label(fact_2308_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2265 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)))) # label(fact_2309_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2266 (all Y all X all Z_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1))))) # label(fact_2310_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2267 (all Z_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1))))) # label(fact_2311_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2268 (all B_1 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,zero_zero_int),B_1) = zero_zero_int) # label(fact_2312_zdiv__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2269 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),hAPP_real_real(abs_abs_real,X))))) # label(fact_2313_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2270 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,X_1)),Y_2)))) # label(fact_2314_real__0__less__add__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2271 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),hAPP_real_real(uminus_uminus_real,X_1))))) # label(fact_2315_real__add__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2272 (all X_1 all Y_2 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2) = zero_zero_real <-> Y_2 = hAPP_real_real(uminus_uminus_real,X_1))) # label(fact_2316_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2273 (all X_1 all Aa (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),hAPP_real_real(uminus_uminus_real,Aa)) = zero_zero_real <-> X_1 = Aa)) # label(fact_2317_real__add__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2274 (all A_2 all B_1 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(uminus_uminus_int,A_2)),B_1)) # label(fact_2318_zdiv__zminus2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2275 (all A_2 all B_1 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(uminus_uminus_int,A_2)),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)) # label(fact_2319_zdiv__zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2276 (all A_31 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_31),zero_z891286103de_int) = zero_z891286103de_int) # label(fact_2320_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2277 (all A_31 hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_31),zero_z126310315umeral) = zero_z126310315umeral) # label(fact_2321_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2278 (all A_31 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_31),zero_zero_nat) = zero_zero_nat) # label(fact_2322_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2279 (all A_31 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_31),zero_zero_int) = zero_zero_int) # label(fact_2323_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2280 (all A_30 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,zero_z891286103de_int),A_30) = zero_z891286103de_int) # label(fact_2324_div__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2281 (all A_30 hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,zero_z126310315umeral),A_30) = zero_z126310315umeral) # label(fact_2325_div__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2282 (all A_30 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,zero_zero_nat),A_30) = zero_zero_nat) # label(fact_2326_div__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2283 (all A_30 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,zero_zero_int),A_30) = zero_zero_int) # label(fact_2327_div__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2284 (all A_29 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_29),one_on1684967323de_int) = A_29) # label(fact_2328_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2285 (all A_29 hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_29),one_on1645066479umeral) = A_29) # label(fact_2329_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2286 (all A_29 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_29),one_one_nat) = A_29) # label(fact_2330_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2287 (all A_29 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_29),one_one_int) = A_29) # label(fact_2331_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2288 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),zero_zero_int))))) # label(fact_2332_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2289 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Aa),Ba)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa))))) # label(fact_2333_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2290 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Aa),Ba)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int))))) # label(fact_2334_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2291 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Y)))))) # label(fact_2335_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2292 (all A_2 (A_2 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),A_2) = one_one_int)) # label(fact_2336_zdiv__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2293 (all A_2 all B_1 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(div_mod_int(A_2),B_1)),B_1) = zero_zero_int) # label(fact_2337_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2294 (all A_2 (hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),zero_zero_int) = zero_zero_int & hAPP_int_int(div_mod_int(A_2),zero_zero_int) = A_2)) # label(fact_2338_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2295 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),hAPP_real_real(uminus_uminus_real,X_1))))) # label(fact_2339_real__add__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2296 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,X_1)),Y_2)))) # label(fact_2340_real__0__le__add__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2297 (all U_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,U_1),U_1))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),X)))) # label(fact_2341_real__minus__mult__self__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2298 (all A_2 all B_1 all C_1 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1)),C_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),C_1)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),C_1))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(div_mod_int(A_2),C_1)),hAPP_int_int(div_mod_int(B_1),C_1))),C_1))) # label(fact_2342_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2299 (all K_2 all L_2 pdivmod(K_2,L_2) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(abs_abs_int,K_2)),hAPP_int_int(abs_abs_int,L_2))),hAPP_int_int(div_mod_int(hAPP_int_int(abs_abs_int,K_2)),hAPP_int_int(abs_abs_int,L_2)))) # label(fact_2343_pdivmod__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2300 (all A_28 all B_25 all C_13 ((C_13 = zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_13),A_28)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_13),B_25)) = zero_z891286103de_int) & (C_13 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_13),A_28)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_13),B_25)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_28),B_25)))) # label(fact_2344_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2301 (all A_28 all B_25 all C_13 ((C_13 = zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_13),A_28)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_13),B_25)) = zero_z126310315umeral) & (C_13 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_13),A_28)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_13),B_25)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_28),B_25)))) # label(fact_2345_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2302 (all A_28 all B_25 all C_13 ((C_13 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_13),A_28)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_13),B_25)) = zero_zero_nat) & (C_13 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_13),A_28)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_13),B_25)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_28),B_25)))) # label(fact_2346_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2303 (all A_28 all B_25 all C_13 ((C_13 = zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_13),A_28)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_13),B_25)) = zero_zero_int) & (C_13 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_13),A_28)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_13),B_25)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_28),B_25)))) # label(fact_2347_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2304 (all A_27 all B_24 (B_24 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_27),B_24)),B_24) = A_27)) # label(fact_2348_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2305 (all A_27 all B_24 (B_24 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_27),B_24)),B_24) = A_27)) # label(fact_2349_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2306 (all A_27 all B_24 (B_24 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_27),B_24)),B_24) = A_27)) # label(fact_2350_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2307 (all A_27 all B_24 (B_24 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_27),B_24)),B_24) = A_27)) # label(fact_2351_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2308 (all A_26 all B_23 (B_23 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_23),A_26)),B_23) = A_26)) # label(fact_2352_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2309 (all A_26 all B_23 (B_23 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_23),A_26)),B_23) = A_26)) # label(fact_2353_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2310 (all A_26 all B_23 (B_23 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_23),A_26)),B_23) = A_26)) # label(fact_2354_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2311 (all A_26 all B_23 (B_23 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_23),A_26)),B_23) = A_26)) # label(fact_2355_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2312 (all A_25 all B_22 all C_12 (C_12 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,A_25),C_12)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_22),C_12)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_25),B_22))) # label(fact_2356_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2313 (all A_25 all B_22 all C_12 (C_12 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,A_25),C_12)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_22),C_12)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_25),B_22))) # label(fact_2357_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2314 (all A_25 all B_22 all C_12 (C_12 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_25),C_12)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_22),C_12)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_25),B_22))) # label(fact_2358_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2315 (all A_25 all B_22 all C_12 (C_12 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_25),C_12)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_22),C_12)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_25),B_22))) # label(fact_2359_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2316 (all A_24 all B_21 all C_11 (C_11 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_11),A_24)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_11),B_21)) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_24),B_21))) # label(fact_2360_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2317 (all A_24 all B_21 all C_11 (C_11 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_11),A_24)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_11),B_21)) = hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_24),B_21))) # label(fact_2361_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2318 (all A_24 all B_21 all C_11 (C_11 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_11),A_24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_11),B_21)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_24),B_21))) # label(fact_2362_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2319 (all A_24 all B_21 all C_11 (C_11 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_11),A_24)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_11),B_21)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_24),B_21))) # label(fact_2363_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2320 (all A_23 (A_23 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_23),A_23) = one_on1684967323de_int)) # label(fact_2364_div__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2321 (all A_23 (A_23 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_23),A_23) = one_on1645066479umeral)) # label(fact_2365_div__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2322 (all A_23 (A_23 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_23),A_23) = one_one_nat)) # label(fact_2366_div__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2323 (all A_23 (A_23 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_23),A_23) = one_one_int)) # label(fact_2367_div__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2324 (all A_22 all B_20 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_22),B_20)),B_20) = zero_z891286103de_int) # label(fact_2368_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2325 (all A_22 all B_20 hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_22),B_20)),B_20) = zero_z126310315umeral) # label(fact_2369_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2326 (all A_22 all B_20 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(div_mod_nat(A_22),B_20)),B_20) = zero_zero_nat) # label(fact_2370_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2327 (all A_22 all B_20 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(div_mod_int(A_22),B_20)),B_20) = zero_zero_int) # label(fact_2371_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2328 (all L_2 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),L_2)) -> negDivAlg(K_2,L_2) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,K_2),L_2)),hAPP_int_int(div_mod_int(K_2),L_2))))) # label(fact_2372_negDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2329 (all I_1 all K_1 (hAPP_int_int(hAPP_int_fun_int_int(div_div_int,I_1),K_1) = zero_zero_int <-> K_1 = zero_zero_int | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),I_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),K_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),zero_zero_int)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),I_1)))) # label(fact_2373_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2330 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa))))) # label(fact_2374_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2331 (all I_1 all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,I_1),K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),I_1))))) # label(fact_2375_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2332 (all Ba all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba))))) # label(fact_2376_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2333 (all B_1 all B_4 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_int,zero_zero_int),B_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_4),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_4))))))) # label(fact_2377_zdiv__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2334 (all B_1 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_int,B_1),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),zero_zero_int))))) # label(fact_2378_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2335 (all B_1 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_int,A_2),B_1)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = zero_zero_int))) # label(fact_2379_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2336 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int))))) # label(fact_2380_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2337 (all B_1 all 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_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),zero_zero_int))))) # label(fact_2381_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2338 (all B_1 all B_4 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_4),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_4)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))))))) # label(fact_2382_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2339 (all B_1 all 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_int,B_1),A_2)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = zero_zero_int))) # label(fact_2383_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2340 (all B_1 all A_2 all A_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),A_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_4),B_1)))))) # label(fact_2384_zdiv__mono1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2341 (all B_1 all A_2 all A_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),A_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_4),B_1)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)))))) # label(fact_2385_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2342 (all K_2 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,one_one_int),K_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),K_2)),X))))) # label(fact_2386_int__div__less__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2343 (all A_2 all B_1 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),C_1)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),C_1))) # label(fact_2387_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2344 (all X all Y all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y),Z_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Z_1)),Y))))) # label(fact_2388_div__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2345 (all A_2 all B_1 A_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))),hAPP_int_int(div_mod_int(A_2),B_1))) # label(fact_2389_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2346 (all A_2 all B_1 all C_1 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)),C_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),C_1))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(div_mod_int(B_1),C_1))),C_1))) # label(fact_2390_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2347 (all B_1 all A_2 all K_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))),hAPP_int_int(div_mod_int(A_2),B_1))),K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),K_2)) # label(fact_2391_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2348 (all A_2 all B_1 all K_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),B_1)),hAPP_int_int(div_mod_int(A_2),B_1))),K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),K_2)) # label(fact_2392_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2349 (all M_1 all N_1 hAPP_int_int(div_mod_int(M_1),N_1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,M_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,M_1),N_1)),N_1))) # label(fact_2393_zmod__zdiv__equality_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2350 (all N_1 all M_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,N_1),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,M_1),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,M_1),hAPP_int_int(div_mod_int(M_1),N_1))) # label(fact_2394_zmult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2351 (all A_2 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(number_number_of_int,min)) = hAPP_int_int(uminus_uminus_int,A_2)) # label(fact_2395_zdiv__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2352 (all A_21 all C_10 all B_19 (B_19 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_21),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_19),C_10))),B_19) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_10),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_21),B_19)))) # label(fact_2396_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2353 (all A_21 all C_10 all B_19 (B_19 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_21),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_19),C_10))),B_19) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,C_10),hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_21),B_19)))) # label(fact_2397_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2354 (all A_21 all C_10 all B_19 (B_19 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_21),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_19),C_10))),B_19) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_21),B_19)))) # label(fact_2398_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2355 (all A_21 all C_10 all B_19 (B_19 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_21),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_19),C_10))),B_19) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_10),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_21),B_19)))) # label(fact_2399_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2356 (all A_20 all C_9 all B_18 (B_18 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_20),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,C_9),B_18))),B_18) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,C_9),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_20),B_18)))) # label(fact_2400_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2357 (all A_20 all C_9 all B_18 (B_18 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_20),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,C_9),B_18))),B_18) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,C_9),hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_20),B_18)))) # label(fact_2401_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2358 (all A_20 all C_9 all B_18 (B_18 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_20),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_9),B_18))),B_18) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_20),B_18)))) # label(fact_2402_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2359 (all A_20 all C_9 all B_18 (B_18 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_20),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_9),B_18))),B_18) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_9),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_20),B_18)))) # label(fact_2403_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2360 (all A_2 all B_1 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (B_1 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = Q_1))) # label(fact_2404_divmod__int__rel__div) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2361 (all A_19 all B_17 (B_17 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_19),B_17)),B_17) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_19),B_17)),one_on1684967323de_int))) # label(fact_2405_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2362 (all A_19 all B_17 (B_17 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_19),B_17)),B_17) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_19),B_17)),one_on1645066479umeral))) # label(fact_2406_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2363 (all A_19 all B_17 (B_17 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),B_17)),B_17) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_19),B_17)),one_one_nat))) # label(fact_2407_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2364 (all A_19 all B_17 (B_17 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_19),B_17)),B_17) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_19),B_17)),one_one_int))) # label(fact_2408_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2365 (all A_18 all B_16 (B_16 != zero_z891286103de_int -> hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,B_16),A_18)),B_16) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_18),B_16)),one_on1684967323de_int))) # label(fact_2409_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2366 (all A_18 all B_16 (B_16 != zero_z126310315umeral -> hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,B_16),A_18)),B_16) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_18),B_16)),one_on1645066479umeral))) # label(fact_2410_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2367 (all A_18 all B_16 (B_16 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),A_18)),B_16) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_18),B_16)),one_one_nat))) # label(fact_2411_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2368 (all A_18 all B_16 (B_16 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_16),A_18)),B_16) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_18),B_16)),one_one_int))) # label(fact_2412_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2369 (all A_17 all B_15 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(div_mo231679042de_int(A_17),B_15)),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_17),B_15)),B_15)) = A_17) # label(fact_2413_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2370 (all A_17 all B_15 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(div_mo1740067990umeral(A_17),B_15)),hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_17),B_15)),B_15)) = A_17) # label(fact_2414_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2371 (all A_17 all B_15 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(div_mod_nat(A_17),B_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_17),B_15)),B_15)) = A_17) # label(fact_2415_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2372 (all A_17 all B_15 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(div_mod_int(A_17),B_15)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_17),B_15)),B_15)) = A_17) # label(fact_2416_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2373 (all B_14 all A_16 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_14),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_16),B_14))),hAPP_Q1762011733de_int(div_mo231679042de_int(A_16),B_14)) = A_16) # label(fact_2417_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2374 (all B_14 all A_16 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_14),hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_16),B_14))),hAPP_C498520661umeral(div_mo1740067990umeral(A_16),B_14)) = A_16) # label(fact_2418_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2375 (all B_14 all A_16 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_16),B_14))),hAPP_nat_nat(div_mod_nat(A_16),B_14)) = A_16) # label(fact_2419_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2376 (all B_14 all A_16 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_14),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_16),B_14))),hAPP_int_int(div_mod_int(A_16),B_14)) = A_16) # label(fact_2420_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2377 (all A_15 all B_13 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_15),B_13)),B_13)),hAPP_Q1762011733de_int(div_mo231679042de_int(A_15),B_13)) = A_15) # label(fact_2421_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2378 (all A_15 all B_13 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_15),B_13)),B_13)),hAPP_C498520661umeral(div_mo1740067990umeral(A_15),B_13)) = A_15) # label(fact_2422_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2379 (all A_15 all B_13 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_15),B_13)),B_13)),hAPP_nat_nat(div_mod_nat(A_15),B_13)) = A_15) # label(fact_2423_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2380 (all A_15 all B_13 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_15),B_13)),B_13)),hAPP_int_int(div_mod_int(A_15),B_13)) = A_15) # label(fact_2424_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2381 (all B_12 all A_14 all C_8 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,B_12),hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_14),B_12))),hAPP_Q1762011733de_int(div_mo231679042de_int(A_14),B_12))),C_8) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_14),C_8)) # label(fact_2425_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2382 (all B_12 all A_14 all C_8 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,B_12),hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_14),B_12))),hAPP_C498520661umeral(div_mo1740067990umeral(A_14),B_12))),C_8) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_14),C_8)) # label(fact_2426_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2383 (all B_12 all A_14 all C_8 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_14),B_12))),hAPP_nat_nat(div_mod_nat(A_14),B_12))),C_8) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_8)) # label(fact_2427_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2384 (all B_12 all A_14 all C_8 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_12),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_14),B_12))),hAPP_int_int(div_mod_int(A_14),B_12))),C_8) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_14),C_8)) # label(fact_2428_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2385 (all A_13 all B_11 all C_7 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_13),B_11)),B_11)),hAPP_Q1762011733de_int(div_mo231679042de_int(A_13),B_11))),C_7) = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,A_13),C_7)) # label(fact_2429_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2386 (all A_13 all B_11 all C_7 hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_13),B_11)),B_11)),hAPP_C498520661umeral(div_mo1740067990umeral(A_13),B_11))),C_7) = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,A_13),C_7)) # label(fact_2430_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2387 (all A_13 all B_11 all C_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_13),B_11)),B_11)),hAPP_nat_nat(div_mod_nat(A_13),B_11))),C_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_7)) # label(fact_2431_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2388 (all A_13 all B_11 all C_7 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_13),B_11)),B_11)),hAPP_int_int(div_mod_int(A_13),B_11))),C_7) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),C_7)) # label(fact_2432_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2389 (all X all Y (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Y))),X)))) # label(fact_2433_zdiv__leq__prop) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2390 (all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(number_number_of_int,min)),B_1) = hAPP_int_int(number_number_of_int,min))) # label(fact_2434_div__eq__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2391 (all A_2 all B_1 all M_1 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),M_1)))),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(div_mod_int(A_2),M_1)),hAPP_int_int(div_mod_int(B_1),M_1)))) # label(fact_2435_zcong__zmod__aux) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2392 (all R_3 all S_2 all T_2 all R_5 all S_4 all M_1 all T_3 all N_1 (R_5 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,S_4),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,T_3),N_1)) -> (R_3 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,S_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,T_2),N_1)) -> hAPP_int_int(div_mod_int(R_5),R_3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,S_4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,R_5),R_3)),S_2))),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,T_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,R_5),R_3)),T_2))),N_1))))) # label(fact_2436_xzgcda__linear__aux2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2393 (all A_2 all B_1 (B_1 != zero_zero_int -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),hAPP_int_int(div_mod_int(A_2),B_1)))))) # label(fact_2437_divmod__int__rel__div__mod) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2394 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),negDivAlg(A_2,B_1)))))) # label(fact_2438_negDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2395 (all P_1 all N all K_1 (hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,N),K_1))) <-> (K_1 = zero_zero_int -> hBOOL(hAPP_int_bool(P_1,zero_zero_int))) & (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) -> (all I_2 all J_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),J_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J_1),K_1)) & N = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_2)),J_1) -> hBOOL(hAPP_int_bool(P_1,I_2))))) & (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),zero_zero_int)) -> (all I_2 all J_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),J_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J_1),zero_zero_int)) & N = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_2)),J_1) -> hBOOL(hAPP_int_bool(P_1,I_2))))))) # label(fact_2439_split__zdiv) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2396 (all A_12 all B_10 all Y all R_6 (A_12 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_10),Y)),R_6) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_6)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_6),B_10))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_10)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_10),R_6)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_6),zero_zero_int))) -> (B_10 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_12),B_10) = Y)))) # label(fact_2440_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2397 (all X all Y all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Y),Z_1)),Z_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Z_1)),Y))))) # label(fact_2441_div__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2398 (all A_2 all B_1 all C_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_1)) -> hAPP_int_int(div_mod_int(A_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),C_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),C_1))),hAPP_int_int(div_mod_int(A_2),B_1)))) # label(fact_2442_zmod__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2399 (all A_2 all B_1 (B_1 != zero_zero_int -> (hAPP_int_int(div_mod_int(A_2),B_1) = zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))) & (hAPP_int_int(div_mod_int(A_2),B_1) != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))),one_one_int)))) # label(fact_2443_zdiv__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2400 (all A_2 all B_1 (B_1 != zero_zero_int -> (hAPP_int_int(div_mod_int(A_2),B_1) = zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(uminus_uminus_int,A_2)),B_1) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))) & (hAPP_int_int(div_mod_int(A_2),B_1) != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(uminus_uminus_int,A_2)),B_1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))),one_one_int)))) # label(fact_2444_zdiv__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2401 (all B_1 all Bq all Br all A_2 all C_1 all Aq all Ar (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,C_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aq),Ar))) -> (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(B_1,C_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Bq),Br))) -> (C_1 != zero_zero_int -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1),C_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aq),Bq)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ar),Br)),C_1))),hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ar),Br)),C_1)))))))) # label(fact_2445_zadd1__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2402 (all L_2 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),L_2)) -> posDivAlg(K_2,L_2) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,K_2),L_2)),hAPP_int_int(div_mod_int(K_2),L_2))))) # label(fact_2446_posDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2403 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1)),zero_zero_int)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = hAPP_int_int(number_number_of_int,min)))) # label(fact_2447_div__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2404 (all P_1 all N all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,N),K_1)),hAPP_int_int(div_mod_int(N),K_1))) <-> (all I_2 all J_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),J_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J_1),K_1)) & N = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_2)),J_1) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,I_2),J_1))))))) # label(fact_2448_split__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2405 (all P_1 all N all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,N),K_1)),hAPP_int_int(div_mod_int(N),K_1))) <-> (all I_2 all J_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),J_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J_1),zero_zero_int)) & N = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_2)),J_1) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,I_2),J_1))))))) # label(fact_2449_split__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2406 (all A_2 all B_1 all C_1 all Q_1 all R_3 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(B_1,C_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3))) -> (C_1 != zero_zero_int -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1),C_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),Q_1)),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),R_3)),C_1))),hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),R_3)),C_1))))))) # label(fact_2450_zmult1__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2407 (all K_2 all L_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),L_2)) -> hAPP_int_int(z3div(K_2),L_2) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,K_2),L_2)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),L_2)) -> hAPP_int_int(z3div(K_2),L_2) = hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,K_2),hAPP_int_int(uminus_uminus_int,L_2)))))) # label(fact_2451_z3div__def) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2408 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_2452_le0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2409 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_2453_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2410 (all A_11 all B_9 A_11 = hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,A_11),B_9)),B_9)),hAPP_Q1762011733de_int(div_mo231679042de_int(A_11),B_9))) # label(fact_2454_mod__div__decomp) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2411 (all A_11 all B_9 A_11 = hAPP_C498520661umeral(hAPP_C1594335432umeral(plus_p1627245867umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(times_1655362735umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,A_11),B_9)),B_9)),hAPP_C498520661umeral(div_mo1740067990umeral(A_11),B_9))) # label(fact_2455_mod__div__decomp) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2412 (all A_11 all B_9 A_11 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_11),B_9)),B_9)),hAPP_nat_nat(div_mod_nat(A_11),B_9))) # label(fact_2456_mod__div__decomp) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2413 (all A_11 all B_9 A_11 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_11),B_9)),B_9)),hAPP_int_int(div_mod_int(A_11),B_9))) # label(fact_2457_mod__div__decomp) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2414 (all U_1 all V_2 all X all Y (X = Y -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,U_1)),V_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),U_1)),Y))),V_2))))) # label(fact_2458_sin__bound__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2415 (all U all M all N all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U)),N)))))) # label(fact_2459_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2416 (all U all M all N all J all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U)),M)),N))))) # label(fact_2460_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2417 (all X all Y all C_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_1),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,C_1),hAPP_real_real(abs_abs_real,Y)))) -> X = zero_zero_real))) # label(fact_2461_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2418 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))))) # label(fact_2462_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2419 (all M_1 all N_1 all K_2 ((K_2 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1)) = zero_zero_nat) & (K_2 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)))) # label(fact_2463_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2420 (all A_2 all B_1 all C_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),C_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_2),B_1)),C_1)) # label(fact_2464_div__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.74 2421 (all K_2 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(div_mod_nat(M_1),N_1)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1))) # label(fact_2465_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2422 (all M_1 all N_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(div_mod_nat(M_1),N_1)),K_2) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_2))) # label(fact_2466_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2423 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(div_mod_nat(M_1),N_1))) # label(fact_2467_div__mod__equality_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2424 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(div_mod_nat(M_1),N_1))) # label(fact_2468_mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2425 (all M_1 all N_1 hAPP_nat_nat(div_mod_nat(M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)),N_1))) # label(fact_2469_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2426 (all K_2 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1))) # label(fact_2470_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2427 (all M_1 all N_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_2))) # label(fact_2471_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2428 (all I all J_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),K_2)),J_2)) # label(fact_2472_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2429 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),M_1)) # label(fact_2473_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2430 (all M_1 all N_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_2))) # label(fact_2474_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2431 (all A_2 all B_1 all C_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_1)),C_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,B_1),C_1))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(div_mod_nat(A_2),C_1)),hAPP_nat_nat(div_mod_nat(B_1),C_1))),C_1))) # label(fact_2475_div__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2432 (all A_2 all B_1 all C_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1)),C_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,B_1),C_1))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),hAPP_nat_nat(div_mod_nat(B_1),C_1))),C_1))) # label(fact_2476_div__mult1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2433 (all A_2 all B_1 all C_1 hAPP_nat_nat(div_mod_nat(A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),C_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_2),B_1)),C_1))),hAPP_nat_nat(div_mod_nat(A_2),B_1))) # label(fact_2477_mod__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2434 (all K_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),K_2))))) # label(fact_2478_div__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2435 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)),M_1))) # label(fact_2479_div__le__dividend) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2436 (all M_1 all N_1 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1))) # label(fact_2480_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2437 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),N_1) = M_1)) # label(fact_2481_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2438 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),M_1)),N_1) = M_1)) # label(fact_2482_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2439 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1) = zero_zero_nat)) # label(fact_2483_div__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2440 (all P_1 all N all K_1 (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N),K_1))) <-> (K_1 = zero_zero_nat -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))) & (K_1 != zero_zero_nat -> (all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_1)) -> (N = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_2)),J_1) -> hBOOL(hAPP_nat_bool(P_1,I_2)))))))) # label(fact_2484_split__div) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2441 (all K_2 all N_1 all M_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_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,K_2),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,K_2),M_1)))))) # label(fact_2485_div__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2442 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)),M_1))))) # label(fact_2486_div__less__dividend) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2443 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N_1) = zero_zero_nat) # label(fact_2487_mult__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2444 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),zero_zero_nat) = zero_zero_nat) # label(fact_2488_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2445 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = zero_zero_nat <-> M = zero_zero_nat | N = zero_zero_nat)) # label(fact_2489_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2446 (all K_1 all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N) <-> K_1 = zero_zero_nat | M = N)) # label(fact_2490_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2447 (all K_1 all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N) <-> M = N | K_1 = zero_zero_nat)) # label(fact_2491_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2448 (all M all K_1 all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1) <-> M = N | K_1 = zero_zero_nat)) # label(fact_2492_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2449 (all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) = zero_zero_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M_1) = zero_zero_nat -> M_1 = N_1))) # label(fact_2493_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2450 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),M_1) = zero_zero_nat) # label(fact_2494_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2451 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),zero_zero_nat) = M_1) # label(fact_2495_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2452 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N_1) = zero_zero_nat) # label(fact_2496_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2453 (all P_1 all M all N ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N),M))) -> ((M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N),M))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N),M))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N),M)))))) # label(fact_2497_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2454 (all S_2 all T_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S_2),T_2)) -> S_2 != T_2)) # label(fact_2498_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2455 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> M_1 != N_1)) # label(fact_2499_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2456 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_2500_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2457 (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_2501_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2458 (all M all N (M != N <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)))) # label(fact_2502_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2459 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1))) # label(fact_2503_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2460 (all L_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),L_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_2),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_2),M_1)))))) # label(fact_2504_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2461 (all N_1 all J_2 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),N_1)),K_2)))) # label(fact_2505_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2462 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),N_1) = M_1) # label(fact_2506_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2463 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)),N_1) = M_1) # label(fact_2507_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2464 (all I all J_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_2))) # label(fact_2508_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2465 (all K_2 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) # label(fact_2509_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2466 (all M_1 all K_2 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) # label(fact_2510_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2467 (all M all K_1 all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1) <-> M = N)) # label(fact_2511_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2468 (all K_1 all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N) <-> M = N)) # label(fact_2512_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2469 (all M_1 all N_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_2))) # label(fact_2513_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2470 (all X all Y all Z_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z_1))) # label(fact_2514_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2471 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)) # label(fact_2515_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2472 (all K_2 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1))) # label(fact_2516_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2473 (all M_1 all N_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_2))) # label(fact_2517_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2474 (all I all U_1 all J_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),U_1)),K_2)) # label(fact_2518_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2475 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),M_1))) # label(fact_2519_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2476 (all L_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_2),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_2),M_1))))) # label(fact_2520_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2477 (all L_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),L_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),L_2))))) # label(fact_2521_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2478 (all I all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),I)) = I)) # label(fact_2522_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2479 (all N all K_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K_1) <-> M = N)))) # label(fact_2523_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2480 (all N_1 all K_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)))) # label(fact_2524_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2481 (all N all K_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))))) # label(fact_2525_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2482 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1))) # label(fact_2526_le__refl) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2483 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)))) # label(fact_2527_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2484 (all M_1 all N_1 (M_1 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_2528_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2485 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2))))) # label(fact_2529_le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2486 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> M_1 = N_1))) # label(fact_2530_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2487 (all K_2 all L_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),L_2)))))) # label(fact_2531_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2488 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),J_2))))) # label(fact_2532_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2489 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),K_2))))) # label(fact_2533_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2490 (all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1))))) # label(fact_2534_le__cube) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2491 (all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1)))) # label(fact_2535_le__square) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2492 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N_1) = N_1) # label(fact_2536_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2493 (all M all N (one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) <-> M = one_one_nat & N = one_one_nat)) # label(fact_2537_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2494 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),one_one_nat) = N_1) # label(fact_2538_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2495 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = one_one_nat <-> M = one_one_nat & N = one_one_nat)) # label(fact_2539_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.62/4.75 2496 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_2540_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2497 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) <-> 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),N)))) # label(fact_2541_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2498 (all M all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),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),N)))) # label(fact_2542_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2499 (all M all N all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N) <-> M = N))) # label(fact_2543_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2500 (all M all N all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_2544_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2501 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),K_2)))))) # label(fact_2545_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2502 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),J_2)))))) # label(fact_2546_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2503 (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_2547_gr0I) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2504 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> N_1 != zero_zero_nat)) # label(fact_2548_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2505 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_2549_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2506 (all N (N != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_2550_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2507 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat))) # label(fact_2551_not__less0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2508 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),M_1))))) # label(fact_2552_diff__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2509 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_2553_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2510 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1) # label(fact_2554_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2511 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),zero_zero_nat) = M_1) # label(fact_2555_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2512 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = zero_zero_nat <-> M = zero_zero_nat & N = zero_zero_nat)) # label(fact_2556_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2513 (all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = M_1 -> N_1 = zero_zero_nat)) # label(fact_2557_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2514 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)) = zero_zero_nat) # label(fact_2558_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2515 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_2559_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2516 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) = zero_zero_nat)) # label(fact_2560_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2517 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1))) # label(fact_2561_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2518 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),zero_zero_nat)) <-> N = zero_zero_nat)) # label(fact_2562_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2519 (all I all J_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),I))) # label(fact_2563_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2520 (all J_2 all I -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),I))) # label(fact_2564_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2521 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_2565_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2522 (all M_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_1))))) # label(fact_2566_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2523 (all M_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J_2))))) # label(fact_2567_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2524 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_2))))) # label(fact_2568_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2525 (all K_2 all L_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2)))))) # label(fact_2569_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2526 (all M_1 all N_1 all K_2 all L_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),L_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N_1) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))))) # label(fact_2570_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2527 (all I all J_2 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)))) # label(fact_2571_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2528 (all M_1 all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = M_1)) # label(fact_2572_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2529 (all I_1 all J all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J)))) # label(fact_2573_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2530 (all M_1 all N_1 (M_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) -> N_1 = one_one_nat | M_1 = zero_zero_nat)) # label(fact_2574_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2531 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) | M_1 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_2575_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2532 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> (M_1 != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))))) # label(fact_2576_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2533 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_2577_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2534 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | M = N)) # label(fact_2578_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2535 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) & M != N)) # label(fact_2579_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2536 (all N all K_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))))) # label(fact_2580_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2537 (all C_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_1),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_1),C_1)))))) # label(fact_2581_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2538 (all I all K_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),J_2))) # label(fact_2582_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2539 (all J all K_1 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1))))) # label(fact_2583_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2540 (all M_1 all K_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)),K_2))))) # label(fact_2584_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2541 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = M_1)) # label(fact_2585_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2542 (all I all K_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_2))) # label(fact_2586_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2543 (all I_1 all K_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J))))) # label(fact_2587_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2544 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1) = M_1)) # label(fact_2588_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2545 (all K_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1) = K_1 <-> J = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),I_1)))) # label(fact_2589_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2546 (all I all K_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_2)))) # label(fact_2590_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2547 (all I all K_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_2)),I) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),K_2))) # label(fact_2591_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2548 (all I all K_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_2)),I))) # label(fact_2592_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2549 (all U all M all N all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U)),N) <-> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U)),N)))) # label(fact_2593_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2550 (all U_1 all M_1 all N_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I)),U_1)),N_1)))) # label(fact_2594_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2551 (all U all M all N all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U)),N)))))) # label(fact_2595_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2552 (all U all M all N all J all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U)),N) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U)),M) = N))) # label(fact_2596_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2553 (all U_1 all M_1 all N_1 all J_2 all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U_1)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_2)),U_1)),M_1)),N_1))) # label(fact_2597_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2554 (all U all M all N all J all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U)),M)),N))))) # label(fact_2598_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2555 (all M_1 all K_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)),N_1)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_1))))) # label(fact_2599_add__leE) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2556 (all M_1 all K_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_2600_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2557 (all M_1 all K_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_1)))) # label(fact_2601_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2558 (all K_2 all L_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2)))))) # label(fact_2602_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2559 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_2))))) # label(fact_2603_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2560 (all M_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J_2))))) # label(fact_2604_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2561 (all M_1 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_1))))) # label(fact_2605_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2562 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_2606_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2563 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) <-> (exists K N = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)))) # label(fact_2607_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2564 (all K_1 all L (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L)) <-> (exists N_2 L = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_2)))) # label(fact_2608_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2565 (all N_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_1)))) # label(fact_2609_le__add1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2566 (all N_1 all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)))) # label(fact_2610_le__add2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2567 (all X_1 all Y_2 all Z_2 (X_1 = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Y_2),Z_2) <-> Y_2 = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Z_2))) # label(fact_2611_eq__diff__eq_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2568 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_2612_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2569 (all P_1 all Aa all Ba (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Aa),Ba))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))) & (all D_2 (Aa = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),D_2) -> hBOOL(hAPP_nat_bool(P_1,D_2)))))) # label(fact_2613_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2570 (all P_1 all Aa all Ba (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Aa),Ba))) <-> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) & -hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) | (exists D_2 (Aa = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),D_2) & -hBOOL(hAPP_nat_bool(P_1,D_2))))))) # label(fact_2614_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2571 (all M all N all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))))) # label(fact_2615_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2572 (all M all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))))) # label(fact_2616_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2573 (all N all P_1 (-hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(P_1,N)) -> (exists K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),N)) & (all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K)) -> -hBOOL(hAPP_nat_bool(P_1,I_2)))) & hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),one_one_nat)))))))) # label(fact_2617_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2574 (all X all N_1 all Y (hAPP_nat_nat(div_mod_nat(X),N_1) = hAPP_nat_nat(div_mod_nat(Y),N_1) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y),X)) -> (exists Q_3 X = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),Q_3)))))) # label(fact_2618_nat__mod__eq__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2575 (all M_1 all D_3 all R_3 (hAPP_nat_nat(div_mod_nat(M_1),D_3) = R_3 -> (exists Q_3 M_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,R_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Q_3),D_3))))) # label(fact_2619_mod__eqD) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2576 (all X_1 all N all Y_2 (hAPP_nat_nat(div_mod_nat(X_1),N) = hAPP_nat_nat(div_mod_nat(Y_2),N) <-> (exists Q1 exists Q2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),Q1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),Q2))))) # label(fact_2620_nat__mod__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2577 (all M_6 all D_4 (hAPP_nat_nat(div_mod_nat(M_6),D_4) = zero_zero_nat -> (exists Q_3 M_6 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,D_4),Q_3)))) # label(fact_2621_mod__eq__0D) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2578 (all M all K_1 all F ((all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M)),K_1)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_1)))))) # label(fact_2622_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2579 (all N all P_1 (-hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(P_1,N)) -> (exists K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) & (all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K)) -> -hBOOL(hAPP_nat_bool(P_1,I_2)))) & hBOOL(hAPP_nat_bool(P_1,K))))))) # label(fact_2623_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2580 (all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (exists K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) & hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K) = J_2)))) # label(fact_2624_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2581 (all N_1 all M_1 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1) -> N_1 = M_1))) # label(fact_2625_mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2582 (all A_2 all B_1 all C_1 all Q_1 all R_3 (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(B_1,C_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Q_1),R_3))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_1)) -> hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1),C_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),Q_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),R_3)),C_1))),hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),R_3)),C_1))))))) # label(fact_2626_divmod__nat__rel__mult1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2583 (all C_1 all A_2 all B_1 all Q_1 all R_3 (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(A_2,B_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Q_1),R_3))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_1)) -> hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(A_2,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),C_1)),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,Q_1),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),hAPP_nat_nat(div_mod_nat(Q_1),C_1))),R_3)))))))) # label(fact_2627_divmod__nat__rel__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2584 (all B_1 all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),B_1)) -> (exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y_1))),D_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),B_1))))))))) # label(fact_2628_lemma__interval) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2585 (all K_2 all L_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_2)) -> (exists N_2 L_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N_2)))) # label(fact_2629_le__Suc__ex) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2586 (all I_1 all J all F ((all I_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_1))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J)))))) # label(fact_2630_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2587 (all D2 all D1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D2)) -> (exists E (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),E)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,E),D1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,E),D2))))))) # label(fact_2631_real__lbound__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2588 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natceiling(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),one_one_real)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,natceiling(X)),one_one_nat))) # label(fact_2632_natceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2589 (all Qr_2 all M_1 all N_1 all Qr_1 (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),Qr_1)) -> (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),Qr_2)) -> Qr_1 = Qr_2))) # label(fact_2633_divmod__nat__rel__unique) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2590 (all N_1 natceiling(hAPP_int_real(number267125858f_real,N_1)) = hAPP_int_nat(number_number_of_nat,N_1)) # label(fact_2634_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2591 (all M_1 all N_1 all Q_1 all R_3 (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Q_1),R_3))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1) = Q_1)) # label(fact_2635_div__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2592 (all M_1 all N_1 all Q_1 all R_3 (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Q_1),R_3))) -> hAPP_nat_nat(div_mod_nat(M_1),N_1) = R_3)) # label(fact_2636_mod__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2593 (all X hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),natceiling(X)))) # label(fact_2638_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2594 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X)),natceiling(Y))))) # label(fact_2639_natceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2595 (all M_1 all N_1 hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)),hAPP_nat_nat(div_mod_nat(M_1),N_1))))) # label(fact_2641_divmod__nat__rel) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2596 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> natceiling(X) = zero_zero_nat)) # label(fact_2642_natceiling__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2597 (all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X_1)),one_one_nat)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),one_one_real)))) # label(fact_2643_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2598 (all B_1 all Bq all Br all A_2 all C_1 all Aq all Ar (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(A_2,C_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aq),Ar))) -> (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(B_1,C_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Bq),Br))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_1)) -> hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_1),C_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aq),Bq)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ar),Br)),C_1))),hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ar),Br)),C_1)))))))) # label(fact_2644_divmod__nat__rel__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2599 (all B_1 all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),B_1)) -> (exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y_1))),D_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),B_1))))))))) # label(fact_2645_lemma__interval__lt) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2600 (all M_1 all N_1 -(all Q_3 all R_1 -hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Q_3),R_1))))) # label(fact_2646_divmod__nat__rel__ex) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2601 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natfloor(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),one_one_real)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,natfloor(X)),one_one_nat))) # label(fact_2647_natfloor__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2602 (all N all M (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M) = one_one_nat <-> N = one_one_nat & M = one_one_nat)) # label(fact_2648_nat__mult__eq__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2603 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,N_1)),one_one_real))) -> natceiling(X) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))) # label(fact_2649_natceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2604 (all X all N_1 (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,N_1))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natceiling(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_int_real(number267125858f_real,N_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,natceiling(X)),hAPP_int_nat(number_number_of_nat,N_1))))) # label(fact_2650_natceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2605 (all B_1 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,zero_zero_int),B_1)) -> divmod_int(A_2,B_1) = posDivAlg(A_2,B_1)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_1)) -> (A_2 = zero_zero_int -> divmod_int(A_2,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),zero_zero_int)) & (A_2 != zero_zero_int -> divmod_int(A_2,B_1) = hAPP_P1975530577nt_int(negateSnd,negDivAlg(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1)))))) & (-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_int,zero_zero_int),B_1)) -> divmod_int(A_2,B_1) = negDivAlg(A_2,B_1)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> divmod_int(A_2,B_1) = hAPP_P1975530577nt_int(negateSnd,posDivAlg(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1))))))) # label(fact_2651_divmod__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2606 (all P_3 all Q_1 divmod_int(P_3,Q_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,P_3),Q_1)),hAPP_int_int(div_mod_int(P_3),Q_1))) # label(fact_2652_divmod__int__mod__div) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2607 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(real_nat,N_1)))) # label(fact_2653_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2608 (all N_1 natfloor(hAPP_nat_real(real_nat,N_1)) = N_1) # label(fact_2654_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2609 (all N hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_nat_real(real_nat,N)),ring_1_Ints_real))) # label(fact_2655_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2610 (all N_1 natfloor(hAPP_int_real(number267125858f_real,N_1)) = hAPP_int_nat(number_number_of_nat,N_1)) # label(fact_2656_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2611 (all N all M (hAPP_nat_real(real_nat,N) = hAPP_nat_real(real_nat,M) <-> N = M)) # label(fact_2657_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2612 (all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_real(real_nat,hAPP_int_nat(number_number_of_nat,V_2)) = zero_zero_real) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_real(real_nat,hAPP_int_nat(number_number_of_nat,V_2)) = hAPP_int_real(number267125858f_real,V_2)))) # label(fact_2658_real__of__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2613 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,natfloor(X))),X)))) # label(fact_2659_real__natfloor__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2614 (all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,X)),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),natfloor(A_2))))) # label(fact_2660_le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2615 (all X hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,X)) = hAPP_nat_real(real_nat,X)) # label(fact_2661_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2616 (all N_1 natceiling(hAPP_nat_real(real_nat,N_1)) = N_1) # label(fact_2664_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2617 (all Aa all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),natfloor(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,Aa)),X_1))))) # label(fact_2665_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2618 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,natfloor(X))),one_one_real)))) # label(fact_2666_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2619 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,A_2)),X)) -> natfloor(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),hAPP_nat_real(real_nat,A_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,natfloor(X)),A_2))) # label(fact_2667_natfloor__subtract) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2620 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),one_one_real)),hAPP_nat_real(real_nat,natfloor(X))))) # label(fact_2668_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2621 (all N (hAPP_nat_real(real_nat,N) = zero_zero_real <-> N = zero_zero_nat)) # label(fact_2670_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2622 (all N_1 -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_1)),zero_zero_real))) # label(fact_2671_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2623 (all N all M (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(real_nat,M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)))) # label(fact_2672_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2624 (all N all M (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(real_nat,M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)))) # label(fact_2673_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2625 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_nat_real(real_nat,N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,natfloor(X)),N_1))))) # label(fact_2674_less__natfloor) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2626 (all M_1 all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,M_1)),hAPP_nat_real(real_nat,N_1))) # label(fact_2675_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2627 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natfloor(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_nat_real(real_nat,A_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,natfloor(X)),A_2))) # label(fact_2676_natfloor__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2628 (all M_1 all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,M_1)),hAPP_nat_real(real_nat,N_1))) # label(fact_2677_real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2629 (all Z_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,natfloor(Z_1)),one_one_nat)),N_1)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z_1),hAPP_nat_real(real_nat,N_1))))) # label(fact_2678_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2630 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,N_1)),one_one_real))) -> natfloor(X) = N_1))) # label(fact_2679_natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2631 (all X_1 all N (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,N))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(number_number_of_nat,N)),natfloor(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,N)),X_1)))))) # label(fact_2681_le__natfloor__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2632 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_nat_real(real_nat,natceiling(X))))) # label(fact_2682_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2633 (all Z_6 (hBOOL(hAPP_int_bool(nat_neg,Z_6)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_6),zero_zero_int)))) # label(fact_2683_neg__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2634 (all X_1 (-hBOOL(hAPP_int_bool(nat_neg,X_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)))) # label(fact_2684_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2635 (all V_2 (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_int_nat(number_number_of_nat,V_2) = zero_zero_nat)) # label(fact_2685_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2636 (all X hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),natfloor(X)))) # label(fact_2688_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2637 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natfloor(X)),natfloor(Y))))) # label(fact_2689_natfloor__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2638 (all X all N_1 (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,N_1))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natfloor(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_int_real(number267125858f_real,N_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,natfloor(X)),hAPP_int_nat(number_number_of_nat,N_1))))) # label(fact_2691_natfloor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2639 (all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N)),zero_zero_real)) <-> N = zero_zero_nat)) # label(fact_2692_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2640 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_nat_real(real_nat,M_1)),hAPP_nat_real(real_nat,N_1)))) # label(fact_2693_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2641 (all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_nat_real(real_nat,A_2))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X)),A_2)))) # label(fact_2694_natceiling__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2642 (all V all V_1 (hAPP_int_nat(number_number_of_nat,V) = hAPP_int_nat(number_number_of_nat,V_1) <-> (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,V_1)),zero_zero_int))) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V))) -> (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_1))) -> hAPP_int_int(number_number_of_int,V) = zero_zero_int) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_1))) -> V = V_1)))) # label(fact_2695_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2643 (all V_3 all K_2 all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_3)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_3)),K_2)) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_3))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_3)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),K_2)) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_3))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_3)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_2),V_3))),K_2))))) # label(fact_2696_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2644 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> natfloor(X) = zero_zero_nat)) # label(fact_2697_natfloor__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2645 (all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(real_nat,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_2698_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2646 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,N)),one_one_real)),hAPP_nat_real(real_nat,M))))) # label(fact_2699_nat__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2647 (all Q_1 all R_3 hAPP_P1975530577nt_int(negateSnd,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),R_3)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Q_1),hAPP_int_int(uminus_uminus_int,R_3))) # label(fact_2700_negateSnd__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2648 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,M)),one_one_real))))) # label(fact_2701_nat__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2649 (all Aa all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_nat_real(real_nat,Aa)))))) # label(fact_2702_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2650 (all A_2 all B_1 all Qr_1 (hBOOL(hAPP_P603027463t_bool(divmod_int_rel(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1)),Qr_1)) -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),hAPP_P1975530577nt_int(negateSnd,Qr_1))))) # label(fact_2703_divmod__int__rel__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2651 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,A_2)),X)) -> natceiling(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),hAPP_nat_real(real_nat,A_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,natceiling(X)),A_2))) # label(fact_2704_natceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2652 (all A_2 all B_1 (B_1 != zero_zero_int -> hBOOL(hAPP_P603027463t_bool(divmod_int_rel(A_2,B_1),divmod_int(A_2,B_1))))) # label(fact_2705_divmod__int__correct) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2653 (all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),natfloor(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X_1)))) # label(fact_2706_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2654 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> natceiling(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_nat_real(real_nat,A_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,natceiling(X)),A_2))) # label(fact_2707_natceiling__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2655 (all X_1 all N (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,N))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,natceiling(X_1)),hAPP_int_nat(number_number_of_nat,N))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_int_real(number267125858f_real,N))))))) # label(fact_2708_natceiling__le__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2656 (all B_1 all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,natfloor(A_2)),natfloor(B_1))),natfloor(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_2),B_1))))))) # label(fact_2709_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2657 (all R_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),R_3)) -> (exists N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),one_one_nat))),R_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),hAPP_nat_real(real_nat,N_2))))))) # label(fact_2710_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2658 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (all Y_1 exists N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),X)))))) # label(fact_2711_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2659 (all X exists N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_nat_real(real_nat,N_2)))) # label(fact_2712_reals__Archimedean2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2660 (all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,W)),zero_zero_int)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,one_one_int),hAPP_int_int(number_number_of_int,W)) = hAPP_P1175774780nt_int(product_fst_int_int,hAPP_P1975530577nt_int(negateSnd,negDivAlg(hAPP_int_int(uminus_uminus_int,one_one_int),hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,W))))))) # label(fact_2713_div__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2661 (all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,W)),zero_zero_int)) -> hAPP_int_int(div_mod_int(one_one_int),hAPP_int_int(number_number_of_int,W)) = hAPP_P1175774780nt_int(product_snd_int_int,hAPP_P1975530577nt_int(negateSnd,negDivAlg(hAPP_int_int(uminus_uminus_int,one_one_int),hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,W))))))) # label(fact_2714_mod__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2662 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Y)) -> natfloor(hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_nat_real(real_nat,Y))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,natfloor(X)),Y)))) # label(fact_2715_natfloor__div__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2663 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),zero_zero_int)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = hAPP_P1175774780nt_int(product_fst_int_int,hAPP_P1975530577nt_int(negateSnd,posDivAlg(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1))))))) # label(fact_2716_div__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2664 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),zero_zero_int)) -> hAPP_int_int(div_mod_int(A_2),B_1) = hAPP_P1175774780nt_int(product_snd_int_int,hAPP_P1975530577nt_int(negateSnd,posDivAlg(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1))))))) # label(fact_2717_mod__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2665 (all P_6 all Q_4 (hAPP_P731461727l_real(produc1935615926l_real,P_6) = hAPP_P731461727l_real(produc1935615926l_real,Q_4) -> (hAPP_P731461727l_real(produc556554744l_real,P_6) = hAPP_P731461727l_real(produc556554744l_real,Q_4) -> P_6 = Q_4))) # label(fact_2718_prod__eqI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2666 (all P_6 all Q_4 (hAPP_P1654798560at_nat(product_fst_nat_nat,P_6) = hAPP_P1654798560at_nat(product_fst_nat_nat,Q_4) -> (hAPP_P1654798560at_nat(product_snd_nat_nat,P_6) = hAPP_P1654798560at_nat(product_snd_nat_nat,Q_4) -> P_6 = Q_4))) # label(fact_2719_prod__eqI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2667 (all P_6 all Q_4 (hAPP_P1175774780nt_int(product_fst_int_int,P_6) = hAPP_P1175774780nt_int(product_fst_int_int,Q_4) -> (hAPP_P1175774780nt_int(product_snd_int_int,P_6) = hAPP_P1175774780nt_int(product_snd_int_int,Q_4) -> P_6 = Q_4))) # label(fact_2720_prod__eqI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2668 (all S_1 all T (S_1 = T <-> hAPP_P731461727l_real(produc1935615926l_real,S_1) = hAPP_P731461727l_real(produc1935615926l_real,T) & hAPP_P731461727l_real(produc556554744l_real,S_1) = hAPP_P731461727l_real(produc556554744l_real,T))) # label(fact_2721_prod__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2669 (all S_1 all T (S_1 = T <-> hAPP_P1654798560at_nat(product_fst_nat_nat,S_1) = hAPP_P1654798560at_nat(product_fst_nat_nat,T) & hAPP_P1654798560at_nat(product_snd_nat_nat,S_1) = hAPP_P1654798560at_nat(product_snd_nat_nat,T))) # label(fact_2722_prod__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2670 (all S_1 all T (S_1 = T <-> hAPP_P1175774780nt_int(product_fst_int_int,S_1) = hAPP_P1175774780nt_int(product_fst_int_int,T) & hAPP_P1175774780nt_int(product_snd_int_int,S_1) = hAPP_P1175774780nt_int(product_snd_int_int,T))) # label(fact_2723_prod__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2671 (all T_4 T_4 = hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,hAPP_P731461727l_real(produc1935615926l_real,T_4)),hAPP_P731461727l_real(produc556554744l_real,T_4))) # label(fact_2724_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2672 (all T_4 T_4 = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_P1654798560at_nat(product_fst_nat_nat,T_4)),hAPP_P1654798560at_nat(product_snd_nat_nat,T_4))) # label(fact_2725_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2673 (all T_4 T_4 = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_P1175774780nt_int(product_fst_int_int,T_4)),hAPP_P1175774780nt_int(product_snd_int_int,T_4))) # label(fact_2726_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2674 (all T T = hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,hAPP_P1477980390t_bool(produc926076176t_bool,T)),hAPP_P1477980390t_bool(produc840788306t_bool,T))) # label(fact_2727_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2675 (all T_4 T_4 = hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,hAPP_P141737927nt_int(produc1096438694nt_int,T_4)),hAPP_P141737927nt_int(produc1011150824nt_int,T_4))) # label(fact_2728_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2676 (all T_4 T_4 = hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,hAPP_P1913525324de_int(produc1968959274de_int,T_4)),hAPP_P1913525324de_int(produc221809260de_int,T_4))) # label(fact_2729_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2677 (all T_4 T_4 = hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,hAPP_P619277728umeral(produc310214954umeral,T_4)),hAPP_P619277728umeral(produc1857364076umeral,T_4))) # label(fact_2730_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.75 2678 (all T_4 T_4 = hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,hAPP_P1502442695at_nat(produc707142054at_nat,T_4)),hAPP_P1502442695at_nat(produc621854184at_nat,T_4))) # label(fact_2731_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2679 (all T_4 T_4 = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,hAPP_P1251258751nt_int(produc2110120675nt_int,T_4)),hAPP_P779853134nt_int(produc8341793nt_int,T_4))) # label(fact_2732_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2680 (all P_5 hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,hAPP_P731461727l_real(produc1935615926l_real,P_5)),hAPP_P731461727l_real(produc556554744l_real,P_5)) = P_5) # label(fact_2733_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2681 (all P_5 hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_P1654798560at_nat(product_fst_nat_nat,P_5)),hAPP_P1654798560at_nat(product_snd_nat_nat,P_5)) = P_5) # label(fact_2734_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2682 (all P_5 hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_P1175774780nt_int(product_fst_int_int,P_5)),hAPP_P1175774780nt_int(product_snd_int_int,P_5)) = P_5) # label(fact_2735_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2683 (all Pa hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,hAPP_P1477980390t_bool(produc926076176t_bool,Pa)),hAPP_P1477980390t_bool(produc840788306t_bool,Pa)) = Pa) # label(fact_2736_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2684 (all P_5 hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,hAPP_P141737927nt_int(produc1096438694nt_int,P_5)),hAPP_P141737927nt_int(produc1011150824nt_int,P_5)) = P_5) # label(fact_2737_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2685 (all P_5 hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,hAPP_P1913525324de_int(produc1968959274de_int,P_5)),hAPP_P1913525324de_int(produc221809260de_int,P_5)) = P_5) # label(fact_2738_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2686 (all P_5 hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,hAPP_P619277728umeral(produc310214954umeral,P_5)),hAPP_P619277728umeral(produc1857364076umeral,P_5)) = P_5) # label(fact_2739_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2687 (all P_5 hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,hAPP_P1502442695at_nat(produc707142054at_nat,P_5)),hAPP_P1502442695at_nat(produc621854184at_nat,P_5)) = P_5) # label(fact_2740_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2688 (all P_5 hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,hAPP_P1251258751nt_int(produc2110120675nt_int,P_5)),hAPP_P779853134nt_int(produc8341793nt_int,P_5)) = P_5) # label(fact_2741_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2689 (all A_10 hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,zero_zero_rat),A_10) = zero_zero_rat) # label(fact_2742_divide__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2690 (all A_10 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,zero_zero_complex),A_10) = zero_zero_complex) # label(fact_2743_divide__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2691 (all A_10 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,zero_zero_real),A_10) = zero_zero_real) # label(fact_2744_divide__zero__left) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2692 (all A_9 hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,A_9),zero_zero_rat) = zero_zero_rat) # label(fact_2745_divide__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2693 (all A_9 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,A_9),zero_zero_complex) = zero_zero_complex) # label(fact_2746_divide__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2694 (all A_9 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,A_9),zero_zero_real) = zero_zero_real) # label(fact_2747_divide__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2695 (all Y_8 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,zero_zero_complex),Y_8) = zero_zero_complex) # label(fact_2748_divide_Ozero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2696 (all Y_8 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,zero_zero_real),Y_8) = zero_zero_real) # label(fact_2749_divide_Ozero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2697 (all X_7 all Y_7 all Z_5 all W_2 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,X_7),Y_7)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,Z_5),W_2)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X_7),Z_5)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Y_7),W_2))) # label(fact_2750_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2698 (all X_7 all Y_7 all Z_5 all W_2 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,X_7),Y_7)),hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,Z_5),W_2)) = hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X_7),Z_5)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Y_7),W_2))) # label(fact_2751_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2699 (all X_7 all Y_7 all Z_5 all W_2 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_7),Y_7)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,Z_5),W_2)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X_7),Z_5)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y_7),W_2))) # label(fact_2752_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2700 (all A_8 all B_8 all C_6 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_8),hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,B_8),C_6)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,A_8),B_8)),C_6)) # label(fact_2753_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2701 (all A_8 all B_8 all C_6 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_8),hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,B_8),C_6)) = hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,A_8),B_8)),C_6)) # label(fact_2754_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2702 (all A_8 all B_8 all C_6 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_8),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,B_8),C_6)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_8),B_8)),C_6)) # label(fact_2755_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2703 (all A_7 all B_7 all C_5 hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,A_7),B_7)),C_5) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,A_7),C_5)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,B_7),C_5))) # label(fact_2756_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2704 (all A_7 all B_7 all C_5 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_7),B_7)),C_5) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,A_7),C_5)),hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,B_7),C_5))) # label(fact_2757_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2705 (all A_7 all B_7 all C_5 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_7),B_7)),C_5) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,A_7),C_5)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,B_7),C_5))) # label(fact_2758_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2706 (all X_6 all Y_6 all Ya_2 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X_6),Y_6)),Ya_2) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,X_6),Ya_2)),hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,Y_6),Ya_2))) # label(fact_2759_divide_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2707 (all X_6 all Y_6 all Ya_2 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_6),Y_6)),Ya_2) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_6),Ya_2)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,Y_6),Ya_2))) # label(fact_2760_divide_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2708 (all A_6 hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,A_6),one_one_rat) = A_6) # label(fact_2761_divide__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2709 (all A_6 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,A_6),one_one_complex) = A_6) # label(fact_2762_divide__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2710 (all A_6 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,A_6),one_one_real) = A_6) # label(fact_2763_divide__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2711 (all A_5 all B_6 all C_4 hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,A_5),B_6)),C_4) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,A_5),C_4)),hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,B_6),C_4))) # label(fact_2764_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2712 (all A_5 all B_6 all C_4 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,A_5),B_6)),C_4) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,A_5),C_4)),hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,B_6),C_4))) # label(fact_2765_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2713 (all A_5 all B_6 all C_4 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_5),B_6)),C_4) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,A_5),C_4)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,B_6),C_4))) # label(fact_2766_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2714 (all X_5 all Y_5 all Ya_1 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X_5),Y_5)),Ya_1) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,X_5),Ya_1)),hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,Y_5),Ya_1))) # label(fact_2767_divide_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2715 (all X_5 all Y_5 all Ya_1 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_5),Y_5)),Ya_1) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_5),Ya_1)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,Y_5),Ya_1))) # label(fact_2768_divide_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2716 (all R_3 all A_2 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),A_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),R_3)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,A_2),R_3)) # label(fact_2769_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2717 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_1),Y_2))) <-> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_2))) & (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),zero_zero_real))))) # label(fact_2770_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2718 (all F all Aa all Ba hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(F,Aa)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(F,Ba)),hAPP_real_real(F,Aa))),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa))),Aa)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(F,Ba)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(F,Ba)),hAPP_real_real(F,Aa))),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa))),Ba))) # label(fact_2771_lemma__MVT) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2719 (all A_2 all B_1 hAPP_int_int(div_mod_int(A_2),B_1) = hAPP_P1175774780nt_int(product_snd_int_int,divmod_int(A_2,B_1))) # label(fact_2772_mod__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2720 (all A_2 all B_1 hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = hAPP_P1175774780nt_int(product_fst_int_int,divmod_int(A_2,B_1))) # label(fact_2773_div__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2721 (all N_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),X))),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(real_nat,N_1)),hAPP_nat_real(real_nat,X))))) # label(fact_2774_real__of__nat__div4) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2722 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hAPP_int_int(div_mod_int(A_2),B_1) = hAPP_P1175774780nt_int(product_snd_int_int,negDivAlg(A_2,B_1))))) # label(fact_2775_mod__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2723 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = hAPP_P1175774780nt_int(product_fst_int_int,negDivAlg(A_2,B_1))))) # label(fact_2776_div__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2724 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_1)) -> hAPP_int_int(div_mod_int(A_2),B_1) = hAPP_P1175774780nt_int(product_snd_int_int,posDivAlg(A_2,B_1))))) # label(fact_2777_mod__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2725 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_1)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = hAPP_P1175774780nt_int(product_fst_int_int,posDivAlg(A_2,B_1))))) # label(fact_2778_div__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2726 (all N_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(real_nat,N_1)),hAPP_nat_real(real_nat,X))),hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),X)))))) # label(fact_2779_real__of__nat__div2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2727 (all N_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(real_nat,N_1)),hAPP_nat_real(real_nat,X))),hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),X)))),one_one_real))) # label(fact_2780_real__of__nat__div3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2728 (all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_int_int(div_mod_int(one_one_int),hAPP_int_int(number_number_of_int,W)) = hAPP_P1175774780nt_int(product_snd_int_int,posDivAlg(one_one_int,hAPP_int_int(number_number_of_int,W))))) # label(fact_2781_mod__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2729 (all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,one_one_int),hAPP_int_int(number_number_of_int,W)) = hAPP_P1175774780nt_int(product_fst_int_int,posDivAlg(one_one_int,hAPP_int_int(number_number_of_int,W))))) # label(fact_2782_div__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2730 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> hAPP_int_int(div_mod_int(A_2),B_1) = hAPP_P1175774780nt_int(product_snd_int_int,hAPP_P1975530577nt_int(negateSnd,negDivAlg(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1))))))) # label(fact_2783_mod__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2731 (all X all D_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),D_3)) -> hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(real_nat,X)),hAPP_nat_real(real_nat,D_3)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),D_3))),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(real_nat,hAPP_nat_nat(div_mod_nat(X),D_3))),hAPP_nat_real(real_nat,D_3))))) # label(fact_2784_real__of__nat__div__aux) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2732 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1) = hAPP_P1175774780nt_int(product_fst_int_int,hAPP_P1975530577nt_int(negateSnd,negDivAlg(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1))))))) # label(fact_2785_div__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2733 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X)),one_one_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,Y)),one_one_real)) -> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(arctan,X)),hAPP_real_real(arctan,Y)) = hAPP_real_real(arctan,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y))))))) # label(fact_2786_arctan__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2734 (all S_1 all T all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S_1),T)) -> hBOOL(hAPP_f115998247l_bool(hAPP_P1876494581l_bool(member180897546at_nat,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),S_1)),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Ba),T))),pair_less))))) # label(fact_2787_pair__lessI2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2735 (all V_3 all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(div_mod_nat(hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_3))) -> hAPP_nat_nat(div_mod_nat(hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(number_number_of_nat,V_2)) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_3))) -> hAPP_nat_nat(div_mod_nat(hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(nat,hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,V_3))))))) # label(fact_2788_mod__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2736 (all V_3 all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,V_3)))))) # label(fact_2789_div__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2737 (all M_1 all N_1 divmod_nat(M_1,N_1) = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1)),hAPP_nat_nat(div_mod_nat(M_1),N_1))) # label(fact_2790_divmod__nat__div__mod) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2738 (all M_1 all N_1 hAPP_nat_nat(div_mod_nat(M_1),N_1) = hAPP_P1654798560at_nat(product_snd_nat_nat,divmod_nat(M_1,N_1))) # label(fact_2791_mod__nat__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2739 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1) = hAPP_P1654798560at_nat(product_fst_nat_nat,divmod_nat(M_1,N_1))) # label(fact_2792_div__nat__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2740 (all X hAPP_real_real(arctan,hAPP_real_real(uminus_uminus_real,X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(arctan,X))) # label(fact_2793_arctan__minus) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2741 (all X_1 all Y_2 all P_1 ((hBOOL(P_1) -> hAPP_int_nat(nat,X_1) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,P_1),X_1),Y_2))) & (-hBOOL(P_1) -> hAPP_int_nat(nat,Y_2) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,P_1),X_1),Y_2))))) # label(fact_2794_nat__if__cong) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2742 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(arctan,X)),hAPP_real_real(arctan,Y))))) # label(fact_2795_arctan__monotone) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2743 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arctan,X)),hAPP_real_real(arctan,Y))))) # label(fact_2797_arctan__monotone_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2744 (all X natceiling(X) = hAPP_int_nat(nat,archim856651990g_real(X))) # label(fact_2798_natceiling__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2745 (all Z_3 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_3)) -> (hAPP_int_nat(nat,Z_2) = hAPP_int_nat(nat,Z_3) <-> Z_2 = Z_3)))) # label(fact_2801_eq__nat__nat__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2746 (all P_1 ((exists X1 hBOOL(hAPP_nat_bool(P_1,X1))) <-> (exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) & hBOOL(hAPP_nat_bool(P_1,hAPP_int_nat(nat,X_2))))))) # label(fact_2802_ex__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2747 (all P_1 ((all X1 hBOOL(hAPP_nat_bool(P_1,X1))) <-> (all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> hBOOL(hAPP_nat_bool(P_1,hAPP_int_nat(nat,X_2))))))) # label(fact_2803_all__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2748 (all Y_2 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_2)) -> (hAPP_int_nat(nat,X_1) = hAPP_int_nat(nat,Y_2) <-> X_1 = Y_2)))) # label(fact_2804_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2749 (all V_2 hAPP_int_nat(number_number_of_nat,V_2) = hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,V_2))) # label(fact_2805_nat__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2750 (all W hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,W)) = hAPP_int_nat(number_number_of_nat,W)) # label(fact_2806_nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2751 (all Z_1 (hBOOL(hAPP_int_bool(nat_neg,Z_1)) -> hAPP_int_nat(nat,Z_1) = zero_zero_nat)) # label(fact_2808_neg__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2752 (all X natfloor(X) = hAPP_int_nat(nat,archim1246769320r_real(X))) # label(fact_2809_natfloor__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2753 (all M_1 all N_1 hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),divmod_nat(M_1,N_1)))) # label(fact_2810_divmod__nat__rel__divmod__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2754 (all M_1 all N_1 all Qr_1 (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M_1,N_1),Qr_1)) -> divmod_nat(M_1,N_1) = Qr_1)) # label(fact_2811_divmod__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2755 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),zero_zero_int)) -> hAPP_int_nat(nat,Z_1) = zero_zero_nat)) # label(fact_2812_nat__le__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2756 (all I_1 (hAPP_int_nat(nat,I_1) = zero_zero_nat <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),zero_zero_int)))) # label(fact_2813_nat__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2757 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat,W_1)),hAPP_int_nat(nat,Z_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2))))) # label(fact_2814_nat__mono__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2758 (all W_1 all Z_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat,W_1)),hAPP_int_nat(nat,Z_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)))) # label(fact_2815_zless__nat__conj) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2759 (all Y_2 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_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(nat,X_1)),hAPP_int_nat(nat,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)))))) # label(fact_2816_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2760 (all W all Z_1 hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,W))),hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,Z_1)))) # label(fact_2817_nat__abs__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2761 (all M all N all Qr (hBOOL(hAPP_P1555980039t_bool(divmod_nat_rel(M,N),Qr)) <-> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_P1654798560at_nat(product_fst_nat_nat,Qr)),N)),hAPP_P1654798560at_nat(product_snd_nat_nat,Qr)) & (N = zero_zero_nat -> hAPP_P1654798560at_nat(product_fst_nat_nat,Qr) = zero_zero_nat) & (N != zero_zero_nat -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_P1654798560at_nat(product_snd_nat_nat,Qr))) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_P1654798560at_nat(product_snd_nat_nat,Qr)),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,N),hAPP_P1654798560at_nat(product_snd_nat_nat,Qr))) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_P1654798560at_nat(product_snd_nat_nat,Qr)),zero_zero_nat)))))) # label(fact_2818_divmod__nat__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2762 (all Z_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(nat,Z_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)))) # label(fact_2819_zero__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2763 (all Z_2 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat,W_1)),hAPP_int_nat(nat,Z_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2))))) # label(fact_2820_nat__less__eq__zless) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2764 (all Y_2 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_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat,X_1)),hAPP_int_nat(nat,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)))))) # label(fact_2821_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2765 (all Z_2 all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),W_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(nat,W_1)),hAPP_int_nat(nat,Z_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2))))) # label(fact_2822_nat__le__eq__zle) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2766 (all Z_4 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),Z_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(nat,Z_1)),hAPP_int_nat(nat,Z_4)))) # label(fact_2823_nat__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2767 (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)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y))))) # label(fact_2824_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2768 (all Z_4 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_4)) -> hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),Z_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(nat,Z_1)),hAPP_int_nat(nat,Z_4))))) # label(fact_2825_nat__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2769 (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)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y))))) # label(fact_2826_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2770 (all M_1 divmod_nat(M_1,zero_zero_nat) = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,zero_zero_nat),M_1)) # label(fact_2827_divmod__nat__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2771 (all Z_1 all Z_4 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_4)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_4),Z_1)) -> hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_1),Z_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(nat,Z_1)),hAPP_int_nat(nat,Z_4))))) # label(fact_2828_nat__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2772 (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)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Y))))) # label(fact_2829_Divides_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2773 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Y)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y)))) # label(fact_2830_nat__div__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2774 (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)) -> hAPP_nat_nat(div_mod_nat(hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y)) = hAPP_int_nat(nat,hAPP_int_int(div_mod_int(X),Y))))) # label(fact_2831_Divides_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2775 (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)) -> hAPP_int_nat(nat,hAPP_int_int(div_mod_int(X),Y)) = hAPP_nat_nat(div_mod_nat(hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y))))) # label(fact_2832_nat__mod__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2776 (all S_1 all T all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) -> hBOOL(hAPP_f115998247l_bool(hAPP_P1876494581l_bool(member180897546at_nat,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),S_1)),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Ba),T))),pair_less)))) # label(fact_2833_pair__lessI1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2777 (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)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y)) = hAPP_int_nat(nat,hAPP_int_int(nat_tsub(X),Y))))) # label(fact_2834_Nat__Transfer_Otransfer__nat__int__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2778 (all Z_4 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),zero_zero_int)) -> hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),Z_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(nat,hAPP_int_int(uminus_uminus_int,Z_1))),hAPP_int_nat(nat,hAPP_int_int(uminus_uminus_int,Z_4))))) # label(fact_2835_nat__mult__distrib__neg) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2779 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> divmod_nat(M_1,N_1) = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,zero_zero_nat),M_1))) # label(fact_2836_divmod__nat__base) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2780 (all I all N_1 hAPP_nat_nat(nat_aux(I),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(nat,I)),N_1)) # label(fact_2837_nat__aux__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2781 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> divmod_nat(M_1,N_1) = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1))),hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1))))) # label(fact_2839_divmod__nat__step) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2782 (all V_3 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_3))) -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,zero_zero_nat)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_nat_nat(suc,zero_zero_nat)) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_3))) -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,zero_zero_nat)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(nat,hAPP_int_int(div_mod_int(one_one_int),hAPP_int_int(number_number_of_int,V_3)))))) # label(fact_2840_one__mod__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2783 (all V_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,one_one_int),hAPP_int_int(number_number_of_int,V_3)))) # label(fact_2841_one__div__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2784 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(arccos,Y)))))) # label(fact_2842_arccos__lbound) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2785 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1))))) # label(fact_2843_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2786 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1)))) # label(fact_2844_lessI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2787 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1)))) # label(fact_2845_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2788 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_2846_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2789 (all Nat_5 all Nat_4 (hAPP_nat_nat(suc,Nat_5) = hAPP_nat_nat(suc,Nat_4) <-> Nat_5 = Nat_4)) # label(fact_2847_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2790 (all N_1 hAPP_nat_nat(suc,N_1) != N_1) # label(fact_2848_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2791 (all N_1 N_1 != hAPP_nat_nat(suc,N_1)) # label(fact_2849_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2792 (all M_1 zero_zero_nat != hAPP_nat_nat(suc,M_1)) # label(fact_2850_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2793 (all Nat_3 zero_zero_nat != hAPP_nat_nat(suc,Nat_3)) # label(fact_2851_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2794 (all M_1 hAPP_nat_nat(suc,M_1) != zero_zero_nat) # label(fact_2852_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2795 (all Nat_2 hAPP_nat_nat(suc,Nat_2) != zero_zero_nat) # label(fact_2853_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2796 (all M_1 zero_zero_nat != hAPP_nat_nat(suc,M_1)) # label(fact_2854_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2797 (all M_1 hAPP_nat_nat(suc,M_1) != zero_zero_nat) # label(fact_2855_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2798 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))))) # label(fact_2856_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2799 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | M = N)) # label(fact_2857_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2800 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_2858_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2801 (all N all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) <-> N = M))) # label(fact_2859_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2802 (all N_1 all M_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_1))) -> M_1 = N_1))) # label(fact_2860_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2803 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))))) # label(fact_2861_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2804 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> (hAPP_nat_nat(suc,M_1) != N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N_1))))) # label(fact_2862_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2805 (all K_2 all I all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_2))))) # label(fact_2863_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2806 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> M_1 = N_1))) # label(fact_2864_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2807 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_2865_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2808 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_2866_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2809 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) # label(fact_2867_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2810 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) # label(fact_2868_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2811 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N_1))) # label(fact_2869_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2812 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_2870_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2813 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_1))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> M_1 = hAPP_nat_nat(suc,N_1)))) # label(fact_2871_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2814 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_1))))) # label(fact_2872_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2815 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),hAPP_nat_nat(suc,M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)))) # label(fact_2873_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2816 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) | M = hAPP_nat_nat(suc,N))) # label(fact_2874_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2817 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M)))) # label(fact_2875_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2818 (all N_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1))) # label(fact_2876_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2819 (all K_1 all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N) <-> M = N)) # label(fact_2877_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2820 (all M_1 all N_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1)),hAPP_nat_nat(suc,K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),K_2)) # label(fact_2878_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2821 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)) # label(fact_2879_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2822 (all M_1 all N_1 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,hAPP_nat_nat(div_mod_nat(M_1),N_1))),N_1)) # label(fact_2880_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2823 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) <-> M = zero_zero_nat | (exists J_1 (M = hAPP_nat_nat(suc,J_1) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),N)))))) # label(fact_2881_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2824 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,zero_zero_nat))) <-> N = zero_zero_nat)) # label(fact_2882_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2825 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) <-> (exists M_2 N = hAPP_nat_nat(suc,M_2)))) # label(fact_2883_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2826 (all M all N (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N = zero_zero_nat | M = zero_zero_nat & N = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_2884_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2827 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N = zero_zero_nat | M = zero_zero_nat & N = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_2885_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2828 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_2886_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2829 (all I all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_1))))) # label(fact_2887_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2830 (all I all M_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),I))))) # label(fact_2888_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2831 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) <-> (exists K N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K))))) # label(fact_2889_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2832 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_2891_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2833 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) <-> N = M))) # label(fact_2892_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2834 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)))) # label(fact_2893_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2835 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))))) # label(fact_2894_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2836 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_2895_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2837 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_2896_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2838 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M)))) # label(fact_2897_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2839 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_2898_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2840 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),hAPP_nat_nat(suc,M_1)))) # label(fact_2899_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2841 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) # label(fact_2900_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2842 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) # label(fact_2901_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2843 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_2902_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2844 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1)) # label(fact_2903_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2845 (all N_1 hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)) # label(fact_2904_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2846 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)))) # label(fact_2905_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2847 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N_1)),one_one_nat) = N_1) # label(fact_2906_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2848 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1)) # label(fact_2907_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2849 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),hAPP_nat_nat(suc,zero_zero_nat)) = M_1) # label(fact_2908_div__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2850 (all M_1 all N_1 ((hAPP_nat_nat(suc,hAPP_nat_nat(div_mod_nat(M_1),N_1)) = N_1 -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,M_1)),N_1) = zero_zero_nat) & (hAPP_nat_nat(suc,hAPP_nat_nat(div_mod_nat(M_1),N_1)) != N_1 -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(div_mod_nat(M_1),N_1))))) # label(fact_2909_mod__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2851 (all M_1 hAPP_nat_nat(div_mod_nat(M_1),hAPP_nat_nat(suc,zero_zero_nat)) = zero_zero_nat) # label(fact_2910_mod__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2852 (all M_1 all K_2 (M_1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_2) -> (M_1 != hAPP_nat_nat(suc,zero_zero_nat) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))))) # label(fact_2911_one__less__m) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2853 (all M_1 all K_2 (M_1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_2) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_2))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),K_2))))) # label(fact_2912_one__less__k) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2854 (all M_1 all K_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = K_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),K_2))))))) # label(fact_2913_prod__mn__less__k) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2855 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1) = M_1 -> N_1 = hAPP_nat_nat(suc,zero_zero_nat)))) # label(fact_2914_mn__eq__m__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2856 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)))))) # label(fact_2915_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2857 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),M_1)))))) # label(fact_2916_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2858 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)))))) # label(fact_2917_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2859 (all I all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(suc,I))),N_1)))) # label(fact_2918_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2860 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_nat_nat(suc,zero_zero_nat))) = N_1)) # label(fact_2919_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2861 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)))) # label(fact_2920_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2862 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_1))))) # label(fact_2921_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2863 (all M_1 all K_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)),hAPP_nat_nat(suc,J_2)))) # label(fact_2924_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2864 (all M_1 all K_2 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_2))),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),M_1)))) # label(fact_2925_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2865 (all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_1)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(real_nat,N_1)),one_one_real)) # label(fact_2926_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2866 (all K_2 all N_1 all M_1 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1)),M_1))),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,M_1)),N_1)) # label(fact_2927_mod__mult__self4) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2867 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)) = N_1)) # label(fact_2928_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2868 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)))) # label(fact_2929_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2869 (all N_1 all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = N_1) & (M_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1))))) # label(fact_2930_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2870 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1))))) # label(fact_2931_div__geq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2871 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1) = zero_zero_nat) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1))))) # label(fact_2932_div__if) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2872 (all M_1 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),K_2)) -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1))),K_2) = one_one_nat)) # label(fact_2933_Suc__times__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2873 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_1)))) -> hAPP_int_nat(nat,archim1246769320r_real(X)) = N_1))) # label(fact_2934_floor__eq3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2874 (all Z_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_int_nat(nat,Z_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Z_2)))) # label(fact_2935_one__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2875 (all V_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,V_2))) -> hAPP_int_nat(number_number_of_nat,V_2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(number_number_of_nat,V_2)),one_one_nat)))) # label(fact_2936_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2876 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hAPP_nat_nat(suc,hAPP_int_nat(nat,Z_1)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_1)))) # label(fact_2937_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2877 (all Qa 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_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),Qa)),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),hAPP_nat_nat(suc,Qa)))) <-> Qa = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M),N)))) # label(fact_2938_split__div__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2878 (all P_1 all M all N (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M),N))) <-> N = zero_zero_nat & hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) | (exists Q_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),Q_3)),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),hAPP_nat_nat(suc,Q_3)))) & hBOOL(hAPP_nat_bool(P_1,Q_3)))))) # label(fact_2939_split__div_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2879 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1))))) # label(fact_2940_le__div__geq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2880 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_1)))) -> hAPP_int_nat(nat,archim1246769320r_real(X)) = N_1))) # label(fact_2941_floor__eq4) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2881 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (exists N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),Y)),X)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_2))),Y)))))))) # label(fact_2942_reals__Archimedean4) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2882 (all R_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),R_3)) -> (exists N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(real_nat,N_2)),R_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_2)))))))) # label(fact_2943_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2883 (all A_2 all C_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,A_2)),C_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,zero_zero_nat)),C_1))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(div_mod_nat(A_2),C_1)),hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,zero_zero_nat)),C_1))),C_1))) # label(fact_2944_div__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2884 (all I_1 all P_1 all Pa ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),Pa)) -> (hBOOL(hAPP_nat_bool(P_1,I_2)) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,I_2)),Pa)))))) -> (hBOOL(hAPP_nat_bool(P_1,I_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),Pa)) -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)))))) # label(fact_2945_mod__induct__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2885 (all J all I_1 all P_1 all Pa ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),Pa)) -> (hBOOL(hAPP_nat_bool(P_1,I_2)) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,I_2)),Pa)))))) -> (hBOOL(hAPP_nat_bool(P_1,I_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),Pa)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),Pa)) -> hBOOL(hAPP_nat_bool(P_1,J))))))) # label(fact_2946_mod__induct) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2886 (all P_1 all I_1 all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) -> (hBOOL(hAPP_nat_bool(P_1,J)) -> ((all I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) -> (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,I_2))) -> hBOOL(hAPP_nat_bool(P_1,I_2))))) -> hBOOL(hAPP_nat_bool(P_1,I_1)))))) # label(fact_2947_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2887 (all X (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)))) -> X = zero_zero_nat | X = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_2948_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2888 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> (exists K N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K))))) # label(fact_2949_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2889 (all M all No all F ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(F,N_2)),hAPP_nat_real(F,hAPP_nat_nat(suc,N_2))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(F,M)),hAPP_nat_real(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),No)))))) # label(fact_2950_lemma__f__mono__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2890 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (exists M_2 N_1 = hAPP_nat_nat(suc,M_2)))) # label(fact_2951_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2891 (all N_1 all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1)) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,V_2))),N_1)))) # label(fact_2952_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2892 (all I_1 all P_1 all K_1 (hBOOL(hAPP_nat_bool(P_1,K_1)) -> ((all N_2 (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_2))) -> hBOOL(hAPP_nat_bool(P_1,N_2)))) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_1),I_1)))))) # label(fact_2953_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2893 (all N_1 all M_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_5)) -> (exists M_2 M_5 = hAPP_nat_nat(suc,M_2)))) # label(fact_2954_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2894 (all I all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)) -> (K_2 != hAPP_nat_nat(suc,I) -> -(all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> K_2 != hAPP_nat_nat(suc,J_1)))))) # label(fact_2955_lessE) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2895 (all I all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_2)) -> -(all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> K_2 != hAPP_nat_nat(suc,J_1))))) # label(fact_2956_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2896 (all N_1 (N_1 != zero_zero_nat -> (exists M_2 N_1 = hAPP_nat_nat(suc,M_2)))) # label(fact_2957_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2897 (all K_2 hAPP_int_int(succ,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int)) # label(fact_2958_succ__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2898 (all K_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_2),min) = hAPP_int_int(succ,K_2)) # label(fact_2959_diff__bin__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2899 (all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(suc,hAPP_int_nat(number_number_of_nat,V_2)) = one_one_nat) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(suc,hAPP_int_nat(number_number_of_nat,V_2)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,V_2))))) # label(fact_2960_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2900 (all P_1 (-hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> ((exists X1 hBOOL(hAPP_nat_bool(P_1,X1))) -> (exists N_2 (-hBOOL(hAPP_nat_bool(P_1,N_2)) & hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_2)))))))) # label(fact_2961_exists__least__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2901 (all Y (Y != zero_zero_nat -> -(all Nat_1 Y != hAPP_nat_nat(suc,Nat_1)))) # label(fact_2962_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2902 (all P_1 all K_1 (hBOOL(hAPP_nat_bool(P_1,K_1)) -> ((all N_2 (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_2))) -> hBOOL(hAPP_nat_bool(P_1,N_2)))) -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))))) # label(fact_2963_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2903 (all N all P_1 (hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> ((all N_2 (hBOOL(hAPP_nat_bool(P_1,N_2)) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_2))))) -> hBOOL(hAPP_nat_bool(P_1,N))))) # label(fact_2964_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2904 (all K_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_2)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,K_2),M_1)),K_2) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,zero_zero_nat)))))) # label(fact_2965_int__power__div__base) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2905 (all S_1 all T all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,S_1),T)) -> hBOOL(hAPP_f115998247l_bool(hAPP_P1876494581l_bool(member180897546at_nat,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),S_1)),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Ba),T))),pair_leq))))) # label(fact_2966_pair__leqI2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2906 (all X all Y all Z_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Y)),Z_1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Y),Z_1))) # label(fact_2967_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2907 (all X all M_1 all Y hAPP_int_int(div_mod_int(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(div_mod_int(X),M_1)),Y)),M_1) = hAPP_int_int(div_mod_int(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Y)),M_1)) # label(fact_2968_zpower__zmod) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2908 (all N_1 all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),N_1))))) # label(fact_2969_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2909 (all X all Y all Z_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Y)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Z_1))) # label(fact_2970_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2910 (all X all N_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(abs_abs_int,X)),N_1)))) # label(fact_2971_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2911 (all X_1 all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(abs_abs_int,X_1)),N))) <-> X_1 != zero_zero_int | N = zero_zero_nat)) # label(fact_2972_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2912 (all A_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),P_3)) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(nat,P_3)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(nat,P_3)),one_one_nat))))) # label(fact_2973_Euler_Oaux__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2913 (all S_1 all T all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) -> hBOOL(hAPP_f115998247l_bool(hAPP_P1876494581l_bool(member180897546at_nat,hAPP_P369611207at_nat(hAPP_P402336767at_nat(produc494345619at_nat,hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Aa),S_1)),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,Ba),T))),pair_leq)))) # label(fact_2974_pair__leqI1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2914 (all M_1 all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M_1),N_1)) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_nat_real(real_nat,M_1)),N_1)) # label(fact_2975_real__of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2915 (all M_1 all N_1 hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_nat_real(real_nat,M_1)),N_1) = hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M_1),N_1))) # label(fact_2976_power__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2916 (all N_1 all X (X = hAPP_nat_real(real_nat,natfloor(X)) -> natfloor(hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,natfloor(X)),N_1))) # label(fact_2977_natfloor__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2917 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M),N) = zero_zero_nat <-> N != zero_zero_nat & M = zero_zero_nat)) # label(fact_2978_nat__power__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2918 (all X_1 all N all Y_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Y_2),hAPP_nat_nat(suc,N)) <-> X_1 = Y_2)) # label(fact_2979_exp__mono__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2919 (all X_1 all M (hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),M) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = zero_zero_nat | X_1 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_2980_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2920 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1) = hAPP_nat_nat(suc,zero_zero_nat)) # label(fact_2981_power__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2921 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_1)) | N = zero_zero_nat)) # label(fact_2982_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2922 (all M_1 all N_1 all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),I)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,I),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,I),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))))) # label(fact_2983_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2923 (all N_1 all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),I)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,I),N_1))))) # label(fact_2984_nat__one__le__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2924 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),N))) <-> N = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_1)))) # label(fact_2985_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2925 (all X_1 all N all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),hAPP_nat_nat(suc,N))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Y_2),hAPP_nat_nat(suc,N)))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)))) # label(fact_2986_exp__mono__lt) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2926 (all X_1 all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),N) = one_one_nat <-> X_1 = one_one_nat | N = zero_zero_nat)) # label(fact_2987_exp__eq__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2927 (all X_1 all N all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),hAPP_nat_nat(suc,N))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Y_2),hAPP_nat_nat(suc,N)))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)))) # label(fact_2988_exp__mono__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2928 (all X_1 all W_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),hAPP_int_nat(number_number_of_nat,W_1)))) <-> hAPP_int_nat(number_number_of_nat,W_1) = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_1)))) # label(fact_2989_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2929 (all P_3 all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),M_1) = one_one_nat) & (M_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)))))) # label(fact_2990_power__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2930 (all N_1 all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_int_nat(nat,X)),N_1) = hAPP_int_nat(nat,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),N_1)))) # label(fact_2991_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2931 (all N_1 all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hAPP_int_nat(nat,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_int_nat(nat,Z_1)),N_1))) # label(fact_2992_nat__power__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2932 (all W all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,W)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,W))) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,W)) = hAPP_int_nat(nat,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,V_2)),hAPP_int_nat(number_number_of_nat,W)))))) # label(fact_2993_power__nat__number__of__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2933 (all N_1 all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_int_nat(number_number_of_nat,V_2)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,zero_zero_nat),N_1)) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_int_nat(number_number_of_nat,V_2)),N_1) = hAPP_int_nat(nat,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,V_2)),N_1))))) # label(fact_2994_power__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2934 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),X)),one_one_real)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),one_one_real)),N_1))))) # label(fact_2995_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2935 (all A_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (exists R_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_1)) & hAPP_nat_real(hAPP_r474017924t_real(power_power_real,R_1),N_1) = A_2))))) # label(fact_2996_realpow__pos__nth) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2936 (all A_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_2)) & hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_2),N_1) = A_2 & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_1)) & hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y_1),N_1) = A_2 -> Y_1 = X_2))))))) # label(fact_2997_realpow__pos__nth__unique) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2937 (all N_1 (hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),N_1) = one_one_int | hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),N_1) = hAPP_int_int(number_number_of_int,min))) # label(fact_2998_neg__one__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2938 (all N_1 all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (exists R_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_1)) & hAPP_nat_real(hAPP_r474017924t_real(power_power_real,R_1),hAPP_nat_nat(suc,N_1)) = A_2)))) # label(fact_2999_realpow__pos__nth2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2939 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_nat(nat,X_1)) = one_one_int))) # label(fact_3000_EvenOdd_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2940 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_nat(nat,X_1)) = hAPP_int_int(number_number_of_int,min)))) # label(fact_3001_EvenOdd_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2941 (all Y_2 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_2)) -> ((hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven))) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_nat(nat,X_1)) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_nat(nat,Y_2)))))) # label(fact_3002_neg__one__power__parity) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2942 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,N_1)),one_one_real))) -> archim856651990g_real(X) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_1),one_one_int)))) # label(fact_3003_ceiling__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2943 (all Aa all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(uminus_uminus_int,Aa)),hAPP_int_nat(nat,X_1)) = hAPP_int_int(uminus_uminus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Aa),hAPP_int_nat(nat,X_1)))))) # label(fact_3004_neg__odd__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2944 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(arccos,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(arccos,Y)),pi))))) # label(fact_3005_arccos__lt__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2945 (all X_1 -(hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)))) # label(fact_3006_even__odd__conj) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2946 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) <-> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)))) # label(fact_3007_odd__iff__not__even) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2947 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)))) # label(fact_3008_even__odd__disj) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2948 (all X_1 (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)))) # label(fact_3009_not__odd__impl__even) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.76 2949 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Y_2)),zEven))))) # label(fact_3010_odd__minus__odd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2950 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Y_2)),zOdd))))) # label(fact_3011_odd__minus__even) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2951 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Y_2)),zOdd))))) # label(fact_3012_even__minus__odd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2952 (all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba)),zOdd)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),zEven)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),zOdd))))) # label(fact_3013_even__plus__odd__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2953 (all Aa all Ba (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba)),zOdd)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),zEven))))) # label(fact_3014_even__plus__odd__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2954 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),zEven)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba)),zOdd))))) # label(fact_3015_IntNatAux_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2955 (all Ba all Aa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),zOdd)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba)),zEven))))) # label(fact_3016_IntNatAux_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2956 (all X_1 all Y_2 (hAPP_int_real(real_int,X_1) = hAPP_int_real(real_int,Y_2) <-> X_1 = Y_2)) # label(fact_3017_real__of__int__inject) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2957 (all N_1 archim1246769320r_real(hAPP_int_real(real_int,N_1)) = N_1) # label(fact_3019_floor__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2958 (all X_1 (hAPP_int_real(real_int,archim1246769320r_real(X_1)) = X_1 <-> (exists N_2 X_1 = hAPP_int_real(real_int,N_2)))) # label(fact_3020_real__of__int__floor__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2959 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),one_one_int)),zEven)))) # label(fact_3021_odd__minus__one__even) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2960 (all N_1 archim856651990g_real(hAPP_int_real(real_int,N_1)) = N_1) # label(fact_3022_ceiling__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2961 (all X_1 (hAPP_int_real(real_int,archim856651990g_real(X_1)) = X_1 <-> (exists N_2 X_1 = hAPP_int_real(real_int,N_2)))) # label(fact_3023_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2962 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2)),zEven)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven)))) # label(fact_3025_EvenOdd_Oeven__product) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2963 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2)),zEven)))) # label(fact_3026_even__times__either) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2964 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_1),Y_2)),zEven))))) # label(fact_3027_EvenOdd_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2965 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Y_2)),zEven))))) # label(fact_3028_even__minus__even) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2966 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Y_2)),zEven)) <-> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven))))) # label(fact_3029_even__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2967 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2)),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)))) # label(fact_3030_odd__mult__odd__prop) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2968 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zOdd)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2)),zOdd))))) # label(fact_3031_EvenOdd_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2969 (all X_1 (hAPP_int_real(real_int,X_1) = zero_zero_real <-> X_1 = zero_zero_int)) # label(fact_3032_real__of__int__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2970 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,X_1)),hAPP_int_real(real_int,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)))) # label(fact_3034_real__of__int__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2971 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,X_1)),hAPP_int_real(real_int,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)))) # label(fact_3035_real__of__int__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2972 (all X all Y hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(real_int,X)),hAPP_int_real(real_int,Y))) # label(fact_3036_real__of__int__mult) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2973 (all V_2 hAPP_int_real(real_int,hAPP_int_int(number_number_of_int,V_2)) = hAPP_int_real(number267125858f_real,V_2)) # label(fact_3038_real__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2974 (all X all Y hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,X)),hAPP_int_real(real_int,Y))) # label(fact_3039_real__of__int__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2975 (all X all N_1 hAPP_int_real(real_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),N_1)) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(real_int,X)),N_1)) # label(fact_3040_real__of__int__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2976 (all X all N_1 hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(real_int,X)),N_1) = hAPP_int_real(real_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),N_1))) # label(fact_3041_power__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2977 (all X all Y hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(real_int,X)),hAPP_int_real(real_int,Y))) # label(fact_3042_real__of__int__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2978 (all X hAPP_int_real(real_int,hAPP_int_int(uminus_uminus_int,X)) = hAPP_real_real(uminus_uminus_real,hAPP_int_real(real_int,X))) # label(fact_3046_real__of__int__minus) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2979 (all X_1 hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_int_real(real_int,X_1)),ring_1_Ints_real))) # label(fact_3047_Ints__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2980 (all X hAPP_int_real(real_int,hAPP_int_int(abs_abs_int,X)) = hAPP_real_real(abs_abs_real,hAPP_int_real(real_int,X))) # label(fact_3048_real__of__int__abs) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2981 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,archim1246769320r_real(R_3))),R_3))) # label(fact_3049_real__of__int__floor__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2982 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,R_3),hAPP_int_real(real_int,archim856651990g_real(R_3))))) # label(fact_3050_real__of__int__ceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2983 (all N_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,N_1),X))),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(real_int,N_1)),hAPP_int_real(real_int,X))))) # label(fact_3051_real__of__int__div4) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2984 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim1246769320r_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_int_real(real_int,Aa))))) # label(fact_3052_floor__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2985 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,A_2)),X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),archim1246769320r_real(X))))) # label(fact_3053_le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2986 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,Aa)),X_1)))) # label(fact_3054_le__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2987 (all A_2 all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),archim1246769320r_real(X))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,A_2)),X)))) # label(fact_3055_real__le__floor) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2988 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,Aa)),X_1)))) # label(fact_3056_less__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2989 (all X all A_2 archim1246769320r_real(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_int_real(real_int,A_2))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim1246769320r_real(X)),A_2)) # label(fact_3057_floor__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2990 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_int_real(real_int,Aa))))) # label(fact_3058_ceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2991 (all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_int_real(real_int,A_2))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X)),A_2)))) # label(fact_3059_ceiling__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2992 (all X all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim856651990g_real(X)),A_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_int_real(real_int,A_2))))) # label(fact_3060_ceiling__le__real) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2993 (all N_1 all X (X = hAPP_int_real(real_int,archim1246769320r_real(X)) -> archim1246769320r_real(hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1)) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,archim1246769320r_real(X)),N_1))) # label(fact_3061_floor__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2994 (all X all A_2 archim1246769320r_real(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),hAPP_int_real(real_int,A_2))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim1246769320r_real(X)),A_2)) # label(fact_3062_floor__subtract) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2995 (all X all A_2 archim856651990g_real(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_int_real(real_int,A_2))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,archim856651990g_real(X)),A_2)) # label(fact_3063_ceiling__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2996 (all N_1 archim1246769320r_real(hAPP_real_real(uminus_uminus_real,hAPP_int_real(real_int,N_1))) = hAPP_int_int(uminus_uminus_int,N_1)) # label(fact_3064_floor__minus__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2997 (all X all A_2 archim856651990g_real(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),hAPP_int_real(real_int,A_2))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,archim856651990g_real(X)),A_2)) # label(fact_3065_ceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2998 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_1),N)),zEven)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven))))) # label(fact_3066_power__preserves__even) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 2999 (all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N)))) # label(fact_3067_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3000 (all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N)),zero_zero_real)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,N),zero_zero_int)))) # label(fact_3068_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3001 (all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N)),zero_zero_real)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N),zero_zero_int)))) # label(fact_3069_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3002 (all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_int_real(real_int,N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N)))) # label(fact_3070_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3003 (all M all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,M)),hAPP_int_real(number267125858f_real,N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,M),hAPP_int_int(number_number_of_int,N))))) # label(fact_3071_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3004 (all N all M (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N)),hAPP_int_real(real_int,M))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N)),M)))) # label(fact_3072_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3005 (all M all N (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,M)),hAPP_int_real(number267125858f_real,N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M),hAPP_int_int(number_number_of_int,N))))) # label(fact_3073_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3006 (all N all M (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,N)),hAPP_int_real(real_int,M))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,N)),M)))) # label(fact_3074_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3007 (all N all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,N),M)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,N)),one_one_real)),hAPP_int_real(real_int,M))))) # label(fact_3075_int__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3008 (all N all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N),M)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,M)),one_one_real))))) # label(fact_3076_int__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3009 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,X)),one_one_real))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),X)))) # label(fact_3077_lemma__floor2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3010 (all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hAPP_nat_real(real_nat,hAPP_int_nat(nat,X)) = hAPP_int_real(real_int,X))) # label(fact_3078_real__nat__eq__real) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3011 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_1),N)),zOdd)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd))))) # label(fact_3079_power__preserves__odd) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3012 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,R_3),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,archim1246769320r_real(R_3))),one_one_real)))) # label(fact_3080_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3013 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,archim1246769320r_real(R_3))),one_one_real)))) # label(fact_3081_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3014 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,N_1)),one_one_real))) -> archim1246769320r_real(X) = N_1))) # label(fact_3082_floor__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3015 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,R_3),one_one_real)),hAPP_int_real(real_int,archim1246769320r_real(R_3))))) # label(fact_3083_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3016 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,R_3),one_one_real)),hAPP_int_real(real_int,archim1246769320r_real(R_3))))) # label(fact_3084_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3017 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,archim856651990g_real(R_3))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,R_3),one_one_real)))) # label(fact_3085_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3018 (all R_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(real_int,archim856651990g_real(R_3))),one_one_real)),R_3))) # label(fact_3086_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3019 (all N_1 all M_1 all R_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,M_1)),R_3)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,N_1)),one_one_real))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M_1),N_1))))) # label(fact_3087_lemma__floor) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3020 (all N_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(real_int,N_1)),hAPP_int_real(real_int,X))),hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,N_1),X)))))) # label(fact_3088_real__of__int__div2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3021 (all N_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(real_int,N_1)),hAPP_int_real(real_int,X))),hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,N_1),X)))),one_one_real))) # label(fact_3089_real__of__int__div3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3022 (all X all D_3 (D_3 != zero_zero_int -> hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(real_int,X)),hAPP_int_real(real_int,D_3)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),D_3))),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(real_int,hAPP_int_int(div_mod_int(X),D_3))),hAPP_int_real(real_int,D_3))))) # label(fact_3090_real__of__int__div__aux) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3023 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,N_1)),one_one_real))) -> archim1246769320r_real(X) = N_1))) # label(fact_3091_floor__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3024 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),archim1246769320r_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,Aa)),one_one_real)),X_1)))) # label(fact_3092_less__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3025 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,archim1246769320r_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,Aa)),one_one_real))))) # label(fact_3093_floor__le__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3026 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(real_int,N_1)),one_one_real)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_int_real(real_int,N_1))) -> archim856651990g_real(X) = N_1))) # label(fact_3094_ceiling__eq3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3027 (all X_1 all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,archim856651990g_real(X_1)),Aa)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(real_int,Aa)),one_one_real))))) # label(fact_3095_ceiling__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3028 (all Aa all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),archim856651990g_real(X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_int_real(real_int,Aa)),one_one_real)),X_1)))) # label(fact_3096_le__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3029 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arccos,Y)),pi))))) # label(fact_3097_arccos__ubound) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3030 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(real_int,N_1)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_int_real(real_int,N_1)),one_one_real))) -> archim856651990g_real(X) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_1),one_one_int)))) # label(fact_3098_ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3031 (all Aa all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(uminus_uminus_int,Aa)),hAPP_int_nat(nat,X_1)) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Aa),hAPP_int_nat(nat,X_1))))) # label(fact_3099_neg__even__power) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3032 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(arccos,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arccos,Y)),pi))))) # label(fact_3100_arccos__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3033 (all R_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),zero_zero_real)) -> (exists N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N_2)),R_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_2),one_one_int)))))))) # label(fact_3101_reals__Archimedean__6c__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3034 (all R_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),R_3)) -> (exists N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N_2)),R_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_2),one_one_int)))))))) # label(fact_3102_reals__Archimedean__6b__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3035 (all R_3 exists N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(real_int,N_2)),R_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_3),hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_2),one_one_int)))))) # label(fact_3103_real__lb__ub__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3036 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(arccos,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arccos,Y)),pi)) & hAPP_real_real(cos,hAPP_real_real(arccos,Y)) = Y))) # label(fact_3104_arccos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3037 (all N_1 hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,pi),hAPP_nat_real(real_nat,N_1))) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)),N_1)) # label(fact_3105_cos__npi2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3038 (all N_1 hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),pi)) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)),N_1)) # label(fact_3106_cos__npi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3039 (all X hAPP_real_real(cos,hAPP_real_real(uminus_uminus_real,X)) = hAPP_real_real(cos,X)) # label(fact_3107_cos__minus) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3040 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(cos,X)),one_one_real))) # label(fact_3108_cos__le__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3041 (all X hAPP_real_real(cos,hAPP_real_real(arctan,X)) != zero_zero_real) # label(fact_3110_cos__arctan__not__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3042 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),pi)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,Y))))))) # label(fact_3111_cos__monotone__0__pi_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3043 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),hAPP_real_real(cos,X)))) # label(fact_3112_cos__ge__minus__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3044 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(cos,X))),one_one_real))) # label(fact_3113_abs__cos__le__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3045 (all X hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),pi)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(cos,X))) # label(fact_3115_cos__periodic__pi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3046 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),pi)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,Y))))))) # label(fact_3116_cos__monotone__0__pi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3047 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,pi)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(cos,Y)),hAPP_real_real(cos,X))))))) # label(fact_3117_cos__monotone__minus__pi__0_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3048 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),pi)) -> hAPP_real_real(arccos,hAPP_real_real(cos,X)) = X))) # label(fact_3118_arccos__cos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3049 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,Y)),one_one_real)) -> hAPP_real_real(cos,hAPP_real_real(arccos,Y)) = Y)) # label(fact_3119_cos__arccos__abs) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3050 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,pi)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(cos,Y)),hAPP_real_real(cos,X))))))) # label(fact_3120_cos__monotone__minus__pi__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3051 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hAPP_real_real(cos,hAPP_real_real(arccos,Y)) = Y))) # label(fact_3121_cos__arccos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3052 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,pi)),X)) -> hAPP_real_real(arccos,hAPP_real_real(cos,X)) = hAPP_real_real(uminus_uminus_real,X)))) # label(fact_3122_arccos__cos2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3053 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> (exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),pi)) & hAPP_real_real(cos,X_2) = Y & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),pi)) & hAPP_real_real(cos,Y_1) = Y -> Y_1 = X_2))))))) # label(fact_3123_cos__total) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3054 (all Y all X (hAPP_real_real(cos,X) != zero_zero_real -> (hAPP_real_real(cos,Y) != zero_zero_real -> (hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)) != zero_zero_real -> hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(tan,X)),hAPP_real_real(tan,Y))),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(tan,X)),hAPP_real_real(tan,Y)))))))) # label(fact_3124_tan__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3055 (all Y all X (hAPP_real_real(cos,X) != zero_zero_real -> (hAPP_real_real(cos,Y) != zero_zero_real -> hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(tan,X)),hAPP_real_real(tan,Y))) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,Y)))))) # label(fact_3125_lemma__tan__add1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3056 (all V_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_int_nat(number_number_of_nat,V_2)) = one_one_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_int_nat(number_number_of_nat,V_2)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,V_2))))) # label(fact_3126_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3057 (all V_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),one_one_nat) = one_one_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,V_2))))) # label(fact_3127_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3058 (all W hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),W) = pls) # label(fact_3132_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3059 (all K_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),K_2) = K_2) # label(fact_3133_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3060 (all K_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),pls) = K_2) # label(fact_3134_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3061 (all K_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_2),pls) = K_2) # label(fact_3135_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3062 (all X hAPP_real_real(tan,hAPP_real_real(uminus_uminus_real,X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(tan,X))) # label(fact_3139_tan__minus) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3063 (all Y hAPP_real_real(tan,hAPP_real_real(arctan,Y)) = Y) # label(fact_3140_tan__arctan) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3064 (all X hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),pi)) = hAPP_real_real(tan,X)) # label(fact_3151_tan__periodic__pi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3065 (all V (zero_zero_nat = hAPP_int_nat(number_number_of_nat,V) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V),pls)))) # label(fact_3154_eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3066 (all V (hAPP_int_nat(number_number_of_nat,V) = zero_zero_nat <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V),pls)))) # label(fact_3155_eq__number__of__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3067 (all V all V_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_int_nat(number_number_of_nat,V_1))) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),V_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_1))) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),V_1)))) # label(fact_3156_less__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3068 (all V all V_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_int_nat(number_number_of_nat,V_1))) <-> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V),V_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V),pls))))) # label(fact_3158_le__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3069 (all V (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(number_number_of_nat,V))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V)))) # label(fact_3159_less__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3070 (all V_3 all V_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(number_number_of_nat,V_3)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_3),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(number_number_of_nat,V_2)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_3),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V_2),V_3)))))) # label(fact_3160_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3071 (all N_1 hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),pi)) = zero_zero_real) # label(fact_3161_tan__npi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3072 (all X all N_1 hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,N_1)),pi))) = hAPP_real_real(tan,X)) # label(fact_3162_tan__periodic__n) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3073 (all X all N_1 hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),pi))) = hAPP_real_real(tan,X)) # label(fact_3163_tan__periodic__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3074 (all X all I hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(real_int,I)),pi))) = hAPP_real_real(tan,X)) # label(fact_3164_tan__periodic__int) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3075 (all V_3 all K_2 all V_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_3)),K_2)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_3)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_2),V_3))),K_2)))) # label(fact_3165_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3076 (all V_3 all V_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,V_2)),hAPP_int_nat(number_number_of_nat,V_3)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V_2),V_3))))) # label(fact_3166_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3077 (all V_2 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(number_number_of_nat,V_2)),one_one_nat) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_2),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(number_number_of_nat,V_2)),one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(pred,V_2))))) # label(fact_3167_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3078 (all M_1 all V_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),hAPP_int_nat(number_number_of_nat,V_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(pred,V_2))))) # label(fact_3168_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3079 (all K_1 all L (hAPP_int_int(bit1,K_1) = hAPP_int_int(bit1,L) <-> K_1 = L)) # label(fact_3169_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3080 (all K_2 hAPP_int_int(uminus_uminus_int,hAPP_int_int(bit1,K_2)) = hAPP_int_int(bit1,hAPP_int_int(pred,hAPP_int_int(uminus_uminus_int,K_2)))) # label(fact_3170_minus__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3081 (all K_2 hAPP_int_int(bit1,K_2) != pls) # label(fact_3171_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3082 (all L_2 pls != hAPP_int_int(bit1,L_2)) # label(fact_3172_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3083 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit1,K_1)),hAPP_int_int(bit1,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)))) # label(fact_3173_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3084 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit1,K1)),hAPP_int_int(bit1,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)))) # label(fact_3174_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3085 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit1,K_1)),hAPP_int_int(bit1,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)))) # label(fact_3175_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3086 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit1,K1)),hAPP_int_int(bit1,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)))) # label(fact_3176_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3087 (all K_1 (hAPP_int_int(bit1,K_1) = min <-> K_1 = min)) # label(fact_3177_rel__simps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3088 (all L (min = hAPP_int_int(bit1,L) <-> min = L)) # label(fact_3178_rel__simps_I43_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3089 (all X hAPP_int_int(succ,hAPP_int_int(pred,X)) = X) # label(fact_3180_succ__pred) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3090 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit1,K_1)),pls)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),pls)))) # label(fact_3181_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3091 (all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit1,W_1)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int)))) # label(fact_3182_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3092 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(bit1,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K_1)))) # label(fact_3183_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3093 (all K_2 hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2)) # label(fact_3184_Bit1__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3094 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit1,K_1)),min)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),min)))) # label(fact_3185_rel__simps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3095 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(bit1,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K_1)))) # label(fact_3186_rel__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3096 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit1,K_1)),min)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),min)))) # label(fact_3187_rel__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3097 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(bit1,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),K_1)))) # label(fact_3188_rel__simps_I26_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3098 (all W_1 (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_1)))) <-> hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,W_1))))) # label(fact_3189_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3099 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(pred,K_1)),L)))) # label(fact_3191_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3100 (all K_2 hAPP_int_int(pred,K_2) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_2),one_one_int)) # label(fact_3193_pred__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3101 (all K_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,min),K_2) = hAPP_int_int(pred,K_2)) # label(fact_3194_add__Min) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3102 (all K_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),min) = hAPP_int_int(pred,K_2)) # label(fact_3195_add__Min__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3103 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(bit1,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K_1)))) # label(fact_3196_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3104 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit1,K_1)),pls)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),pls)))) # label(fact_3197_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3105 (all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,pls),hAPP_int_int(bit1,L_2)) = hAPP_int_int(bit1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,min),L_2))) # label(fact_3201_diff__bin__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3106 (all N_1 hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,N_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),N_1)) # label(fact_3205_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3107 (all A_2 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(uminus_uminus_int,A_2)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))) = hAPP_int_int(uminus_uminus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))))) # label(fact_3208_power3__minus) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3108 (all X hAPP_int_int(abs_abs_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(abs_abs_int,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))))) # label(fact_3209_abs__power3__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3109 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(number_number_of_nat,pls)),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,pls)))))) # label(fact_3210_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3110 (all M_1 all V_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,M_1)))),hAPP_int_nat(number_number_of_nat,V_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),M_1)),hAPP_int_nat(number_number_of_nat,V_2))) # label(fact_3211_Suc__div__eq__add3__div__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3111 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,M_1)))),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),M_1)),N_1)) # label(fact_3212_Suc__div__eq__add3__div) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3112 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,N_1)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),N_1))) # label(fact_3213_div__Suc__eq__div__add3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3113 (all M_1 all V_2 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,M_1)))),hAPP_int_nat(number_number_of_nat,V_2)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),M_1)),hAPP_int_nat(number_number_of_nat,V_2))) # label(fact_3214_Suc__mod__eq__add3__mod__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3114 (all M_1 all N_1 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,M_1)))),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),M_1)),N_1)) # label(fact_3215_Suc__mod__eq__add3__mod) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3115 (all M_1 all N_1 hAPP_nat_nat(div_mod_nat(M_1),hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,N_1)))) = hAPP_nat_nat(div_mod_nat(M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),N_1))) # label(fact_3216_mod__Suc__eq__mod__add3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3116 (all V (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) <-> hAPP_int_nat(number_number_of_nat,V) = zero_zero_nat)) # label(fact_3217_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3117 (all X (hAPP_real_real(cos,X) != zero_zero_real -> (hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X)) != zero_zero_real -> hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(tan,X))),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(tan,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3218_tan__double) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3118 (all M_1 hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,pi),hAPP_nat_real(real_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),M_1))))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = zero_zero_real) # label(fact_3219_cos__pi__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3119 (all P_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3220_Euler_Oaux____2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3120 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) -> hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_1),one_one_int)),A_2))),one_one_int))) # label(fact_3221_neg__zmod__mult__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3121 (all V_2 all W ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,V_2))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,W)))),one_one_int)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,V_2))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_2)),one_one_int)),hAPP_int_int(number_number_of_int,W)))),one_one_int)))) # label(fact_3222_zmod__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3122 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arctan,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(arctan,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(tan,hAPP_real_real(arctan,Y)) = Y)) # label(fact_3223_arctan) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3123 (all K_1 all L (hAPP_int_int(bit0,K_1) = hAPP_int_int(bit0,L) <-> K_1 = L)) # label(fact_3224_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3124 (all K_2 all L_2 hAPP_int_int(bit0,K_2) != hAPP_int_int(bit1,L_2)) # label(fact_3225_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3125 (all K_2 all L_2 hAPP_int_int(bit1,K_2) != hAPP_int_int(bit0,L_2)) # label(fact_3226_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3126 (all L (pls = hAPP_int_int(bit0,L) <-> pls = L)) # label(fact_3228_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3127 (all K_1 (hAPP_int_int(bit0,K_1) = pls <-> K_1 = pls)) # label(fact_3229_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3128 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit0,K1)),hAPP_int_int(bit0,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)))) # label(fact_3230_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3129 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit0,K_1)),hAPP_int_int(bit0,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)))) # label(fact_3231_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3130 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit0,K1)),hAPP_int_int(bit0,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)))) # label(fact_3232_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3131 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit0,K_1)),hAPP_int_int(bit0,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)))) # label(fact_3233_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3132 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit0,K_2)),L_2) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),L_2))) # label(fact_3234_mult__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3133 (all K_2 hAPP_int_int(bit0,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2)) # label(fact_3235_Bit0__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3134 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(bit0,K_2)),hAPP_int_int(bit0,L_2)) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),L_2))) # label(fact_3236_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3135 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(bit0,K_2)),hAPP_int_int(bit0,L_2)) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_2),L_2))) # label(fact_3237_diff__bin__simps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3136 (all L_2 min != hAPP_int_int(bit0,L_2)) # label(fact_3238_rel__simps_I42_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3137 (all K_2 hAPP_int_int(bit0,K_2) != min) # label(fact_3239_rel__simps_I45_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3138 (all K_2 hAPP_int_int(uminus_uminus_int,hAPP_int_int(bit0,K_2)) = hAPP_int_int(bit0,hAPP_int_int(uminus_uminus_int,K_2))) # label(fact_3240_minus__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3139 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit1,K1)),hAPP_int_int(bit0,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)))) # label(fact_3241_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3140 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit1,K_1)),hAPP_int_int(bit0,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)))) # label(fact_3242_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3141 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit0,K_1)),pls)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),pls)))) # label(fact_3243_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3142 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(bit0,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),K_1)))) # label(fact_3244_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3143 (all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit0,W_1)),zero_zero_int)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int)))) # label(fact_3245_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3144 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit0,K_1)),hAPP_int_int(bit1,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)))) # label(fact_3246_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3145 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit0,K1)),hAPP_int_int(bit1,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)))) # label(fact_3247_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3146 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit0,K_1)),pls)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),pls)))) # label(fact_3248_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3147 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(bit0,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K_1)))) # label(fact_3249_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3148 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(bit1,K_2)),hAPP_int_int(bit0,L_2)) = hAPP_int_int(bit1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),L_2))) # label(fact_3250_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3149 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(bit0,K_2)),hAPP_int_int(bit1,L_2)) = hAPP_int_int(bit1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),L_2))) # label(fact_3251_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3150 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(bit1,K_2)),hAPP_int_int(bit0,L_2)) = hAPP_int_int(bit1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_2),L_2))) # label(fact_3252_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3151 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(bit1,K_2)),hAPP_int_int(bit1,L_2)) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_2),L_2))) # label(fact_3253_diff__bin__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3152 (all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,pls),hAPP_int_int(bit0,L_2)) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,pls),L_2))) # label(fact_3254_diff__bin__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3153 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),hAPP_int_int(bit0,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K_1)))) # label(fact_3255_rel__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3154 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit0,K_1)),min)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),min)))) # label(fact_3256_rel__simps_I28_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3155 (all V_2 all W hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,V_2))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W))) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,W))) # label(fact_3257_zdiv__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3156 (all W_1 (hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_1)))) <-> hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,W_1))))) # label(fact_3258_neg__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3157 (all K_2 hAPP_int_int(pred,hAPP_int_int(bit1,K_2)) = hAPP_int_int(bit0,K_2)) # label(fact_3259_pred__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3158 (all K_2 hAPP_int_int(pred,hAPP_int_int(bit0,K_2)) = hAPP_int_int(bit1,hAPP_int_int(pred,K_2))) # label(fact_3260_pred__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3159 (all K_2 hAPP_int_int(succ,hAPP_int_int(bit1,K_2)) = hAPP_int_int(bit0,hAPP_int_int(succ,K_2))) # label(fact_3262_succ__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3160 (all K_2 hAPP_int_int(succ,hAPP_int_int(bit0,K_2)) = hAPP_int_int(bit1,K_2)) # label(fact_3263_succ__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3161 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit0,K_1)),hAPP_int_int(bit1,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),L)))) # label(fact_3264_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3162 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit0,K1)),hAPP_int_int(bit1,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)))) # label(fact_3265_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3163 (all K_1 all L (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit1,K_1)),hAPP_int_int(bit0,L))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),L)))) # label(fact_3266_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3164 (all K1 all K2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(bit1,K1)),hAPP_int_int(bit0,K2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)))) # label(fact_3267_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3165 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(bit1,K_2)),L_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),L_2))),L_2)) # label(fact_3268_mult__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3166 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(bit0,K_1)),min)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K_1),min)))) # label(fact_3269_rel__simps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3167 (all K_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),hAPP_int_int(bit0,K_1))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K_1)))) # label(fact_3270_rel__simps_I25_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3168 (all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,min),hAPP_int_int(bit1,L_2)) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,min),L_2))) # label(fact_3271_diff__bin__simps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3169 (all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,min),hAPP_int_int(bit0,L_2)) = hAPP_int_int(bit1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,min),L_2))) # label(fact_3272_diff__bin__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3170 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(bit0,K_2)),hAPP_int_int(bit1,L_2)) = hAPP_int_int(bit1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(pred,K_2)),L_2))) # label(fact_3273_diff__bin__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3171 (all K_2 all L_2 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(bit1,K_2)),hAPP_int_int(bit1,L_2)) = hAPP_int_int(bit0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(succ,L_2)))) # label(fact_3274_add__Bit1__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3172 (all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,N_1)))) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,N_1)))))) # label(fact_3275_number__of1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3173 (all X hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3276_quartic__square__square) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3174 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,N_1))) # label(fact_3280_add__2__eq__Suc_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3175 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,N_1))) # label(fact_3281_add__2__eq__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3176 (all Z_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Z_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Z_1),Z_1)) # label(fact_3283_nat__mult__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3177 (all Z_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Z_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Z_1),Z_1)) # label(fact_3284_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3178 (all X_1 all Y_2 all Z_2 (X_1 = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,Y_2),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Z_2)) <-> hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,Y_2),Z_2))) # label(fact_3287_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3179 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,M_1))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3289_div2__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3180 (all X hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3290_power2__ge__self) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3181 (all M_1 hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(suc,hAPP_nat_nat(suc,M_1))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(div_mod_nat(M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) # label(fact_3291_mod2__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3182 (all A_2 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))))) # label(fact_3294_cube__square) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3183 (all X hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = X) # label(fact_3295_real__sum__of__halves) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3184 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),M_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = M_1) # label(fact_3296_add__self__div__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3185 (all V_2 all W hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,V_2))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,W)))) # label(fact_3297_zmod__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3186 (all Aa all Ba (hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Aa),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Ba),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) <-> hAPP_int_int(abs_abs_int,Aa) = hAPP_int_int(abs_abs_int,Ba))) # label(fact_3299_power2__eq__iff__abs__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3187 (all A_2 hAPP_int_int(abs_abs_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(abs_abs_int,A_2)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) # label(fact_3300_abs__power2__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3188 (all X_1 all K_1 (X_1 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),K_1) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)))) # label(fact_3301_zEvenI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3189 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) -> N_1 = zero_zero_nat | N_1 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_3302_less__2__cases) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3190 (all X_1 all Y_2 (hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = zero_zero_real <-> X_1 = zero_zero_real & Y_2 = zero_zero_real)) # label(fact_3304_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3191 (all X hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) # label(fact_3307_four__x__squared) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3192 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1)))) # label(fact_3308_two__realpow__ge__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3193 (all X_1 (hAPP_int_int(div_mod_int(X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int <-> hAPP_int_int(div_mod_int(X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = one_one_int)) # label(fact_3309_neq__one__mod__two) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3194 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(real_nat,N_1)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1)))) # label(fact_3310_two__realpow__gt) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3195 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),Y)))) # label(fact_3311_real__gt__half__sum) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3196 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3312_real__less__half__sum) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3197 (all U_1 all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,U_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3313_realpow__square__minus__le) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3198 (all M_1 (hAPP_nat_nat(div_mod_nat(M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = zero_zero_nat | hAPP_nat_nat(div_mod_nat(M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = one_one_nat | hAPP_nat_nat(div_mod_nat(M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) | hAPP_nat_nat(div_mod_nat(M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))))) # label(fact_3314_mod__exhaust__less__4) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3199 (all B_1 all A_2 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_1),A_2)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),A_2) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_1),A_2)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) # label(fact_3318_real__average__minus__second) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3200 (all A_2 all B_1 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_2),B_1)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),A_2) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_1),A_2)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) # label(fact_3319_real__average__minus__first) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3201 (all A_2 (hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = one_one_int -> hAPP_int_int(abs_abs_int,A_2) = one_one_int)) # label(fact_3320_power2__eq1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3202 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> hAPP_int_int(div_mod_int(X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int)) # label(fact_3321_even__div__2__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3203 (all X_1 all Y_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Y_2),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3322_even__div__2__l) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3204 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = X_1)) # label(fact_3323_even__div__2__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3205 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),Y_2))) # label(fact_3324_even__prod__div__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3206 (all Y_2 all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),zEven)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_1),Y_2)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Y_2),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3325_even__sum__div__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3207 (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_int,X),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) -> X = zero_zero_int | X = one_one_int))) # label(fact_3326_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3208 (all N_1 (N_1 != zero_zero_nat -> hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1))) # label(fact_3327_Suc__Suc__mult__two__diff__two) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3209 (all N_1 (N_1 != zero_zero_nat -> hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),N_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),N_1))) # label(fact_3328_lemma__Suc__Suc__4n__diff__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3210 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3329_div__2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3211 (all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(div_mod_nat(M),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) <-> hAPP_nat_nat(div_mod_nat(M),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = one_one_nat)) # label(fact_3330_mod2__gr__0) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3212 (all N_1 hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),N_1))) # label(fact_3331_fact__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3213 (all V_2 all W ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,V_2))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W))) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(number_number_of_int,V_2)),hAPP_int_int(number_number_of_int,W))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,V_2))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W))) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,V_2)),one_one_int)),hAPP_int_int(number_number_of_int,W))))) # label(fact_3334_zdiv__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3214 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,X)),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_real)))) # label(fact_3335_less__one__imp__sqr__less__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3215 (all A_2 all B_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),A_2)),B_1))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3336_zadd__power2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.77 3216 (all A_2 all B_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),A_2)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))))) # label(fact_3337_zadd__power3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3217 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Y)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X),Y))) # label(fact_3338_diff__square) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3218 (all A_2 all B_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_1)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3339_zspecial__product) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3219 (all X hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),pi))) = hAPP_real_real(cos,X)) # label(fact_3343_cos__periodic) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3220 (all X_1 all K_1 (X_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),K_1)),one_one_int) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)))) # label(fact_3345_zOddI) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3221 (all X hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),pi))) = hAPP_real_real(tan,X)) # label(fact_3346_tan__periodic) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3222 (all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(arctan,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3348_arctan__ubound) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3223 (all N_1 (N_1 != zero_zero_nat -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1)),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1))) # label(fact_3350_Suc__mult__two__diff__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3224 (all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3351_Int2_Oaux__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3225 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3352_Suc__n__div__2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3226 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X))),one_one_real))))) # label(fact_3353_cos__double__less__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3227 (all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(nat,P_3)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3354_Int2_Oaux__1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3228 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(cos,X)))))) # label(fact_3355_cos__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3229 (all A_2 all B_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))),A_2)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls)))))) # label(fact_3356_zdiff__power3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3230 (all A_2 all B_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),A_2)),B_1))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3357_zdiff__power2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3231 (all N_1 hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_real(real_nat,N_1))),pi)) = one_one_real) # label(fact_3360_cos__2npi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3232 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(tan,X)))))) # label(fact_3361_tan__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3233 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(tan,Y)),hAPP_real_real(tan,X))))))) # label(fact_3362_tan__monotone) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3234 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),Y_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(tan,Y_2)),hAPP_real_real(tan,X_1))))))))) # label(fact_3363_tan__monotone_H) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3235 (all Y hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_real_real(tan,Y)) = hAPP_real_real(tan,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),Y))) # label(fact_3364_tan__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3236 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arctan,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(arctan,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3365_arctan__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3237 (all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arctan,Y)))) # label(fact_3366_arctan__lbound) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3238 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_1),one_one_int)),A_2))) # label(fact_3367_neg__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3239 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),A_2))) # label(fact_3368_pos__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3240 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) -> hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),A_2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(div_mod_int(B_1),A_2))))) # label(fact_3369_pos__zmod__mult__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3241 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(cos,X)))))) # label(fact_3370_cos__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3242 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(cos,X)))))) # label(fact_3371_cos__gt__zero__pi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3243 (all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Pa),zOdd)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3372_Euler_Oaux__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3244 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(uminus_uminus_real,pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(tan,X)),zero_zero_real))))) # label(fact_3373_tan__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3245 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hAPP_real_real(arctan,hAPP_real_real(tan,X)) = X))) # label(fact_3375_arctan__tan) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3246 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,X)),one_one_real)) -> (exists Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),Z)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) & hAPP_real_real(tan,Z) = X)))) # label(fact_3376_tan__total__pi4) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3247 (all Y_2 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (exists N_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Y_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,N_2),X_1))))),X_1)))))) # label(fact_3377_best__odd__division__abs) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3248 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> (exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(tan,X_2) = Y)))) # label(fact_3378_tan__total__pos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3249 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X)) -> (exists N_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Y),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,N_2),X))))),X))))) # label(fact_3379_best__division__abs) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3250 (all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),P_3)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))))))))) # label(fact_3380_inv__inv__aux) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3251 (all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M_1)) -> hAPP_nat_nat(suc,hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,M_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,M_1),one_one_int)))) # label(fact_3381_inv__is__inv__aux) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3252 (all Y exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(tan,X_2) = Y & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(tan,Y_1) = Y -> Y_1 = X_2)))) # label(fact_3382_tan__total) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3253 (all Y exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(tan,X_2) = Y)) # label(fact_3383_lemma__tan__total1) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3254 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> (exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),hAPP_real_real(tan,X_2))))))) # label(fact_3384_lemma__tan__total) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3255 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> -(all K X_1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),K)),one_one_int)))) # label(fact_3385_zOddE) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3256 (all X all Y hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X)),Y))) # label(fact_3386_real__sum__squared__expand) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3257 (exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) & hAPP_real_real(cos,X_2) = zero_zero_real & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) & hAPP_real_real(cos,Y_1) = zero_zero_real -> Y_1 = X_2)))) # label(fact_3387_cos__is__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3258 (all X_1 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zEven)) -> -(all K X_1 != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),K)))) # label(fact_3388_zEvenE) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3259 (all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W)))) -> negDivAlg(one_one_int,hAPP_int_int(number_number_of_int,W)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W)))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W)))) -> negDivAlg(one_one_int,hAPP_int_int(number_number_of_int,W)) = hAPP_P1975530577nt_int(adjust(hAPP_int_int(number_number_of_int,W)),negDivAlg(one_one_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(number_number_of_int,W))))))) # label(fact_3389_negDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3260 (all W all V_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(number_number_of_int,V_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W)),hAPP_int_int(number_number_of_int,V_2)))) -> negDivAlg(hAPP_int_int(number_number_of_int,W),hAPP_int_int(number_number_of_int,V_2)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W)),hAPP_int_int(number_number_of_int,V_2)))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W)),hAPP_int_int(number_number_of_int,V_2)))) -> negDivAlg(hAPP_int_int(number_number_of_int,W),hAPP_int_int(number_number_of_int,V_2)) = hAPP_P1975530577nt_int(adjust(hAPP_int_int(number_number_of_int,V_2)),negDivAlg(hAPP_int_int(number_number_of_int,W),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(number_number_of_int,V_2))))))) # label(fact_3390_negDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3261 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1))) -> negDivAlg(A_2,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1))) -> negDivAlg(A_2,B_1) = hAPP_P1975530577nt_int(adjust(B_1),negDivAlg(A_2,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1)))))) # label(fact_3391_negDivAlg__eqn) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3262 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_1)) -> posDivAlg(A_2,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),A_2)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_1)) -> posDivAlg(A_2,B_1) = hAPP_P1975530577nt_int(adjust(B_1),posDivAlg(A_2,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1)))))) # label(fact_3392_posDivAlg__eqn) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3263 (all W all V_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(number_number_of_int,V_2))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,W)),hAPP_int_int(number_number_of_int,V_2))) -> posDivAlg(hAPP_int_int(number_number_of_int,W),hAPP_int_int(number_number_of_int,V_2)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,W)),hAPP_int_int(number_number_of_int,V_2))) -> posDivAlg(hAPP_int_int(number_number_of_int,W),hAPP_int_int(number_number_of_int,V_2)) = hAPP_P1975530577nt_int(adjust(hAPP_int_int(number_number_of_int,V_2)),posDivAlg(hAPP_int_int(number_number_of_int,W),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(number_number_of_int,V_2))))))) # label(fact_3393_posDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3264 (all A_2 all B_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),zero_zero_int)) -> posDivAlg(A_2,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),A_2)) & (-(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),zero_zero_int))) -> posDivAlg(A_2,B_1) = hAPP_P1975530577nt_int(adjust(B_1),posDivAlg(A_2,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1)))))) # label(fact_3394_posDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3265 (all W (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(number_number_of_int,W))) -> posDivAlg(one_one_int,hAPP_int_int(number_number_of_int,W)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),one_one_int)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(number_number_of_int,W))) -> posDivAlg(one_one_int,hAPP_int_int(number_number_of_int,W)) = hAPP_P1975530577nt_int(adjust(hAPP_int_int(number_number_of_int,W)),posDivAlg(one_one_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(number_number_of_int,W))))))) # label(fact_3395_posDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3266 (all A_2 all B_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1))) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),zero_zero_int)) -> negDivAlg(A_2,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1))) & (-(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_1))) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),zero_zero_int))) -> negDivAlg(A_2,B_1) = hAPP_P1975530577nt_int(adjust(B_1),negDivAlg(A_2,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_1)))))) # label(fact_3396_negDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3267 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arcsin,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(arcsin,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3397_arcsin__lt__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3268 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arcsin,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arcsin,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3398_arcsin__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3269 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arcsin,Y)))))) # label(fact_3399_arcsin__lbound) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3270 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arcsin,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3400_arcsin__ubound) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3271 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N_1)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,zero_zero_real),N_1)) = zero_zero_real)) # label(fact_3401_lemma__STAR__cos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3272 (all N_1 hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N_1)) != zero_zero_real) # label(fact_3402_real__of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3273 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N_1))))) # label(fact_3403_real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3274 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N_1))))) # label(fact_3404_real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3275 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_1))) -> hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N_1)),hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1))))) # label(fact_3405_fact__diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3276 (all N_1 all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_nat_nat(fact_fact_nat,N_1)) & (M_1 != zero_zero_nat -> hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N_1)))))) # label(fact_3406_fact__add__num__eq__if2__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3277 (all M_1 all N_1 ((hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = zero_zero_nat -> hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = one_one_nat) & (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) != zero_zero_nat -> hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),one_one_nat)))))) # label(fact_3407_fact__add__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3278 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_nat_nat(fact_fact_nat,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat))))) # label(fact_3408_fact__reduce__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3279 (all M_1 ((M_1 = zero_zero_nat -> hAPP_nat_nat(fact_fact_nat,M_1) = one_one_nat) & (M_1 != zero_zero_nat -> hAPP_nat_nat(fact_fact_nat,M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)))))) # label(fact_3409_fact__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3280 (all N hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(hAPP_b646336293l_real(if_real,hAPP_nat_bool(even_odd_even_nat,N)),zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,zero_zero_real),N)) = zero_zero_real) # label(fact_3410_lemma__STAR__sin) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3281 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_1),Y_2))) <-> hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) | hBOOL(hAPP_nat_bool(even_odd_even_nat,Y_2)))) # label(fact_3412_even__product__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3282 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),Y_2))) <-> hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) & hBOOL(hAPP_nat_bool(even_odd_even_nat,Y_2)) | -hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) & -hBOOL(hAPP_nat_bool(even_odd_even_nat,Y_2)))) # label(fact_3413_even__sum__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3283 (all M all N (hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) <-> (hBOOL(hAPP_nat_bool(even_odd_even_nat,M)) <-> hBOOL(hAPP_nat_bool(even_odd_even_nat,N))))) # label(fact_3414_even__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3284 (all M all N (-hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) <-> -(-hBOOL(hAPP_nat_bool(even_odd_even_nat,M)) <-> -hBOOL(hAPP_nat_bool(even_odd_even_nat,N))))) # label(fact_3415_odd__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3285 (all X_1 (hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(suc,X_1))) <-> -hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)))) # label(fact_3416_even__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3286 (all N_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_3418_odd__pos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3287 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) | hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) & hBOOL(hAPP_nat_bool(even_odd_even_nat,Y_2)) | -hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) & -hBOOL(hAPP_nat_bool(even_odd_even_nat,Y_2)))) # label(fact_3419_even__difference__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3288 (all X_1 (hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) <-> (exists Y_1 X_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),Y_1)))) # label(fact_3420_even__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3289 (all X_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) <-> (exists Y_1 X_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),Y_1))))) # label(fact_3421_odd__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3290 (all X (hBOOL(hAPP_nat_bool(even_odd_even_nat,X)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,X)),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))))) # label(fact_3422_even__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3291 (all X (-hBOOL(hAPP_nat_bool(even_odd_even_nat,X)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(suc,X)),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)))))) # label(fact_3423_odd__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3292 (all X (-hBOOL(hAPP_nat_bool(even_odd_even_nat,X)) -> hAPP_nat_nat(div_mod_nat(X),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_3424_odd__nat__mod__two__eq__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3293 (all X (hBOOL(hAPP_nat_bool(even_odd_even_nat,X)) -> hAPP_nat_nat(div_mod_nat(X),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = zero_zero_nat)) # label(fact_3425_even__nat__mod__two__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3294 (all X_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) <-> hAPP_nat_nat(div_mod_nat(X_1),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_3426_odd__nat__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3295 (all X_1 (hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) <-> hAPP_nat_nat(div_mod_nat(X_1),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = zero_zero_nat)) # label(fact_3427_even__nat__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3296 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_1),Y_2))) <-> hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Y_2)))) # label(fact_3428_even__power__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3297 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) <-> -hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)))))) # label(fact_3429_even__num__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3298 (all X (hBOOL(hAPP_nat_bool(even_odd_even_nat,X)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)))) = X)) # label(fact_3430_even__nat__div__two__times__two) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3299 (all X (-hBOOL(hAPP_nat_bool(even_odd_even_nat,X)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))))) = X)) # label(fact_3431_odd__nat__div__two__times__two__plus__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3300 (all N (hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) <-> (exists M_2 N = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),M_2)))) # label(fact_3432_even__mult__two__ex) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3301 (all N (hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) <-> hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(div_mod_nat(N),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3433_even__even__mod__4__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3302 (all N (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) <-> (exists M_2 N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),M_2))))) # label(fact_3434_odd__Suc__mult__two__ex) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3303 (all N_1 (hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3435_lemma__even__div2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3304 (all N_1 hAPP_nat_nat(fact_fact_nat,N_1) != zero_zero_nat) # label(fact_3436_fact__nonzero__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3305 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(fact_fact_nat,M_1)),hAPP_nat_nat(fact_fact_nat,N_1))))) # label(fact_3437_fact__mono__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3306 (all N_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3439_lemma__not__even__div2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3307 (all N_1 (hAPP_nat_nat(div_mod_nat(N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))) -> -hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3440_lemma__odd__mod__4__div__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3308 (all N_1 (hAPP_nat_nat(div_mod_nat(N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = one_one_nat -> hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3441_lemma__even__mod__4__div__2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3309 (all N_1 all M_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,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(fact_fact_nat,M_1)),hAPP_nat_nat(fact_fact_nat,N_1)))))) # label(fact_3444_fact__less__mono__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3310 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(fact_fact_nat,N_1)))) # label(fact_3445_fact__gt__zero__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3311 (all X_1 (hAPP_real_real(cos,X_1) = zero_zero_real <-> (exists N_2 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_2)) & X_1 = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) | (exists N_2 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_2)) & X_1 = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3446_cos__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3312 (all X hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(suc,X)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X)),hAPP_nat_nat(fact_fact_nat,X))) # label(fact_3447_Fact_Ofact__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3313 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(fact_fact_nat,N_1)))) # label(fact_3448_fact__ge__one__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3314 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(fact_fact_nat,N_1)))) # label(fact_3449_fact__ge__Suc__0__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3315 (all N_1 hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)),hAPP_nat_nat(fact_fact_nat,N_1))) # label(fact_3450_fact__plus__one__nat) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3316 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(fact_fact_nat,N_1)),hAPP_nat_nat(fact_fact_nat,M_1)) = zero_zero_nat)) # label(fact_3451_fact__mod) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3317 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hAPP_real_real(cos,X) = zero_zero_real -> (exists N_2 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_2)) & X = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3452_cos__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3318 (all N_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> (exists X_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X_2)),one_one_nat)))) # label(fact_3453_odd__square) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3319 (all X_2 ((hBOOL(hAPP_nat_bool(even_odd_even_nat,X_2)) -> hAPP_nat_real(sin_coeff,X_2) = zero_zero_real) & (-hBOOL(hAPP_nat_bool(even_odd_even_nat,X_2)) -> hAPP_nat_real(sin_coeff,X_2) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_2),hAPP_nat_nat(suc,zero_zero_nat))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,X_2)))))) # label(fact_3454_sin__coeff__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3320 (all N_1 (hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> (exists X_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X_2)))) # label(fact_3455_even__square) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3321 (all X_2 ((hBOOL(hAPP_nat_bool(even_odd_even_nat,X_2)) -> hAPP_nat_real(cos_coeff,X_2) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,X_2)))) & (-hBOOL(hAPP_nat_bool(even_odd_even_nat,X_2)) -> hAPP_nat_real(cos_coeff,X_2) = zero_zero_real))) # label(fact_3456_cos__coeff__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3322 (all P_3 all A_2 hAPP_int_int(inv(P_3),A_2) = hAPP_int_int(div_mod_int(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),P_3)) # label(fact_3457_WilsonRuss_Oinv__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3323 (all X (X != zero_zero_real -> hAPP_real_real(arctan,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),X)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sgn_sgn_real,X)),pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_real_real(arctan,X)))) # label(fact_3458_arctan__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3324 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hAPP_real_real(tan,X) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X))),one_one_real))))) # label(fact_3459_tan__half) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3325 (all N_1 hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1)))),pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)),N_1)) # label(fact_3460_sin__cos__npi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3326 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X))),X))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3461_abs__ln__one__plus__x__minus__x__bound__nonpos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3327 (all X hAPP_real_real(sin,hAPP_real_real(uminus_uminus_real,X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X))) # label(fact_3463_sin__minus) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3328 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(sin,X)),one_one_real))) # label(fact_3464_sin__le__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3329 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(ln,X)),X)))) # label(fact_3466_ln__less__self) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3330 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_2)) -> (hAPP_real_real(ln,X_1) = hAPP_real_real(ln,Y_2) <-> X_1 = Y_2)))) # label(fact_3467_ln__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3331 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(ln,X_1)),hAPP_real_real(ln,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)))))) # label(fact_3468_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3332 (all X hAPP_real_real(sgn_sgn_real,X) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_real_real(abs_abs_real,X))) # label(fact_3470_real__sgn__eq) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3333 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hAPP_real_real(ln,X) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),one_one_real) -> X = one_one_real))) # label(fact_3471_ln__eq__minus__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3334 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),pi)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(sin,X)))))) # label(fact_3472_sin__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3335 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),pi)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(sin,X)))))) # label(fact_3473_sin__gt__zero__pi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3336 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),hAPP_real_real(sin,X)))) # label(fact_3474_sin__ge__minus__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3337 (all X (hAPP_real_real(cos,X) = one_one_real -> hAPP_real_real(sin,X) = zero_zero_real)) # label(fact_3475_cos__one__sin__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3338 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(sin,X))),one_one_real))) # label(fact_3476_abs__sin__le__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3339 (all X all Y hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,X)),hAPP_real_real(cos,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(sin,Y)))) # label(fact_3477_sin__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3340 (all X all Y hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,X)),hAPP_real_real(cos,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(sin,Y)))) # label(fact_3478_sin__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3341 (all X all Y hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,Y)),hAPP_real_real(sin,X))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,Y)),hAPP_real_real(cos,X)))) # label(fact_3479_sin__diff2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3342 (all X hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,pi),X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X))) # label(fact_3480_sin__periodic__pi2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3343 (all X hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),pi)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X))) # label(fact_3481_sin__periodic__pi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3344 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(ln,X_1)),hAPP_real_real(ln,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)))))) # label(fact_3482_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3345 (all X hAPP_real_real(tan,X) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(sin,X)),hAPP_real_real(cos,X))) # label(fact_3483_tan__def) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3346 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(ln,X))))) # label(fact_3484_ln__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3347 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(ln,X))))) # label(fact_3485_ln__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3348 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(ln,X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X_1))))) # label(fact_3486_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3349 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hAPP_real_real(ln,X_1) = zero_zero_real <-> X_1 = one_one_real))) # label(fact_3487_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3350 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(ln,X_1)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real))))) # label(fact_3488_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3351 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(ln,X)),zero_zero_real))))) # label(fact_3489_ln__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3352 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(ln,X))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X))))) # label(fact_3490_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3353 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(sgn_sgn_real,X) = one_one_real)) # label(fact_3491_real__sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3354 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(ln,X)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),one_one_real))))) # label(fact_3492_ln__le__minus__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3355 (all N_1 hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,pi),hAPP_nat_real(real_nat,N_1))) = zero_zero_real) # label(fact_3493_sin__npi2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3356 (all N_1 hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),pi)) = zero_zero_real) # label(fact_3494_sin__npi) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3357 (all X hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,X))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,X)),hAPP_real_real(sin,X))) = one_one_real) # label(fact_3495_sin__cos__squared__add3) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3358 (all X (hAPP_real_real(sin,X) = zero_zero_real -> hAPP_real_real(abs_abs_real,hAPP_real_real(cos,X)) = one_one_real)) # label(fact_3496_sin__zero__abs__cos__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3359 (all X all Y hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,Y)),hAPP_real_real(cos,X))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,Y)),hAPP_real_real(sin,X)))) # label(fact_3497_cos__diff2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3360 (all X all Y hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,X)),hAPP_real_real(sin,Y)))) # label(fact_3498_cos__diff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3361 (all X all Y hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,X)),hAPP_real_real(sin,Y)))) # label(fact_3499_cos__add) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3362 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(ln,X))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X))))) # label(fact_3500_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3363 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(ln,X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X_1))))) # label(fact_3501_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3364 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(ln,X)),hAPP_real_real(ln,Y))))) # label(fact_3502_ln__mult) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3365 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X))),X)))) # label(fact_3503_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3366 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(ln,X)),hAPP_real_real(ln,Y))))) # label(fact_3504_ln__div) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3367 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X))),X)))) # label(fact_3505_ln__add__one__self__le__self2) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3368 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),X))),hAPP_real_real(uminus_uminus_real,X)))))) # label(fact_3506_ln__one__minus__pos__upper__bound) # label(axiom) # label(non_clause). [assumption].
% 4.71/4.78 3369 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),one_one_real)) -> hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),X))))))) # label(fact_3507_aux5) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3370 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),zero_zero_real)) -> hAPP_real_real(sgn_sgn_real,X) = hAPP_int_real(number267125858f_real,min))) # label(fact_3508_real__sgn__neg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3371 (all A_2 ((A_2 = zero_zero_real -> hAPP_real_real(sgn_sgn_real,A_2) = zero_zero_real) & (A_2 != zero_zero_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> hAPP_real_real(sgn_sgn_real,A_2) = one_one_real) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> hAPP_real_real(sgn_sgn_real,A_2) = hAPP_real_real(uminus_uminus_real,one_one_real))))) # label(fact_3509_sgn__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3372 (all X ((X = zero_zero_real -> hAPP_real_real(sgn_sgn_real,X) = zero_zero_real) & (X != zero_zero_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(sgn_sgn_real,X) = one_one_real) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(sgn_sgn_real,X) = hAPP_real_real(uminus_uminus_real,one_one_real))))) # label(fact_3510_real__sgn__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3373 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hAPP_real_real(sin,hAPP_real_real(arcsin,Y)) = Y))) # label(fact_3511_sin__arcsin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3374 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(ln,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),hAPP_real_real(ln,X)))) # label(fact_3512_ln__realpow) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3375 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(sin,X)))))) # label(fact_3513_sin__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3376 (all X hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(sin,X))),hAPP_real_real(cos,X))) # label(fact_3514_sin__double) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3377 (all Y all X (hAPP_real_real(cos,X) != zero_zero_real -> (hAPP_real_real(cos,Y) != zero_zero_real -> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(tan,X)),hAPP_real_real(tan,Y)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,Y)))))) # label(fact_3515_add__tan__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3378 (all X hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),pi))) = hAPP_real_real(sin,X)) # label(fact_3517_sin__periodic) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3379 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(sin,X)))))) # label(fact_3520_sin__gt__zero2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3380 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X))))))) # label(fact_3521_ln__one__plus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3381 (all R_3 all A_2 hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_real_real(cos,A_2))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_real_real(sin,A_2))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,R_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) # label(fact_3522_sin__cos__squared__add2__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3382 (all N_1 hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_real(real_nat,N_1))),pi)) = zero_zero_real) # label(fact_3523_sin__2npi) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3383 (all X hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sin,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(cos,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = one_one_real) # label(fact_3524_sin__cos__squared__add) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3384 (all X hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(cos,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sin,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = one_one_real) # label(fact_3525_sin__cos__squared__add2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3385 (all X hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sin,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(cos,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3526_sin__squared__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3386 (all X hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(cos,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sin,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3527_cos__squared__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3387 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(sin,Y)),hAPP_real_real(sin,X))))))) # label(fact_3528_sin__monotone__2pi_H) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3388 (all X hAPP_real_real(cos,X) = hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X))) # label(fact_3529_cos__sin__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3389 (all X hAPP_real_real(sin,X) = hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X))) # label(fact_3530_sin__cos__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3390 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X))),X))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3531_abs__ln__one__plus__x__minus__x__bound__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3391 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(uminus_uminus_real,pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),zero_zero_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(sin,X)),zero_zero_real))))) # label(fact_3532_sin__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3392 (all X hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(cos,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sin,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3533_cos__double) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3393 (all X hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X)) = hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3535_minus__sin__cos__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3394 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hAPP_real_real(arcsin,hAPP_real_real(sin,X)) = X))) # label(fact_3536_arcsin__sin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3395 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,X)),hAPP_real_real(cos,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(sin,Y))))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),Y))),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X)),hAPP_real_real(cos,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sin,X)),hAPP_real_real(sin,Y))))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = zero_zero_real) # label(fact_3537_sin__cos__add) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3396 (all X hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(sin,hAPP_real_real(uminus_uminus_real,X))),hAPP_real_real(sin,X))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(cos,hAPP_real_real(uminus_uminus_real,X))),hAPP_real_real(cos,X))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = zero_zero_real) # label(fact_3538_sin__cos__minus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3397 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(uminus_uminus_real,X)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),X))))))) # label(fact_3539_ln__one__minus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3398 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X))),X))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3540_abs__ln__one__plus__x__minus__x__bound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3399 (all X all M_1 hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,hAPP_nat_nat(suc,M_1))),pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,M_1)),pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3541_sin__expansion__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3400 (all X_1 (hAPP_real_real(sin,X_1) = zero_zero_real <-> (exists N_2 (hBOOL(hAPP_nat_bool(even_odd_even_nat,N_2)) & X_1 = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) | (exists N_2 (hBOOL(hAPP_nat_bool(even_odd_even_nat,N_2)) & X_1 = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3542_sin__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3401 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arcsin,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arcsin,Y)),pi)) & hAPP_real_real(sin,hAPP_real_real(arcsin,Y)) = Y))) # label(fact_3543_arcsin__pi) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3402 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(arcsin,Y))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(arcsin,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(sin,hAPP_real_real(arcsin,Y)) = Y))) # label(fact_3544_arcsin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3403 (all X all M_1 hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,hAPP_nat_nat(suc,M_1))),pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,M_1)),pi)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3545_cos__expansion__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3404 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hAPP_real_real(sin,X) = zero_zero_real -> (exists N_2 (hBOOL(hAPP_nat_bool(even_odd_even_nat,N_2)) & X = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_2)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3546_sin__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3405 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),Y)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),one_one_real)) -> (exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(sin,X_2) = Y & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) & hAPP_real_real(sin,Y_1) = Y -> Y_1 = X_2))))))) # label(fact_3547_sin__total) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3406 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(inverse_inverse_real,hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),N_1))))))) # label(fact_3548_Ln_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3407 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hAPP_real_real(cos,hAPP_real_real(arcsin,X)) = hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3549_cos__arcsin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3408 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_int_real(number267125858f_real,min)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hAPP_real_real(sin,hAPP_real_real(arccos,X)) = hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3550_sin__arccos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3409 (all X hAPP_real_real(sqrt,hAPP_real_real(uminus_uminus_real,X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(sqrt,X))) # label(fact_3552_real__sqrt__minus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3410 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(sqrt,X_1)),hAPP_real_real(sqrt,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)))) # label(fact_3553_real__sqrt__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3411 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(sqrt,X)),hAPP_real_real(sqrt,Y))))) # label(fact_3554_real__sqrt__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3412 (all X_1 (hAPP_real_real(sqrt,X_1) = zero_zero_real <-> X_1 = zero_zero_real)) # label(fact_3555_real__sqrt__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3413 (all X hAPP_real_real(sqrt,hAPP_real_real(inverse_inverse_real,X)) = hAPP_real_real(inverse_inverse_real,hAPP_real_real(sqrt,X))) # label(fact_3557_real__sqrt__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3414 (all X_1 all Y_2 (hAPP_real_real(sqrt,X_1) = hAPP_real_real(sqrt,Y_2) <-> X_1 = Y_2)) # label(fact_3558_real__sqrt__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3415 (all X all Y hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(sqrt,X)),hAPP_real_real(sqrt,Y))) # label(fact_3559_real__sqrt__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3416 (all X_1 (hAPP_real_real(sqrt,X_1) = one_one_real <-> X_1 = one_one_real)) # label(fact_3561_real__sqrt__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3417 (all X all K_2 hAPP_real_real(sqrt,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),K_2)) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sqrt,X)),K_2)) # label(fact_3562_real__sqrt__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3418 (all X all Y hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(sqrt,X)),hAPP_real_real(sqrt,Y))) # label(fact_3563_real__sqrt__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3419 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(sqrt,X)),hAPP_real_real(sqrt,Y))))) # label(fact_3564_real__sqrt__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3420 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(sqrt,X_1)),hAPP_real_real(sqrt,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)))) # label(fact_3565_real__sqrt__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3421 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(sqrt,X)),X) = hAPP_real_real(inverse_inverse_real,hAPP_real_real(sqrt,X)))) # label(fact_3566_sqrt__divide__self__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3422 (all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(sqrt,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_2)))) # label(fact_3567_real__sqrt__ge__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3423 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(sqrt,X_1)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real)))) # label(fact_3568_real__sqrt__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3424 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(sqrt,X))))) # label(fact_3569_real__sqrt__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.78 3425 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hAPP_real_real(sqrt,X) = zero_zero_real -> X = zero_zero_real))) # label(fact_3570_real__sqrt__eq__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3426 (all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(sqrt,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_2)))) # label(fact_3571_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3427 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(sqrt,X_1)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)))) # label(fact_3572_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3428 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(sqrt,X) != zero_zero_real)) # label(fact_3573_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3429 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(sqrt,X))))) # label(fact_3574_real__sqrt__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3430 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(sqrt,X))))) # label(fact_3575_real__sqrt__ge__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3431 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(sqrt,X_1)),one_one_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),one_one_real)))) # label(fact_3576_real__sqrt__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3432 (all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(sqrt,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),Y_2)))) # label(fact_3577_real__sqrt__ge__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3433 (all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(sqrt,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),Y_2)))) # label(fact_3578_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3434 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(sqrt,X_1)),one_one_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)))) # label(fact_3579_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3435 (all X hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),X)) = hAPP_real_real(abs_abs_real,X)) # label(fact_3580_real__sqrt__abs2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3436 (all R all S_5 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,R),S_5) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R),hAPP_real_real(inverse_inverse_real,S_5))) # label(fact_3581_real__divide__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3437 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),Y) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),hAPP_real_real(inverse_inverse_real,Y))) # label(fact_3582_divide__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3438 (all X all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),X)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y),Y)))))) # label(fact_3583_le__real__sqrt__sumsq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3439 (all Y all U_1 all X1_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X1_2),Y)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),U_1))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y),hAPP_real_real(inverse_inverse_real,X))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,U_1),hAPP_real_real(inverse_inverse_real,X1_2)))))))) # label(fact_3584_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3440 (all Y all U_1 all X1_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X1_2),Y)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),U_1))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(inverse_inverse_real,X)),Y)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(inverse_inverse_real,X1_2)),U_1))))))) # label(fact_3585_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3441 (all X (X != zero_zero_real -> hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(inverse_inverse_real,X)),X) = one_one_real)) # label(fact_3586_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3442 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(inverse_inverse_real,hAPP_real_real(sqrt,X))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_real_real(inverse_inverse_real,X))) # label(fact_3587_real__inv__sqrt__pow2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3443 (all X all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),X)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y),Y)))))) # label(fact_3588_real__sqrt__mult__self__sum__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3444 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(inverse_inverse_real,hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N_1)))))) # label(fact_3589_inv__real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3445 (all N_1 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(inverse_inverse_real,hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N_1)))))) # label(fact_3590_inv__real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3446 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(ln,hAPP_real_real(inverse_inverse_real,X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(ln,X)))) # label(fact_3591_ln__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3447 (all I ((I = zero_zero_int -> hAPP_int_int(sgn_sgn_int,I) = zero_zero_int) & (I != zero_zero_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),I)) -> hAPP_int_int(sgn_sgn_int,I) = one_one_int) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),I)) -> hAPP_int_int(sgn_sgn_int,I) = hAPP_int_int(uminus_uminus_int,one_one_int))))) # label(fact_3592_zsgn__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3448 (all X hAPP_real_real(sqrt,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_real_real(abs_abs_real,X)) # label(fact_3596_real__sqrt__abs) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3449 (all X_1 (hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sqrt,X_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = X_1 <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)))) # label(fact_3598_real__sqrt__pow2__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3450 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sqrt,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = X)) # label(fact_3599_real__sqrt__pow2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3451 (all Y all X (hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = X -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> hAPP_real_real(sqrt,X) = Y))) # label(fact_3600_real__sqrt__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3452 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sqrt,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3601_real__sqrt__pow2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3453 (all U_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_1)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,U_1),hAPP_real_real(sqrt,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),U_1)))) # label(fact_3602_lemma__real__divide__sqrt__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3454 (all A_2 all C_1 all B_1 all D_3 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_2),C_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_1),D_3)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,C_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,D_3),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3603_real__sqrt__sum__squares__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3455 (all Y all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3604_real__sqrt__sum__squares__ge2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3456 (all X all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3605_real__sqrt__sum__squares__ge1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3457 (all X all Y (hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = X -> Y = zero_zero_real)) # label(fact_3606_real__sqrt__sum__squares__eq__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3458 (all X all Y (hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) = Y -> X = zero_zero_real)) # label(fact_3607_real__sqrt__sum__squares__eq__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3459 (all X all Y all Xa_2 all Ya hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Xa_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Ya),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Xa_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Ya),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3608_real__sqrt__sum__squares__mult__squared__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3460 (all X all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3613_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3461 (all Y all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,Y)),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3614_real__sqrt__ge__abs2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3462 (all X all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X)),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3615_real__sqrt__ge__abs1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3463 (all X all Y all Xa_2 all Ya hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Xa_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Ya),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3617_real__sqrt__sum__squares__mult__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3464 (all X_4 all Y_4 hAPP_real_real(cos,hAPP_real_real(arccos,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_4),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_4),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3618_cos__arccos__lemma1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3465 (all X all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))),one_one_real))) # label(fact_3619_cos__x__y__le__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3466 (all Y all X all U_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,X)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,U_1),hAPP_real_real(sqrt,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,U_1),hAPP_real_real(sqrt,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),U_1))))) # label(fact_3620_real__sqrt__sum__squares__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3467 (all X (hAPP_real_real(cos,X) != zero_zero_real -> hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(tan,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(inverse_inverse_real,hAPP_real_real(cos,X))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3621_tan__sec) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3468 (all Y all X all U_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,U_1),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,U_1),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),U_1)))))))) # label(fact_3622_lemma__sqrt__hcomplex__capprox) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3469 (all X hAPP_real_real(arctan,X) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(arctan,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))))) # label(fact_3623_arctan__half) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3470 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,Y)),one_one_real)) -> hAPP_real_real(sin,hAPP_real_real(arccos,Y)) = hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3624_sin__arccos__abs) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3471 (all X_4 all Y_4 hAPP_real_real(sin,hAPP_real_real(arccos,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_4),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) = hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X_4),hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y_4),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3625_sin__arccos__lemma1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3472 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (exists N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(inverse_inverse_real,hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_2)))),X))))) # label(fact_3626_reals__Archimedean) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3473 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)) -> hBOOL(hAPP_real_bool(deriv_real(arccos,X_1),hAPP_real_real(inverse_inverse_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))))))) # label(fact_3627_DERIV__arccos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3474 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)) -> hBOOL(hAPP_real_bool(deriv_real(arcsin,X_1),hAPP_real_real(inverse_inverse_real,hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))))) # label(fact_3628_DERIV__arcsin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3475 (all P_1 all N all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_P731461727l_real(produc556554744l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N))),hAPP_P731461727l_real(produc1935615926l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N))) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N)))) # label(fact_3629_Bolzano__bisect__diff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3476 (all P_1 all Aa all Ba hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),zero_zero_nat) = hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba)) # label(fact_3630_Bolzano__bisect_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3477 (all P_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> (all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_P731461727l_real(produc1935615926l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2))),hAPP_P731461727l_real(produc556554744l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2))))))) # label(fact_3631_Bolzano__bisect__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3478 (all X_1 hBOOL(hAPP_real_bool(deriv_real(sin,X_1),hAPP_real_real(cos,X_1)))) # label(fact_3632_DERIV__sin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3479 (all X_1 hBOOL(hAPP_real_bool(deriv_real(cos,X_1),hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X_1))))) # label(fact_3633_DERIV__cos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3480 (all P_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> (all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_P731461727l_real(produc1935615926l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2))),hAPP_P731461727l_real(produc1935615926l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),hAPP_nat_nat(suc,N_2)))))))) # label(fact_3634_Bolzano__bisect__fst__le__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3481 (all P_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> (all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_P731461727l_real(produc556554744l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),hAPP_nat_nat(suc,N_2)))),hAPP_P731461727l_real(produc556554744l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2))))))) # label(fact_3635_Bolzano__bisect__Suc__le__snd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3482 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hBOOL(hAPP_real_bool(deriv_real(ln,X_1),hAPP_real_real(inverse_inverse_real,X_1))))) # label(fact_3636_DERIV__ln) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3483 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hBOOL(hAPP_real_bool(deriv_real(ln,X_1),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),X_1))))) # label(fact_3637_DERIV__ln__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3484 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hBOOL(hAPP_real_bool(deriv_real(sqrt,X_1),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(inverse_inverse_real,hAPP_real_real(sqrt,X_1))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3638_DERIV__real__sqrt) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3485 (all X_1 (hAPP_real_real(cos,X_1) != zero_zero_real -> hBOOL(hAPP_real_bool(deriv_real(tan,X_1),hAPP_real_real(inverse_inverse_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(cos,X_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3639_DERIV__tan) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3486 (all X_1 hBOOL(hAPP_real_bool(deriv_real(arctan,X_1),hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3640_DERIV__arctan) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3487 (all D_1 all X_1 (X_1 != zero_zero_real -> ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> D_1 = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(inverse_inverse_real,hAPP_real_real(sqrt,X_1))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) -> ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)) -> D_1 = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(inverse_inverse_real,hAPP_real_real(sqrt,X_1)))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) -> hBOOL(hAPP_real_bool(deriv_real(sqrt,X_1),D_1)))))) # label(fact_3641_DERIV__real__sqrt__generic) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3488 (all V all K_1 all Aa all Ba (Aa != Ba -> ((all X_2 hBOOL(hAPP_real_bool(deriv_real(V,X_2),K_1))) -> hAPP_real_real(V,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Aa),Ba)),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(V,Aa)),hAPP_real_real(V,Ba))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3642_DERIV__const__average) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3489 (all D all F all X_1 all L (hBOOL(hAPP_real_bool(deriv_real(F,X_1),L)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) -> ((all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),Y_1))),D)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(F,Y_1)),hAPP_real_real(F,X_1))))) -> L = zero_zero_real)))) # label(fact_3643_DERIV__local__max) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3490 (all D all F all X_1 all L (hBOOL(hAPP_real_bool(deriv_real(F,X_1),L)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) -> ((all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),Y_1))),D)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(F,X_1)),hAPP_real_real(F,Y_1))))) -> L = zero_zero_real)))) # label(fact_3644_DERIV__local__min) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3491 (all D all F all X_1 all L (hBOOL(hAPP_real_bool(deriv_real(F,X_1),L)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) -> ((all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),Y_1))),D)) -> hAPP_real_real(F,X_1) = hAPP_real_real(F,Y_1))) -> L = zero_zero_real)))) # label(fact_3645_DERIV__local__const) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3492 (all N all Aa all Ba all P_1 ((all A_1 all B_3 all C_3 (hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))) -> (hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,B_3),C_3))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),B_3)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_3),C_3)) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),C_3)))))))) -> (-hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> -hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,hAPP_P731461727l_real(produc1935615926l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N))),hAPP_P731461727l_real(produc556554744l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N))))))))) # label(fact_3646_not__P__Bolzano__bisect) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3493 (all Aa all Ba all P_1 ((all A_1 all B_3 all C_3 (hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))) & hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,B_3),C_3))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),B_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_3),C_3)) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),C_3))))) -> (-hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> (all N_2 -hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,hAPP_P731461727l_real(produc1935615926l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2))),hAPP_P731461727l_real(produc556554744l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2)))))))))) # label(fact_3647_not__P__Bolzano__bisect_H) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3494 (all F all X_1 all L (hBOOL(hAPP_real_bool(deriv_real(F,X_1),L)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),L)) -> (exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all H_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H_1),D_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),H_1))),hAPP_real_real(F,X_1))))))))))) # label(fact_3648_DERIV__pos__inc__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3495 (all F all X_1 all L (hBOOL(hAPP_real_bool(deriv_real(F,X_1),L)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,L),zero_zero_real)) -> (exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all H_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H_1),D_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,X_1)),hAPP_real_real(F,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),H_1)))))))))))) # label(fact_3649_DERIV__neg__dec__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3496 (all F all X_1 all L (hBOOL(hAPP_real_bool(deriv_real(F,X_1),L)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),L)) -> (exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all H_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H_1),D_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,X_1)),hAPP_real_real(F,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),H_1)))))))))))) # label(fact_3650_DERIV__pos__inc__right) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3497 (all F all X_1 all L (hBOOL(hAPP_real_bool(deriv_real(F,X_1),L)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,L),zero_zero_real)) -> (exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all H_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H_1),D_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),H_1))),hAPP_real_real(F,X_1))))))))))) # label(fact_3651_DERIV__neg__dec__right) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3498 (all F all K_1 all Aa all Ba (Aa != Ba -> ((all X_2 hBOOL(hAPP_real_bool(deriv_real(F,X_2),K_1))) -> hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(F,Ba)),hAPP_real_real(F,Aa))),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa)) = K_1))) # label(fact_3652_DERIV__const__ratio__const2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3499 (all F all K_1 all Aa all Ba (Aa != Ba -> ((all X_2 hBOOL(hAPP_real_bool(deriv_real(F,X_2),K_1))) -> hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(F,Ba)),hAPP_real_real(F,Aa)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa)),K_1)))) # label(fact_3653_DERIV__const__ratio__const) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3500 (all D_1 all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (X_1 != zero_zero_real -> ((hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> D_1 = hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))))))) -> ((hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)) -> D_1 = hAPP_real_real(uminus_uminus_real,hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat)))))))) -> ((-hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) -> D_1 = hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat)))))) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(root,N),X_1),D_1)))))))) # label(fact_3654_DERIV__real__root__generic) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3501 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(root,N),X_1),hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,hAPP_nat_real(real_nat,N))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))))))))))) # label(fact_3655_DERIV__even__real__root) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3502 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(ln,X)),X)))) # label(fact_3656_ln__bound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3503 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(root,N),X_1),hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat)))))))))) # label(fact_3657_DERIV__real__root) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3504 (all N_1 hAPP_real_real(hAPP_n546711566l_real(root,N_1),zero_zero_real) = zero_zero_real) # label(fact_3658_real__root__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3505 (all X hAPP_real_real(hAPP_n546711566l_real(root,hAPP_nat_nat(suc,zero_zero_nat)),X) = X) # label(fact_3659_real__root__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3506 (all X all N_1 all M_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)) -> hAPP_real_real(hAPP_n546711566l_real(root,M_1),hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)) = hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(hAPP_n546711566l_real(root,M_1),X))))) # label(fact_3660_real__root__commute) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3507 (all X_1 all Y_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hAPP_real_real(hAPP_n546711566l_real(root,N),X_1) = hAPP_real_real(hAPP_n546711566l_real(root,N),Y_2) <-> X_1 = Y_2))) # label(fact_3661_real__root__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3508 (all X all N_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1)) = X)) # label(fact_3662_odd__real__root__power__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3509 (all X all N_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),N_1) = X)) # label(fact_3663_odd__real__root__pow) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3510 (all Y all X all N_1 (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N_1)) -> (hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),N_1) = X -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),X) = Y))) # label(fact_3664_odd__real__root__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3511 (all X all Y all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),Y)))))) # label(fact_3665_real__root__le__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3512 (all X_1 all Y_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_real_real(hAPP_n546711566l_real(root,N),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2))))) # label(fact_3666_real__root__le__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3513 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hAPP_real_real(hAPP_n546711566l_real(root,N),X_1) = zero_zero_real <-> X_1 = zero_zero_real))) # label(fact_3667_real__root__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3514 (all X all Y all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),Y)))))) # label(fact_3668_real__root__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3515 (all X_1 all Y_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_real_real(hAPP_n546711566l_real(root,N),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2))))) # label(fact_3669_real__root__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3516 (all X all Y all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),Y)))) # label(fact_3670_real__root__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3517 (all X all N_1 all M_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)) -> hAPP_real_real(hAPP_n546711566l_real(root,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),X) = hAPP_real_real(hAPP_n546711566l_real(root,M_1),hAPP_real_real(hAPP_n546711566l_real(root,N_1),X))))) # label(fact_3671_real__root__mult__exp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3518 (all X all K_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),K_2)) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),K_2))) # label(fact_3672_real__root__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3519 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hAPP_real_real(hAPP_n546711566l_real(root,N),X_1) = one_one_real <-> X_1 = one_one_real))) # label(fact_3673_real__root__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3520 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),one_one_real) = one_one_real)) # label(fact_3674_real__root__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3521 (all X all Y all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),Y)))) # label(fact_3675_real__root__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3522 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(uminus_uminus_real,X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)))) # label(fact_3676_real__root__minus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3523 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(abs_abs_real,X)) = hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)))) # label(fact_3677_real__root__abs) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3524 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(inverse_inverse_real,X)) = hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)))) # label(fact_3678_real__root__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3525 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)))))) # label(fact_3679_real__root__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3526 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real))))) # label(fact_3680_real__root__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3527 (all Y_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_n546711566l_real(root,N),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_2))))) # label(fact_3681_real__root__ge__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3528 (all Y_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_n546711566l_real(root,N),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_2))))) # label(fact_3682_real__root__gt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3529 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),zero_zero_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real))))) # label(fact_3683_real__root__lt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3530 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)))))) # label(fact_3684_real__root__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3531 (all X all N_6 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_6)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_n546711566l_real(root,N_6),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),X))))))) # label(fact_3685_real__root__decreasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3532 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),one_one_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),one_one_real))))) # label(fact_3686_real__root__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3533 (all Y_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(hAPP_n546711566l_real(root,N),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),Y_2))))) # label(fact_3687_real__root__ge__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3534 (all X all N_6 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_6)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_n546711566l_real(root,N_6),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),X))))))) # label(fact_3688_real__root__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3535 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),one_one_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real))))) # label(fact_3689_real__root__lt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3536 (all Y_2 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(hAPP_n546711566l_real(root,N),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),Y_2))))) # label(fact_3690_real__root__gt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3537 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(hAPP_n546711566l_real(root,hAPP_nat_nat(suc,N_1)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_nat_nat(suc,N_1))) = X)) # label(fact_3691_real__root__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3538 (all Y all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),Y))))))) # label(fact_3692_real__root__less__mono__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3539 (all X_4 all N_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_7)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_4)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_n546711566l_real(root,N_7),X_4)))))) # label(fact_3693_real__root__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3540 (all Y all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_1),Y)))))) # label(fact_3694_real__root__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3541 (all X all N_1 all M_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)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(hAPP_n546711566l_real(root,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),X) = hAPP_real_real(hAPP_n546711566l_real(root,M_1),hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)))))) # label(fact_3695_real__root__pos__mult__exp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3542 (all X all Y all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> (hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),N_1) = X -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),X) = Y)))) # label(fact_3696_real__root__pos__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3543 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),N_1) = X))) # label(fact_3697_real__root__pow__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3544 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1)) = X))) # label(fact_3698_real__root__pos2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3545 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),N_1) = X))) # label(fact_3699_real__root__pow__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3546 (all X all N_6 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_6)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_6),X)))))))) # label(fact_3700_real__root__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3547 (all X all N_6 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_6)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X)),hAPP_real_real(hAPP_n546711566l_real(root,N_6),X)))))))) # label(fact_3701_real__root__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3548 (all X all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hAPP_real_real(hAPP_n546711566l_real(root,N_1),hAPP_real_real(inverse_inverse_real,X)) = hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_n546711566l_real(root,N_1),X))))) # label(fact_3703_real__root__inverse__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3549 (all X_1 all N (-hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) -> (X_1 != zero_zero_real -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(root,N),X_1),hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_n546711566l_real(root,N),X_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat)))))))))) # label(fact_3704_DERIV__odd__real__root) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3550 (all Aa all Ba (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(negDivAlg_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aa),Ba))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba))) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),zero_zero_int)) -> negDivAlg(Aa,Ba) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,min)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba))) & (-(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba))) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),zero_zero_int))) -> negDivAlg(Aa,Ba) = hAPP_P1975530577nt_int(adjust(Ba),negDivAlg(Aa,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Ba)))))) # label(fact_3705_negDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3551 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(exp_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X)))))) # label(fact_3706_aux4) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3552 (all F all F_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> hBOOL(hAPP_real_bool(deriv_real(F,X_2),hAPP_real_real(F_1,X_2))))) -> (exists Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Z)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Z),Ba)) & hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(F,Ba)),hAPP_real_real(F,Aa)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Ba),Aa)),hAPP_real_real(F_1,Z))))))) # label(fact_3707_MVT2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3553 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> (exists R_1 exists A_1 (X = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_1),hAPP_real_real(cos,A_1)) & Y = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_1),hAPP_real_real(sin,A_1)))))) # label(fact_3708_polar__ex1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3554 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(exp_real,X)),hAPP_real_real(exp_real,Y))))) # label(fact_3709_exp__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3555 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(exp_real,X_1)),hAPP_real_real(exp_real,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)))) # label(fact_3710_exp__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3556 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(exp_real,X_1)),hAPP_real_real(exp_real,Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)))) # label(fact_3711_exp__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3557 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(exp_real,X)),hAPP_real_real(exp_real,Y))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)))) # label(fact_3712_exp__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3558 (all X_1 all Y_2 (hAPP_real_real(exp_real,X_1) = hAPP_real_real(exp_real,Y_2) <-> X_1 = Y_2)) # label(fact_3713_exp__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3559 (all X hAPP_real_real(abs_abs_real,hAPP_real_real(exp_real,X)) = hAPP_real_real(exp_real,X)) # label(fact_3714_abs__exp__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3560 (all Y all X (hAPP_real_real(exp_real,Y) = X -> hAPP_real_real(ln,X) = Y)) # label(fact_3715_ln__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3561 (all U_1 all X (hAPP_real_real(exp_real,U_1) = X -> hAPP_real_real(ln,X) = U_1)) # label(fact_3716_exp__ln__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3562 (all X hAPP_real_real(ln,hAPP_real_real(exp_real,X)) = X) # label(fact_3717_ln__exp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3563 (all X -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(exp_real,X)),zero_zero_real))) # label(fact_3718_not__exp__le__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3564 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(exp_real,X)))) # label(fact_3719_exp__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3565 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(exp_real,X)))) # label(fact_3720_exp__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3566 (all X -hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(exp_real,X)),zero_zero_real))) # label(fact_3721_not__exp__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3567 (all X_1 (hAPP_real_real(exp_real,X_1) = one_one_real <-> X_1 = zero_zero_real)) # label(fact_3722_exp__eq__one__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3568 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(exp_real,X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)))) # label(fact_3723_one__le__exp__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3569 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(exp_real,X_1)),one_one_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),zero_zero_real)))) # label(fact_3724_exp__le__one__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3570 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(exp_real,X))))) # label(fact_3725_exp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3571 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(exp_real,X_1)),one_one_real)) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)))) # label(fact_3726_exp__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3572 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(exp_real,X_1))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)))) # label(fact_3727_one__less__exp__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3573 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X)),hAPP_real_real(exp_real,X)))) # label(fact_3728_exp__ge__add__one__self) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3574 (all N_1 all X hAPP_real_real(exp_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),X)) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(exp_real,X)),N_1)) # label(fact_3729_exp__real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3575 (all X_1 (hAPP_real_real(exp_real,hAPP_real_real(ln,X_1)) = X_1 <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)))) # label(fact_3730_exp__ln__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3576 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(exp_real,hAPP_real_real(ln,X)) = X)) # label(fact_3731_exp__ln) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3577 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X)),hAPP_real_real(exp_real,X))))) # label(fact_3732_exp__ge__add__one__self__aux) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3578 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(exp_real,one_one_real)),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(ln,Y)),Y)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(ln,X)),X)))))) # label(fact_3733_ln__x__over__x__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3579 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),one_one_real)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(exp_real,X)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3734_exp__bound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3580 (all P_1 all A0 all A1 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(negDivAlg_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A0),A1))) -> ((all A_1 all B_3 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(negDivAlg_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_1),B_3))) -> ((-(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),B_3))) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_3),zero_zero_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_3)))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A_1),B_3))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A0),A1))))) # label(fact_3735_negDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3581 (all Aa all Ba (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(posDivAlg_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aa),Ba))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),zero_zero_int)) -> posDivAlg(Aa,Ba) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),Aa)) & (-(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),zero_zero_int))) -> posDivAlg(Aa,Ba) = hAPP_P1975530577nt_int(adjust(Ba),posDivAlg(Aa,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Ba)))))) # label(fact_3736_posDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3582 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),Y)) -> (exists X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Y),one_one_real))) & hAPP_real_real(exp_real,X_2) = Y)))) # label(fact_3737_lemma__exp__total) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3583 (all P_1 all A0 all A1 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(posDivAlg_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A0),A1))) -> ((all A_1 all B_3 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(posDivAlg_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_1),B_3))) -> ((-(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),B_3)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_3),zero_zero_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),B_3)))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A_1),B_3))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A0),A1))))) # label(fact_3738_posDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3584 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(log(hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(ln,hAPP_real_real(exp_real,one_one_real))),hAPP_real_real(ln,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))),hAPP_real_real(ln,X)))) # label(fact_3739_log__base__10__eq1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3585 (all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(log(hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),X) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(log(hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_real_real(exp_real,one_one_real))),hAPP_real_real(ln,X)))) # label(fact_3740_log__base__10__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3586 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> (exists X_2 hAPP_real_real(exp_real,X_2) = Y))) # label(fact_3741_exp__total) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3587 (all X all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),zero_zero_real)) -> (exists R_1 exists A_1 (X = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_1),hAPP_real_real(cos,A_1)) & Y = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_1),hAPP_real_real(sin,A_1)))))) # label(fact_3742_polar__ex2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3588 (all A_2 hAPP_real_real(log(A_2),one_one_real) = zero_zero_real) # label(fact_3743_log__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3589 (all A_2 all X hAPP_real_real(log(A_2),X) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(ln,X)),hAPP_real_real(ln,A_2))) # label(fact_3744_Log_Olog__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3590 (all Y_2 all X_1 all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),Aa)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(log(Aa),X_1)),hAPP_real_real(log(Aa),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2))))))) # label(fact_3745_log__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3591 (all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (A_2 != one_one_real -> hAPP_real_real(log(A_2),A_2) = one_one_real))) # label(fact_3746_log__eq__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3592 (all X hAPP_real_real(ln,X) = hAPP_real_real(log(hAPP_real_real(exp_real,one_one_real)),X)) # label(fact_3747_log__ln) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3593 (all Y_2 all X_1 all Aa (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),Aa)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(log(Aa),X_1)),hAPP_real_real(log(Aa),Y_2))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2))))))) # label(fact_3748_log__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3594 (all B_1 all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(log(B_1),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),hAPP_real_real(log(B_1),X)))) # label(fact_3749_log__nat__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3595 (all Y all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (A_2 != one_one_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(log(A_2),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(log(A_2),X)),hAPP_real_real(log(A_2),Y))))))) # label(fact_3750_log__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3596 (all Y all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (A_2 != one_one_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(log(A_2),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(log(A_2),X)),hAPP_real_real(log(A_2),Y))))))) # label(fact_3751_log__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3597 (all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (A_2 != one_one_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(log(A_2),hAPP_real_real(inverse_inverse_real,X)) = hAPP_real_real(uminus_uminus_real,hAPP_real_real(log(A_2),X)))))) # label(fact_3752_log__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3598 (all X all B_1 all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (A_2 != one_one_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_1)) -> (B_1 != one_one_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(log(A_2),X) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(ln,B_1)),hAPP_real_real(ln,A_2))),hAPP_real_real(log(B_1),X)))))))) # label(fact_3753_log__eq__div__ln__mult__log) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3599 (all X (-hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_int) = X)) # label(fact_3754_two__times__odd__div__two__plus__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3600 (all X_1 all Y_2 all F ((all X_2 hBOOL(hAPP_real_bool(deriv_real(F,X_2),zero_zero_real))) -> hAPP_real_real(F,X_1) = hAPP_real_real(F,Y_2))) # label(fact_3755_DERIV__isconst__all) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3601 (all K_2 ((K_2 = zero_z126310315umeral -> code_int_of(K_2) = zero_zero_int) & (K_2 != zero_z126310315umeral -> (hAPP_C498520661umeral(div_mo1740067990umeral(K_2),hAPP_i769753017umeral(number1443263063umeral,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_z126310315umeral -> code_int_of(K_2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),code_int_of(hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,K_2),hAPP_i769753017umeral(number1443263063umeral,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) & (hAPP_C498520661umeral(div_mo1740067990umeral(K_2),hAPP_i769753017umeral(number1443263063umeral,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_z126310315umeral -> code_int_of(K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),code_int_of(hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,K_2),hAPP_i769753017umeral(number1443263063umeral,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),one_one_int))))) # label(fact_3756_Code__Numeral_Oint__of__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3602 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),P_3)) -> hAPP_int_int(inv(P_3),hAPP_int_int(inv(P_3),A_2)) = A_2))))) # label(fact_3757_inv__inv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3603 (all X_1 (hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(uminus_uminus_int,X_1))) <-> hBOOL(hAPP_int_bool(even_odd_even_int,X_1)))) # label(fact_3758_even__neg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3604 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Y_2))) <-> hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) & hBOOL(hAPP_int_bool(even_odd_even_int,Y_2)) | -hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) & -hBOOL(hAPP_int_bool(even_odd_even_int,Y_2)))) # label(fact_3760_even__difference) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3605 (all Y all X (-hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> (-hBOOL(hAPP_int_bool(even_odd_even_int,Y)) -> hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_3761_Parity_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3606 (all Y all X (-hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> (hBOOL(hAPP_int_bool(even_odd_even_int,Y)) -> -hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_3762_odd__plus__even) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3607 (all Y all X (hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> (-hBOOL(hAPP_int_bool(even_odd_even_int,Y)) -> -hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_3763_Parity_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3608 (all Y all X (hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> (hBOOL(hAPP_int_bool(even_odd_even_int,Y)) -> hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_3764_Parity_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3609 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_1),Y_2))) <-> hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) & hBOOL(hAPP_int_bool(even_odd_even_int,Y_2)) | -hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) & -hBOOL(hAPP_int_bool(even_odd_even_int,Y_2)))) # label(fact_3765_even__sum) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3610 (all Y all X (-hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> (-hBOOL(hAPP_int_bool(even_odd_even_int,Y)) -> -hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)))))) # label(fact_3766_Parity_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3611 (all X all Y (hBOOL(hAPP_int_bool(even_odd_even_int,Y)) -> hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y))))) # label(fact_3767_anything__times__even) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3612 (all Y all X (hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y))))) # label(fact_3768_even__times__anything) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3613 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2))) <-> hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) | hBOOL(hAPP_int_bool(even_odd_even_int,Y_2)))) # label(fact_3769_Parity_Oeven__product) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3614 (all N_1 all X (-hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> -hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),N_1))))) # label(fact_3772_odd__pow) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3615 (all X_1 all N (hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_1),N))) <-> hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) & N != zero_zero_nat)) # label(fact_3773_even__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3616 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(inv(P_3),A_2)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))))))) # label(fact_3776_inv__less__p__minus__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3617 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(inv(P_3),A_2))))))) # label(fact_3777_inv__g__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3618 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))) -> hAPP_int_int(inv(P_3),A_2) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))))) # label(fact_3778_inv__not__p__minus__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3619 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))) -> hAPP_int_int(inv(P_3),A_2) != one_one_int)))) # label(fact_3779_inv__not__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3620 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))) -> A_2 != hAPP_int_int(inv(P_3),A_2))))) # label(fact_3780_inv__distinct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3621 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> (hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) <-> hBOOL(hAPP_nat_bool(even_odd_even_nat,hAPP_int_nat(nat,X_1)))))) # label(fact_3781_pos__int__even__equiv__nat__even) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3622 (all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (P_3 != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) -> (P_3 != hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit1,pls))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),P_3)))))) # label(fact_3782_prime__g__5) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3623 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))) -> hAPP_int_int(inv(P_3),A_2) != zero_zero_int)))) # label(fact_3783_inv__not__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3624 (all X_1 (hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) <-> (exists Y_1 X_1 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Y_1)))) # label(fact_3784_even__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3625 (all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Pa),zOdd)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa))))) # label(fact_3785_zprime__zOdd__eq__grt__2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3626 (all X_1 (hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) <-> hAPP_int_int(div_mod_int(X_1),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int)) # label(fact_3786_even__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3627 (all X (hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = X)) # label(fact_3787_two__times__even__div__two) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3628 (all X_1 (-hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) <-> (exists Y_1 X_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Y_1)),one_one_int)))) # label(fact_3789_odd__equiv__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3629 (all X (-hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int))) # label(fact_3790_odd__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3630 (all X (hBOOL(hAPP_int_bool(even_odd_even_int,X)) -> hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) # label(fact_3791_even__plus__one__div__two) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.79 3631 (all N_1 all M_1 code_d418564891umeral(N_1,M_1) = hAPP_C2132160860umeral(hAPP_C1614127039umeral(produc2136830103umeral,hAPP_C498520661umeral(hAPP_C1594335432umeral(div_di1218280263umeral,N_1),M_1)),hAPP_C498520661umeral(div_mo1740067990umeral(N_1),M_1))) # label(fact_3792_div__mod__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3632 (all Ba all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(Aa),Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(inv(Pa),Ba)),hAPP_i1948725293t_bool(wset(Aa),Pa)))))))) # label(fact_3793_wset__mem__inv__mem) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3633 (all Ba all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Ba)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(inv(Pa),Ba)),hAPP_i1948725293t_bool(wset(Aa),Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(Aa),Pa)))))))))) # label(fact_3794_wset__inv__mem__mem) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3634 (all A_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),P_3)))))) # label(fact_3795_Euler__part2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3635 (all M_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(M_1),zero_zero_int),M_1))) # label(fact_3796_zcong__id) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3636 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),zero_zero_int)) <-> Aa = Ba)) # label(fact_3797_IntPrimes_Ozcong__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3637 (all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(div_mod_int(Aa),M)),hAPP_int_int(div_mod_int(Ba),M)),M)))) # label(fact_3798_zcong__zmod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3638 (all A_2 all B_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),one_one_int))) # label(fact_3799_zcong__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3639 (all C_1 all D_3 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C_1),D_3),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),C_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),D_3)),M_1))))) # label(fact_3800_zcong__zmult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3640 (all K_2 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),A_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),B_1)),M_1)))) # label(fact_3801_zcong__scalar2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3641 (all K_2 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),K_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),K_2)),M_1)))) # label(fact_3802_zcong__scalar) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3642 (all C all D all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,D),Aa)),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,D),Ba)),M))))) # label(fact_3803_zcong__zmult__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3643 (all C all D all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),D)),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),D)),M))))) # label(fact_3804_zcong__zmult__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3644 (all A_2 all M_1 all B_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),M_1)),M_1))) # label(fact_3805_zcong__zmult__self) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3645 (all C_1 all D_3 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C_1),D_3),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_1),D_3)),M_1))))) # label(fact_3806_zcong__zadd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3646 (all C_1 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_1),C_1)),M_1)))) # label(fact_3807_zcong__shift) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3647 (all C_1 all D_3 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C_1),D_3),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),C_1)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,B_1),D_3)),M_1))))) # label(fact_3808_zcong__zdiff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3648 (all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),hAPP_int_int(uminus_uminus_int,M))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)))) # label(fact_3809_zcong__zminus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3649 (all Z_1 all X all Y all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),Y),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Z_1)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),Z_1)),M_1)))) # label(fact_3810_zcong__zpower) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3650 (all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Ba),Aa),M)))) # label(fact_3811_zcong__sym) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3651 (all K_2 all M_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(K_2),K_2),M_1))) # label(fact_3812_zcong__refl) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3652 (all D_3 all C_1 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> (B_1 = C_1 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(C_1),D_3),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),D_3),M_1)))))) # label(fact_3813_zcong__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3653 (all C_1 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(B_1),C_1),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),C_1),M_1))))) # label(fact_3814_zcong__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3654 (all B_1 all M_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),A_2)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1))))))) # label(fact_3815_zcong__not) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3655 (all M_1 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),M_1)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),M_1))))) # label(fact_3816_zcong__not__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3656 (all M_1 all Y 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,zero_zero_int),Y)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),Y),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),M_1)) -> X = Y))))))) # label(fact_3817_zcong__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3657 (all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) <-> (exists K Ba = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),K))))) # label(fact_3818_zcong__iff__lin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3658 (all M_1 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_int,X),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),M_1)) -> X = zero_zero_int)))) # label(fact_3819_Int2_Ozcong__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3659 (all M_1 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_int,A_2),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),M_1)) -> A_2 = zero_zero_int)))) # label(fact_3820_zcong__zless__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3660 (all B_1 all M_1 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_int,A_2),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> A_2 = B_1)))))) # label(fact_3821_zcong__zless__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3661 (all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) <-> hAPP_int_int(div_mod_int(Aa),M) = hAPP_int_int(div_mod_int(Ba),M)))) # label(fact_3822_zcong__zmod__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3662 (all Aa all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))),one_one_int),Pa)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int)),Pa)))) # label(fact_3823_inv__not__p__minus__1__aux) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3663 (all Z_1 all X all Y all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),Y)),one_one_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Y),Z_1))),one_one_int),P_3)))) # label(fact_3824_zcong__zpower__zmult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3664 (all Pa all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Aa)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),hAPP_i1948725293t_bool(wset(Aa),Pa))))) # label(fact_3825_wset__mem__mem) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3665 (all Y all X all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Y),zero_zero_int),P_3)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)),zero_zero_int),P_3)))))) # label(fact_3826_zcong__zmult__prop3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3666 (all B_1 all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) & -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(B_1),zero_zero_int),P_3)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)),zero_zero_int),P_3)))))) # label(fact_3827_zcong__zprime__prod__zero__contra) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3667 (all B_1 all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)),zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(B_1),zero_zero_int),P_3)))))) # label(fact_3828_zcong__zprime__prod__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3668 (all Ba all Pa all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Aa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),one_one_int)),Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(Aa),Pa)))))) # label(fact_3829_wset__subset) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3669 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),A_2)),one_one_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),one_one_int),P_3)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),P_3)))))) # label(fact_3830_zcong__square) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3670 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),A_2)),one_one_int),P_3)) -> A_2 = one_one_int | A_2 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)))))) # label(fact_3831_zcong__square__zless) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3671 (all Ba all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(Aa),Pa))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Ba)))))) # label(fact_3832_wset__g__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3672 (all Ba all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(Aa),Pa))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))))))) # label(fact_3833_wset__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3673 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(inv(P_3),A_2))),one_one_int),P_3)))))) # label(fact_3834_inv__is__inv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3674 (all Ba all Pa all Aa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Aa)) -> (-hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),one_one_int)),Pa))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(Aa),Pa))) -> Ba = Aa | Ba = hAPP_int_int(inv(Pa),Aa))))) # label(fact_3835_wset__mem__imp__or) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3675 (all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(zfact,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))),hAPP_int_int(number_number_of_int,min)),P_3)))) # label(fact_3836_Wilson__Russ) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3676 (all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),M_1)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(one_one_int),hAPP_int_int(number_number_of_int,min)),M_1)))) # label(fact_3837_one__not__neg__one__mod__m) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3677 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),hAPP_int_int(number_number_of_int,min)),P_3)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),one_one_int),P_3))))) # label(fact_3838_zcong__neg__1__impl__ne__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3678 (all J_2 all K_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),J_2)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),K_2)),M_1)) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),J_2) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(number_number_of_int,min)),K_2)))) # label(fact_3839_neg__one__power__eq__mod__m) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3679 (all Ba all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Ba)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(wset(Aa),Pa)))))))) # label(fact_3840_wset__mem) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3680 (all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> hAPP_i1948725293t_bool(d22set,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) = hAPP_i1948725293t_bool(wset(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),Pa))) # label(fact_3841_d22set__eq__wset) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3681 (all A_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(legendre(A_2),P_3)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),P_3))))) # label(fact_3842_Euler__Criterion) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3682 (all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,P_3),A_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(zfact,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),P_3))))))) # label(fact_3843_zfact__prop) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3683 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,P_3),X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_int_int(number_number_of_int,min)),P_3))))))) # label(fact_3844_Euler__part1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3684 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,P_3),X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),one_one_int),P_3))))))) # label(fact_3845_Euler__part3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3685 (all A_2 all P_3 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) -> hAPP_int_int(legendre(A_2),P_3) = zero_zero_int) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,P_3),A_2)) -> hAPP_int_int(legendre(A_2),P_3) = one_one_int) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,P_3),A_2)) -> hAPP_int_int(legendre(A_2),P_3) = hAPP_int_int(number_number_of_int,min))))) # label(fact_3846_Legendre__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3686 (all M all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,M),X_1)) <-> (exists Y_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X_1),M))))) # label(fact_3847_QuadRes__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3687 (all A_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),M_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),X_2),M_1)) & (all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),M_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),Y_1),M_1)) -> Y_1 = X_2)))))) # label(fact_3848_zcong__zless__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3688 (all N_1 all I ((I = zero_z126310315umeral -> hAPP_nat_nat(code_nat_of_aux(I),N_1) = N_1) & (I != zero_z126310315umeral -> hAPP_nat_nat(code_nat_of_aux(I),N_1) = hAPP_nat_nat(code_nat_of_aux(hAPP_C498520661umeral(hAPP_C1594335432umeral(minus_1690775515umeral,I),one_on1645066479umeral)),hAPP_nat_nat(suc,N_1))))) # label(fact_3849_nat__of__aux__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3689 (all X all M_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),hAPP_int_int(div_mod_int(X),M_1)),M_1))) # label(fact_3850_mod__mod__is__mod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3690 (all X all M_1 all Y (hAPP_int_int(div_mod_int(X),M_1) = hAPP_int_int(div_mod_int(Y),M_1) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),Y),M_1)))) # label(fact_3851_Residues_Oaux) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3691 (all J_2 all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,P_3),A_2)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),J_2))),P_3)))))))) # label(fact_3852_MultInvPair__distinct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3692 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(multInv(P_3),X)),X)),one_one_int),P_3)))))) # label(fact_3853_MultInv__prop2a) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3693 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),hAPP_int_int(multInv(P_3),X))),one_one_int),P_3)))))) # label(fact_3854_MultInv__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3694 (all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> phi(P_3) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)))) # label(fact_3855_phi__prime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3695 (all J_2 all A_2 all P_3 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),K_2))),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,J_2),K_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),K_2))),K_2)),P_3)))) # label(fact_3856_aux______1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3696 (all J_2 all K_2 all A_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,J_2),K_2)),A_2),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(multInv(P_3),J_2)),J_2)),K_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(multInv(P_3),J_2)),A_2)),P_3)))) # label(fact_3857_aux______3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3697 (all X all Y all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),Y),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(multInv(P_3),X)),hAPP_int_int(multInv(P_3),Y)),P_3))))) # label(fact_3858_MultInv__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3698 (all A_2 all J_2 all K_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),K_2),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),J_2))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),K_2))),P_3))))) # label(fact_3859_MultInv__zcong__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3699 (all P_3 all X hAPP_int_int(multInv(P_3),X) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3860_MultInv__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3700 (all Y all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Y),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(multInv(P_3),X)),hAPP_int_int(multInv(P_3),Y)),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),Y),P_3)))))))) # label(fact_3861_MultInv__prop5) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3701 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(multInv(P_3),hAPP_int_int(multInv(P_3),X))),X),P_3)))))) # label(fact_3862_MultInv__prop4) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3702 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(multInv(P_3),X)),zero_zero_int),P_3)))))) # label(fact_3863_MultInv__prop3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3703 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(multInv(P_3),hAPP_int_int(multInv(P_3),X))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),hAPP_int_int(multInv(P_3),X))),hAPP_int_int(multInv(P_3),hAPP_int_int(multInv(P_3),X)))),P_3)))))) # label(fact_3864_Int2_Oaux____1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3704 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),hAPP_int_int(multInv(P_3),X))),hAPP_int_int(multInv(P_3),hAPP_int_int(multInv(P_3),X)))),X),P_3)))))) # label(fact_3865_Int2_Oaux____2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3705 (all J_2 all K_2 all A_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(K_2),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),J_2))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),K_2))),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),K_2),P_3))))))))) # label(fact_3866_MultInv__zcong__prop3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3706 (all A_2 all J_2 all K_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(K_2),zero_zero_int),P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),K_2))),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(K_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),J_2))),P_3)))))))) # label(fact_3867_MultInv__zcong__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3707 (all J_2 all A_2 all K_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(K_2),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,J_2),K_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),K_2))),K_2)),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,J_2),K_2)),A_2),P_3))))))) # label(fact_3868_aux______2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3708 (all K_2 all A_2 all J_2 all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J_2),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(multInv(P_3),J_2)),J_2)),K_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(multInv(P_3),J_2)),A_2)),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(K_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),hAPP_int_int(multInv(P_3),J_2))),P_3))))))) # label(fact_3869_aux______4) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3709 (all Pa hAPP_i1948725293t_bool(sr,Pa) = collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),Pa)))) # label(fact_3870_SR__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3710 (all X all Y all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(standardRes(M_1),X)),hAPP_int_int(standardRes(M_1),Y))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)),M_1)))) # label(fact_3871_StandardRes__prop4) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3711 (all A_2 all B_1 hAPP_complex_complex(invers1449016382omplex,hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,A_2),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(uminus_uminus_real,B_1)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,A_2),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,B_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_3872_complex__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3712 (all N_1 all M_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,N_1))),hAPP_nat_int(semiri1621563631at_int,M_1)))) # label(fact_3873_negative__zle) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3713 (all N_1 all M_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1)))),hAPP_nat_int(semiri1621563631at_int,M_1)))) # label(fact_3874_negative__zless) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3714 (all Aa all Ba (hAPP_real_complex(hAPP_r265291036omplex(complex,Aa),Ba) = zero_zero_complex <-> Aa = zero_zero_real & Ba = zero_zero_real)) # label(fact_3876_Complex__eq__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3715 (all X all Y hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,X),Y) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X),hAPP_complex_complex(invers1449016382omplex,Y))) # label(fact_3877_complex__divide__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3716 (all M_1 hAPP_int_int(abs_abs_int,hAPP_nat_int(semiri1621563631at_int,M_1)) = hAPP_nat_int(semiri1621563631at_int,M_1)) # label(fact_3878_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3717 (all N_1 hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,N_1)) = N_1) # label(fact_3881_nat__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3718 (all A_2 all B_1 all C_1 all D_3 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)),hAPP_real_complex(hAPP_r265291036omplex(complex,C_1),D_3)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_2),C_1)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,B_1),D_3))) # label(fact_3882_complex__add) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3719 (all Real1_2 all Real2_2 all Real1_1 all Real2_1 (hAPP_real_complex(hAPP_r265291036omplex(complex,Real1_2),Real2_2) = hAPP_real_complex(hAPP_r265291036omplex(complex,Real1_1),Real2_1) <-> Real1_2 = Real1_1 & Real2_2 = Real2_1)) # label(fact_3883_complex_Oinject) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3720 (all A_2 all B_1 hAPP_complex_complex(uminus473333897omplex,hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(uminus_uminus_real,A_2)),hAPP_real_real(uminus_uminus_real,B_1))) # label(fact_3884_complex__minus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3721 (all N_1 -hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_3885_not__neg__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3722 (all A_2 all B_1 all C_1 all D_3 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)),hAPP_real_complex(hAPP_r265291036omplex(complex,C_1),D_3)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_2),C_1)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_1),D_3))) # label(fact_3886_complex__diff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3723 (all X_1 all Pa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sr,Pa))) -> hAPP_int_int(standardRes(Pa),X_1) = X_1)) # label(fact_3887_StandardRes__SR__prop) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3724 (all X all M_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),hAPP_int_int(standardRes(M_1),X)),M_1))) # label(fact_3888_StandardRes__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3725 (all M_1 all X hAPP_int_int(standardRes(M_1),X) = hAPP_int_int(div_mod_int(X),M_1)) # label(fact_3889_StandardRes__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3726 (all N (hAPP_nat_int(semiri1621563631at_int,N) = zero_zero_int <-> N = zero_zero_nat)) # label(fact_3890_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3727 (all K_2 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K_2)),zero_zero_int))) # label(fact_3893_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3728 (all N_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N_1)))) # label(fact_3894_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3729 (all Z_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))) # label(fact_3895_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3730 (all P_1 ((exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) & hBOOL(hAPP_int_bool(P_1,X_2)))) <-> (exists X_2 hBOOL(hAPP_int_bool(P_1,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_3896_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3731 (all P_1 ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> hBOOL(hAPP_int_bool(P_1,X_2)))) <-> (all X_2 hBOOL(hAPP_int_bool(P_1,hAPP_nat_int(semiri1621563631at_int,X_2)))))) # label(fact_3897_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3732 (all M all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_3898_zless__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3733 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)))) # label(fact_3899_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3734 (all M all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_3900_zle__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3735 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)))) # label(fact_3901_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3736 (all M_1 all N_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) # label(fact_3902_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3737 (all M_1 all N_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1))) # label(fact_3903_int__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3738 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y))) # label(fact_3904_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3739 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2)) <-> (exists N_2 Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,N_2))))) # label(fact_3905_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3740 (all M_1 all N_1 all Z_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,N_1)),Z_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))),Z_1)) # label(fact_3906_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3741 (all M_1 all N_1 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) # label(fact_3907_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3742 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Y))) # label(fact_3908_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3743 (all N all M (hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,M) <-> N = zero_zero_nat & M = zero_zero_nat)) # label(fact_3911_negative__eq__positive) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3744 (all N_1 all M_1 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,N_1)),hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,M_1))))) # label(fact_3912_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3745 (all Aa all Ba all W_1 (hAPP_real_complex(hAPP_r265291036omplex(complex,Aa),Ba) = hAPP_int_complex(number528085621omplex,W_1) <-> Aa = hAPP_int_real(number267125858f_real,W_1) & Ba = zero_zero_real)) # label(fact_3913_Complex__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3746 (all Aa all Ba (hAPP_real_complex(hAPP_r265291036omplex(complex,Aa),Ba) = one_one_complex <-> Aa = one_one_real & Ba = zero_zero_real)) # label(fact_3914_Complex__eq__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3747 (all N_1 hAPP_int_real(real_int,hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_real(real_nat,N_1)) # label(fact_3916_real__of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3748 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),Y))) # label(fact_3917_Divides_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3749 (all A_2 all B_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_2),B_1)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_nat_int(semiri1621563631at_int,A_2)),hAPP_nat_int(semiri1621563631at_int,B_1))) # label(fact_3918_zdiv__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3750 (all X all Y hAPP_int_int(div_mod_int(hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(div_mod_nat(X),Y))) # label(fact_3919_Divides_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3751 (all A_2 all B_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(div_mod_nat(A_2),B_1)) = hAPP_int_int(div_mod_int(hAPP_nat_int(semiri1621563631at_int,A_2)),hAPP_nat_int(semiri1621563631at_int,B_1))) # label(fact_3920_zmod__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3752 (all M_1 all N_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M_1)),N_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M_1),N_1))) # label(fact_3921_zpower__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3753 (all M_1 all N_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M_1),N_1)) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M_1)),N_1)) # label(fact_3922_int__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3754 (all X all N_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,X)),N_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N_1))) # label(fact_3923_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3755 (all Z_1 (-hBOOL(hAPP_int_bool(nat_neg,Z_1)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_int_nat(nat,Z_1)) = Z_1)) # label(fact_3924_not__neg__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3756 (all N_1 archim1246769320r_real(hAPP_nat_real(real_nat,N_1)) = hAPP_nat_int(semiri1621563631at_int,N_1)) # label(fact_3925_floor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3757 (all X_1 (hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_nat_int(semiri1621563631at_int,X_1))) <-> hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)))) # label(fact_3926_Parity_Otransfer__int__nat__relations) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3758 (all X_1 (hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) <-> hBOOL(hAPP_int_bool(even_odd_even_int,hAPP_nat_int(semiri1621563631at_int,X_1))))) # label(fact_3927_even__nat__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3759 (all N_1 archim856651990g_real(hAPP_nat_real(real_nat,N_1)) = hAPP_nat_int(semiri1621563631at_int,N_1)) # label(fact_3928_ceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3760 (all X all Y hAPP_int_int(nat_tsub(hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X),Y))) # label(fact_3929_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3761 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(standardRes(P_3),X)),P_3)))) # label(fact_3930_StandardRes__ubound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3762 (all X_1 all Pa (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X_1),zero_zero_int),Pa)) <-> hAPP_int_int(standardRes(Pa),X_1) != zero_zero_int)) # label(fact_3931_StandardRes__prop3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3763 (all M all X_1 (hAPP_int_int(standardRes(M),X_1) = zero_zero_int <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X_1),zero_zero_int),M)))) # label(fact_3932_StandardRes__eq__zcong) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3764 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,N)),zero_zero_int)) <-> N = zero_zero_nat)) # label(fact_3933_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3765 (all W_1 all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) <-> (exists N_2 Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_2)))))) # label(fact_3935_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3766 (all M_1 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M_1))) # label(fact_3936_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3767 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_int_nat(nat,Z_1)) = Z_1)) # label(fact_3937_nat__0__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3768 (all M all Z_2 (hAPP_nat_int(semiri1621563631at_int,M) = Z_2 <-> M = hAPP_int_nat(nat,Z_2) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_2)))) # label(fact_3938_int__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3769 (all Z_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_int_nat(nat,Z_1)) = Z_1) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_int_nat(nat,Z_1)) = zero_zero_int))) # label(fact_3939_int__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3770 (all M all Z_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_int_nat(nat,Z_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),Z_2)))) # label(fact_3940_zless__nat__eq__int__zless) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3771 (all N all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,N)),hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,M)))) <-> N = zero_zero_nat & M = zero_zero_nat)) # label(fact_3941_int__zle__neg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3772 (all N_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,N_1))),zero_zero_int))) # label(fact_3942_negative__zle__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3773 (all N_1 hAPP_int_nat(nat,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,N_1))) = zero_zero_nat) # label(fact_3943_nat__zminus__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3774 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)))) # label(fact_3944_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3775 (all A_2 all B_1 all C_1 all D_3 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)),hAPP_real_complex(hAPP_r265291036omplex(complex,C_1),D_3)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_2),C_1)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_1),D_3))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_2),D_3)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_1),C_1)))) # label(fact_3945_complex__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3776 (all N_1 hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1)))))) # label(fact_3946_neg__zminus__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3777 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_3947_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3778 (all K_2 all I all J_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_2)),I)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_2)),J_2)))))) # label(fact_3948_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3779 (all P_1 all I_1 (hBOOL(hAPP_nat_bool(P_1,hAPP_int_nat(nat,I_1))) <-> (all N_2 (I_1 = hAPP_nat_int(semiri1621563631at_int,N_2) -> hBOOL(hAPP_nat_bool(P_1,N_2)))) & (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),zero_zero_int)) -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))))) # label(fact_3950_split__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3780 (all W_1 all M (hAPP_int_nat(nat,W_1) = M <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1)) -> W_1 = hAPP_nat_int(semiri1621563631at_int,M)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1)) -> M = zero_zero_nat))) # label(fact_3951_nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3781 (all M all W_1 (M = hAPP_int_nat(nat,W_1) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1)) -> W_1 = hAPP_nat_int(semiri1621563631at_int,M)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1)) -> M = zero_zero_nat))) # label(fact_3952_nat__eq__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3782 (all N_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1)))),zero_zero_int))) # label(fact_3953_negative__zless__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3783 (all N_1 -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1)))))) # label(fact_3954_not__zle__0__negative) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3784 (all M all V (hAPP_nat_int(semiri1621563631at_int,M) = hAPP_int_int(number_number_of_int,V) <-> M = hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,V)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,V))))) # label(fact_3955_int__eq__iff__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3785 (all V_2 ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_int(semiri1621563631at_int,hAPP_int_nat(number_number_of_nat,V_2)) = zero_zero_int) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,V_2))) -> hAPP_nat_int(semiri1621563631at_int,hAPP_int_nat(number_number_of_nat,V_2)) = hAPP_int_int(number_number_of_int,V_2)))) # label(fact_3956_int__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3786 (all X all P_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),P_3)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(standardRes(P_3),X))))) # label(fact_3957_StandardRes__lbound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3787 (all X1_1 all X2 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hAPP_int_int(standardRes(M),X1_1) = hAPP_int_int(standardRes(M),X2) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X1_1),X2),M))))) # label(fact_3958_StandardRes__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3788 (all N_1 archim1246769320r_real(hAPP_real_real(uminus_uminus_real,hAPP_nat_real(real_nat,N_1))) = hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,N_1))) # label(fact_3959_floor__minus__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3789 (all M all W_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat,W_1)),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_nat_int(semiri1621563631at_int,M)))))) # label(fact_3961_nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3790 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_int_bool(P_1,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_2)))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_2))))) & (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) -> hBOOL(hAPP_int_bool(P_1,zero_zero_int))))) # label(fact_3962_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3791 (all X_1 all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sRStar,Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(standardRes(Pa),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),hAPP_int_int(multInv(Pa),X_1)))),hAPP_i1948725293t_bool(sRStar,Pa)))))))) # label(fact_3963_SRStar__mult__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3792 (all X_1 all Y_2 (hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,Y_2) <-> X_1 = Y_2)) # label(fact_3964_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3793 (all X_1 all Y_2 all P_1 ((hBOOL(P_1) -> hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,P_1),X_1),Y_2))) & (-hBOOL(P_1) -> hAPP_nat_int(semiri1621563631at_int,Y_2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,P_1),X_1),Y_2))))) # label(fact_3965_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3794 (all M all N (hAPP_nat_int(semiri1621563631at_int,M) = hAPP_nat_int(semiri1621563631at_int,N) <-> M = N)) # label(fact_3966_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3795 (all X all Y hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X),Y) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X),hAPP_complex_complex(uminus473333897omplex,Y))) # label(fact_3967_complex__diff__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3796 (all R_3 hAPP_real_real(norm_norm_real,R_3) = hAPP_real_real(abs_abs_real,R_3)) # label(fact_3968_real__norm__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3797 (all X_1 all Pa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sRStar,Pa))) -> hAPP_int_int(standardRes(Pa),X_1) = X_1)) # label(fact_3969_StandardRes__SRStar__prop3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3798 (all B_1 all A_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,B_1),A_2))),hAPP_complex_real(norm_norm_complex,B_1))),hAPP_complex_real(norm_norm_complex,A_2)))) # label(fact_3970_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3799 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_complex_real(norm_norm_complex,X))),hAPP_complex_real(norm_norm_complex,X)))) # label(fact_3971_complex__mod__minus__le__complex__mod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3800 (all X_1 all Pa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sRStar,Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sr,Pa))))) # label(fact_3972_SRStar__SR__prop) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3801 (all Pa hAPP_i1948725293t_bool(sRStar,Pa) = collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),Pa)))) # label(fact_3973_SRStar__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3802 (all X_1 all Pa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sRStar,Pa))) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X_1),zero_zero_int),Pa)))) # label(fact_3974_StandardRes__SRStar__prop1a) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3803 (all A_2 hAPP_complex_real(norm_norm_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(cos,A_2)),hAPP_real_real(sin,A_2))) = one_one_real) # label(fact_3975_cmod__unit__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3804 (all X all Y hAPP_complex_real(norm_norm_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,X),Y)) = hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_3976_complex__norm) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3805 (all X_1 all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sRStar,Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(standardRes(Pa),X_1)),hAPP_i1948725293t_bool(sRStar,Pa))))))) # label(fact_3977_StandardRes__SRStar__prop4) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3806 (all X_1 all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(standardRes(Pa),X_1)),hAPP_i1948725293t_bool(sRStar,Pa))) <-> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X_1),zero_zero_int),Pa))))) # label(fact_3978_StandardRes__SRStar__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3807 (all Y_2 all X_1 all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sRStar,Pa))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_2),hAPP_i1948725293t_bool(sRStar,Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(standardRes(Pa),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X_1),Y_2))),hAPP_i1948725293t_bool(sRStar,Pa)))))))) # label(fact_3979_SRStar__mult__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3808 (all X_1 all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),hAPP_i1948725293t_bool(sRStar,Pa))) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(standardRes(Pa),hAPP_int_int(multInv(Pa),X_1))),hAPP_i1948725293t_bool(sRStar,Pa))))))) # label(fact_3980_StandardRes__SRStar__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3809 (all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),zero_zero_int)) -> (exists N_2 X = hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_2)))))) # label(fact_3981_negD) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3810 (all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_2)) -> (exists N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) & K_2 = hAPP_nat_int(semiri1621563631at_int,N_2))))) # label(fact_3982_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3811 (all Real1 all Real2 complex_size(hAPP_real_complex(hAPP_r265291036omplex(complex,Real1),Real2)) = zero_zero_nat) # label(fact_3983_complex_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3812 (all X all Y ((Y = zero_zero_nat -> bezw(X,Y) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,one_one_int),zero_zero_int)) & (Y != zero_zero_nat -> bezw(X,Y) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_P1175774780nt_int(product_snd_int_int,bezw(Y,hAPP_nat_nat(div_mod_nat(X),Y)))),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_P1175774780nt_int(product_fst_int_int,bezw(Y,hAPP_nat_nat(div_mod_nat(X),Y)))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_P1175774780nt_int(product_snd_int_int,bezw(Y,hAPP_nat_nat(div_mod_nat(X),Y)))),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),Y)))))))) # label(fact_3984_bezw_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3813 (all X bezw(X,zero_zero_nat) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,one_one_int),zero_zero_int)) # label(fact_3985_bezw__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3814 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Y)) -> bezw(X,Y) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_P1175774780nt_int(product_snd_int_int,bezw(Y,hAPP_nat_nat(div_mod_nat(X),Y)))),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_P1175774780nt_int(product_fst_int_int,bezw(Y,hAPP_nat_nat(div_mod_nat(X),Y)))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_P1175774780nt_int(product_snd_int_int,bezw(Y,hAPP_nat_nat(div_mod_nat(X),Y)))),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,X),Y))))))) # label(fact_3986_bezw__non__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3815 (all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> (exists N_2 K_2 = hAPP_nat_int(semiri1621563631at_int,N_2)))) # label(fact_3987_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3816 (all Z_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_1)) -> -(all M_2 Z_1 != hAPP_nat_int(semiri1621563631at_int,M_2)))) # label(fact_3988_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3817 (all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> -(all N_2 K_2 != hAPP_nat_int(semiri1621563631at_int,N_2)))) # label(fact_3989_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3818 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y),zero_zero_real)) -> hAPP_real_real(cos,arg(hAPP_real_complex(hAPP_r265291036omplex(complex,zero_zero_real),Y))) = zero_zero_real)) # label(fact_3990_cos__arg__i__mult__zero__neg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3819 (all Y (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(cos,arg(hAPP_real_complex(hAPP_r265291036omplex(complex,zero_zero_real),Y))) = zero_zero_real)) # label(fact_3991_cos__arg__i__mult__zero__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3820 (all X hAPP_nat_int(semiri1621563631at_int,hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,X))) = hAPP_int_int(abs_abs_int,X)) # label(fact_3992_int__nat__abs) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3821 (all Y (Y != zero_zero_real -> hAPP_real_real(cos,arg(hAPP_real_complex(hAPP_r265291036omplex(complex,zero_zero_real),Y))) = zero_zero_real)) # label(fact_3993_cos__arg__i__mult__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3822 (all Real1 all Real2 hAPP_complex_nat(size_size_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,Real1),Real2)) = zero_zero_nat) # label(fact_3994_complex_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3823 (all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(sRStar,Pa))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) # label(fact_3995_SRStar__card) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3824 (all Z_1 -(all M_2 all N_2 Z_1 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_2)),hAPP_nat_int(semiri1621563631at_int,N_2)))) # label(fact_3996_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3825 (all J all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,Pa),Aa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(J),zero_zero_int),Pa)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(multInvPair(Aa,Pa),J)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_3997_MultInvPair__card__two) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3826 (all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,Pa),Aa)) -> (all X_2 (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_2),setS(Aa,Pa))) -> hAPP_f957591787ol_nat(finite_card_int,X_2) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_3998_SetS__elems__card) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3827 (all W ii != hAPP_int_complex(number528085621omplex,W)) # label(fact_4002_complex__i__not__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3828 (all X hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,ii),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,ii),X)) = hAPP_complex_complex(uminus473333897omplex,X)) # label(fact_4003_complex__i__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3829 (all X_1 all Y_2 (hAPP_real_complex(hAPP_r265291036omplex(complex,X_1),Y_2) = ii <-> X_1 = zero_zero_real & Y_2 = one_one_real)) # label(fact_4006_Complex__eq__i) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3830 (all A_2 all B_1 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)),ii) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(uminus_uminus_real,B_1)),A_2)) # label(fact_4007_Complex__mult__i) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3831 (all A_2 all B_1 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,ii),hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(uminus_uminus_real,B_1)),A_2)) # label(fact_4008_i__mult__Complex) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3832 (all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,Pa),Aa)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_f521865025ol_nat(finite1876863882t_bool,setS(Aa,Pa))) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_4011_SetS__card) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3833 (all X all Y hAPP_complex_complex(invers1449016382omplex,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,of_real_complex(X)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,ii),of_real_complex(Y)))) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,of_real_complex(hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,ii),of_real_complex(hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,Y),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))))) # label(fact_4012_complex__inverse__complex__split) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3834 (all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> comple219730294t_bool(setS(Aa,Pa)) = hAPP_i1948725293t_bool(sRStar,Pa))))) # label(fact_4013_MultInvPair__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3835 (all X_1 all Y_2 all Xa_1 (hAPP_real_complex(hAPP_r265291036omplex(complex,X_1),Y_2) = of_real_complex(Xa_1) <-> X_1 = Xa_1 & Y_2 = zero_zero_real)) # label(fact_4014_complex__eq__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3836 (all R_3 of_real_complex(R_3) = hAPP_real_complex(hAPP_r265291036omplex(complex,R_3),zero_zero_real)) # label(fact_4015_complex__of__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3837 (all Z_1 hAPP_complex_complex(sgn_sgn_complex,Z_1) = hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,Z_1),of_real_complex(hAPP_complex_real(norm_norm_complex,Z_1)))) # label(fact_4016_sgn__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3838 (all X all Y all R_3 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,X),Y)),of_real_complex(R_3)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),R_3)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y),R_3))) # label(fact_4017_Complex__mult__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3839 (all R_3 all X all Y hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(R_3)),hAPP_real_complex(hAPP_r265291036omplex(complex,X),Y)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),X)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),Y))) # label(fact_4018_complex__of__real__mult__Complex) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3840 (all R_3 all X all Y hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,of_real_complex(R_3)),hAPP_real_complex(hAPP_r265291036omplex(complex,X),Y)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,R_3),X)),Y)) # label(fact_4019_complex__of__real__add__Complex) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3841 (all X all Y all R_3 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_real_complex(hAPP_r265291036omplex(complex,X),Y)),of_real_complex(R_3)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X),R_3)),Y)) # label(fact_4020_Complex__add__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3842 (all R_3 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,ii),of_real_complex(R_3)) = hAPP_real_complex(hAPP_r265291036omplex(complex,zero_zero_real),R_3)) # label(fact_4022_i__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3843 (all R_3 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(R_3)),ii) = hAPP_real_complex(hAPP_r265291036omplex(complex,zero_zero_real),R_3)) # label(fact_4023_complex__of__real__i) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3844 (all R_3 all A_2 hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(R_3)),hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(cos,A_2)),hAPP_real_real(sin,A_2)))) = hAPP_real_real(abs_abs_real,R_3)) # label(fact_4025_cmod__complex__polar) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3845 (all A_2 all B_1 expi(hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,A_2),B_1)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,expi(A_2)),expi(B_1))) # label(fact_4027_expi__add) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3846 (all Z_1 exists R_1 exists A_1 Z_1 = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(R_1)),hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(cos,A_1)),hAPP_real_real(sin,A_1)))) # label(fact_4029_complex__split__polar) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3847 (all Aa all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,comple219730294t_bool(setS(Aa,Pa)))))) # label(fact_4030_Union__SetS__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3848 (all Aa all Pa hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(wset(Aa),Pa)))) # label(fact_4031_wset__fin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3849 (all Aa hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(d22set,Aa)))) # label(fact_4032_d22set__fin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3850 (all Aa all Pa all X_2 (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_2),setS(Aa,Pa))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X_2)))) # label(fact_4033_SetS__elems__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3851 (all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(sRStar,Pa))))) # label(fact_4034_SRStar__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3852 (all Aa all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,setS(Aa,Pa))))) # label(fact_4035_SetS__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3853 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> (exists Y_1 (hBOOL(hAPP_real_bool(deriv_real(F,X_2),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),zero_zero_real)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,Ba)),hAPP_real_real(F,Aa)))))) # label(fact_4036_DERIV__neg__imp__decreasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3854 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> (exists Y_1 (hBOOL(hAPP_real_bool(deriv_real(F,X_2),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_1)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,Aa)),hAPP_real_real(F,Ba)))))) # label(fact_4037_DERIV__pos__imp__increasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3855 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_4038_coprime__sos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3856 (all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,Aa),Ba)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,Ba),Aa)))) # label(fact_4039_coprime__commute) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3857 (all D_3 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),B_1)))) # label(fact_4040_coprime__lmul2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3858 (all D_3 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),A_2)))) # label(fact_4041_coprime__rmul2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3859 (all B_1 all D_3 all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),A_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1)))))) # label(fact_4042_coprime__mul) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3860 (all D all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D),Aa)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D),Ba)))) # label(fact_4043_coprime__mul__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3861 (all A_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,one_one_nat),A_2))) # label(fact_4044_coprime__1_H) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3862 (all A_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),one_one_nat))) # label(fact_4045_coprime__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.80 3863 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,N),N)) <-> N = one_one_nat)) # label(fact_4046_coprime__refl) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3864 (all N_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_2),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,B_1),N_1))))) # label(fact_4047_coprime__exp__imp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3865 (all N_1 all D_3 all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_2),N_1))))) # label(fact_4048_coprime__exp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3866 (all A_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,hAPP_nat_nat(suc,zero_zero_nat)),A_2))) # label(fact_4049_coprime__Suc0_H) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3867 (all A_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),hAPP_nat_nat(suc,zero_zero_nat)))) # label(fact_4050_coprime__Suc0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3868 (all D (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D),zero_zero_nat)) <-> D = one_one_nat)) # label(fact_4051_coprime__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3869 (all D (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,zero_zero_nat),D)) <-> D = one_one_nat)) # label(fact_4052_coprime__0_H) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3870 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)),N_1))) # label(fact_4053_coprime__plus1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3871 (all Aa all N all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Aa),hAPP_nat_nat(suc,N))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Ba),hAPP_nat_nat(suc,N)))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,Aa),Ba)))) # label(fact_4054_coprime__exp2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3872 (all N_1 (N_1 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)),N_1)))) # label(fact_4055_coprime__minus1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3873 (all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,Aa),Ba)) <-> (exists X_2 exists Y_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),X_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ba),Y_1)) = one_one_nat | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ba),X_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),Y_1)) = one_one_nat)))) # label(fact_4056_coprime__bezout) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3874 (all Nat hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_4057_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3875 (all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),B_1)) -> (B_1 != one_one_nat -> (exists X_2 exists Y_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),X_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),Y_1)),one_one_nat))))) # label(fact_4058_coprime__bezout__strong) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3876 (all Nat hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_4060_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3877 (all Z_1 exists A_1 exists R_1 Z_1 = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(R_1)),expi(A_1))) # label(fact_4061_complex__expi__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3878 (all X_3 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hBOOL(hAPP_f448129468l_bool(resSet(M),X_3)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X_3))))) # label(fact_4062_ResSet__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3879 (all N_1 hAPP_nat_nat(size_size_nat,N_1) = N_1) # label(fact_4063_nat__size) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3880 (all M all X_3 (hBOOL(hAPP_f448129468l_bool(resSet(M),X_3)) <-> (all Y1 all Y2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y1),X_3)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y2),X_3)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Y1),Y2),M)) -> Y1 = Y2)))) # label(fact_4064_ResSet__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3881 (all Pa hBOOL(hAPP_f448129468l_bool(resSet(Pa),hAPP_i1948725293t_bool(sRStar,Pa)))) # label(fact_4066_ResSet__SRStar__prop) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3882 (all Z_1 hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1))) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(norm_norm_complex,Z_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) # label(fact_4068_complex__mod__mult__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3883 (all X hAPP_complex_complex(cnj,of_real_complex(X)) = of_real_complex(X)) # label(fact_4069_complex__cnj__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3884 (all X all Y hAPP_complex_complex(cnj,hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,X),Y)) = hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,hAPP_complex_complex(cnj,X)),hAPP_complex_complex(cnj,Y))) # label(fact_4070_complex__cnj__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3885 (all X all N_1 hAPP_complex_complex(cnj,hAPP_nat_complex(hAPP_c1088319240omplex(power_power_complex,X),N_1)) = hAPP_nat_complex(hAPP_c1088319240omplex(power_power_complex,hAPP_complex_complex(cnj,X)),N_1)) # label(fact_4071_complex__cnj__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3886 (all N_1 hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N_1)) = hAPP_nat_complex(semiri2020571505omplex,N_1)) # label(fact_4072_complex__cnj__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3887 (all X all Y hAPP_complex_complex(cnj,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X),Y)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_complex_complex(cnj,X)),hAPP_complex_complex(cnj,Y))) # label(fact_4074_complex__cnj__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3888 (all X all Y hAPP_complex_complex(cnj,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X),Y)) = hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,hAPP_complex_complex(cnj,X)),hAPP_complex_complex(cnj,Y))) # label(fact_4075_cnj_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3889 (all W hAPP_complex_complex(cnj,hAPP_int_complex(number528085621omplex,W)) = hAPP_int_complex(number528085621omplex,W)) # label(fact_4076_complex__cnj__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3890 (all Z_2 (hAPP_complex_complex(cnj,Z_2) = zero_zero_complex <-> Z_2 = zero_zero_complex)) # label(fact_4078_complex__cnj__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3891 (all Z_1 hAPP_complex_complex(cnj,hAPP_complex_complex(cnj,Z_1)) = Z_1) # label(fact_4079_complex__cnj__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3892 (all X_1 all Y_2 (hAPP_complex_complex(cnj,X_1) = hAPP_complex_complex(cnj,Y_2) <-> X_1 = Y_2)) # label(fact_4080_complex__cnj__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3893 (all X hAPP_complex_complex(cnj,hAPP_complex_complex(invers1449016382omplex,X)) = hAPP_complex_complex(invers1449016382omplex,hAPP_complex_complex(cnj,X))) # label(fact_4081_complex__cnj__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3894 (all Z_1 hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(cnj,Z_1)) = hAPP_complex_real(norm_norm_complex,Z_1)) # label(fact_4082_complex__mod__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3895 (all X all Y hAPP_complex_complex(cnj,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X),Y)) = hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,hAPP_complex_complex(cnj,X)),hAPP_complex_complex(cnj,Y))) # label(fact_4083_cnj_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3896 (all X hAPP_complex_complex(cnj,hAPP_complex_complex(uminus473333897omplex,X)) = hAPP_complex_complex(uminus473333897omplex,hAPP_complex_complex(cnj,X))) # label(fact_4084_cnj_Ominus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3897 (all A_2 all B_1 hAPP_complex_complex(cnj,hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)) = hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),hAPP_real_real(uminus_uminus_real,B_1))) # label(fact_4085_complex__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3898 (exists K_4 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),K_4)) & (all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(cnj,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))))) # label(fact_4087_cnj_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3899 (exists K_4 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),K_4)) & (all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(cnj,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))))) # label(fact_4088_cnj_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3900 (exists K_4 all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(cnj,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))) # label(fact_4089_cnj_Obounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3901 (all Z_1 hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,Z_1),hAPP_complex_complex(cnj,Z_1)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_complex_real(im,Z_1)))),ii)) # label(fact_4090_complex__diff__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3902 (all Z_1 hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,Z_1),hAPP_complex_complex(cnj,Z_1)) = of_real_complex(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_complex_real(re,Z_1)))) # label(fact_4091_complex__add__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3903 (all Code_numeral_1 code_c271388182l_size(code_S1047413653umeral(Code_numeral_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,code_c271388182l_size(Code_numeral_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_4092_code__numeral_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3904 (all Z_1 hAPP_complex_real(re,of_real_complex(Z_1)) = Z_1) # label(fact_4093_Re__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3905 (all X all Y hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X),Y) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_complex_real(re,X)),hAPP_complex_real(re,Y))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_complex_real(im,X)),hAPP_complex_real(im,Y)))) # label(fact_4094_complex__add__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3906 (all X all Y hAPP_complex_real(im,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(re,X)),hAPP_complex_real(im,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(im,X)),hAPP_complex_real(re,Y)))) # label(fact_4095_complex__Im__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3907 (all Code_numeral_5 all Code_numeral_4 (code_S1047413653umeral(Code_numeral_5) = code_S1047413653umeral(Code_numeral_4) <-> Code_numeral_5 = Code_numeral_4)) # label(fact_4096_code__numeral_Oinject) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3908 (all X_1 all Y_2 (X_1 = Y_2 <-> hAPP_complex_real(re,X_1) = hAPP_complex_real(re,Y_2) & hAPP_complex_real(im,X_1) = hAPP_complex_real(im,Y_2))) # label(fact_4097_complex__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3909 (all X all Y (hAPP_complex_real(re,X) = hAPP_complex_real(re,Y) -> (hAPP_complex_real(im,X) = hAPP_complex_real(im,Y) -> X = Y))) # label(fact_4098_complex__eqI) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3910 (all Z_1 hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_complex_real(re,Z_1)),hAPP_complex_real(im,Z_1)) = Z_1) # label(fact_4099_complex__surj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3911 (all X all Y hAPP_complex_real(re,hAPP_real_complex(hAPP_r265291036omplex(complex,X),Y)) = X) # label(fact_4100_Re) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3912 (all X all Y hAPP_complex_real(im,hAPP_real_complex(hAPP_r265291036omplex(complex,X),Y)) = Y) # label(fact_4101_Im) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3913 (all X all Y hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(re,X)),hAPP_complex_real(re,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(im,X)),hAPP_complex_real(im,Y)))) # label(fact_4102_complex__Re__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3914 (all X hAPP_complex_complex(uminus473333897omplex,X) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(uminus_uminus_real,hAPP_complex_real(re,X))),hAPP_real_real(uminus_uminus_real,hAPP_complex_real(im,X)))) # label(fact_4103_complex__minus__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3915 (all Z_1 hAPP_complex_complex(cnj,Z_1) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_complex_real(re,Z_1)),hAPP_real_real(uminus_uminus_real,hAPP_complex_real(im,Z_1)))) # label(fact_4104_cnj__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3916 (all X hAPP_complex_real(re,hAPP_complex_complex(cnj,X)) = hAPP_complex_real(re,X)) # label(fact_4105_complex__Re__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3917 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_complex_real(re,X)),hAPP_complex_real(norm_norm_complex,X)))) # label(fact_4106_complex__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3918 (all X hAPP_complex_real(im,hAPP_complex_complex(cnj,X)) = hAPP_real_real(uminus_uminus_real,hAPP_complex_real(im,X))) # label(fact_4107_complex__Im__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3919 (all Z_1 hAPP_complex_real(im,of_real_complex(Z_1)) = zero_zero_real) # label(fact_4109_Im__complex__of__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3920 (all Code_numeral_3 code_S1047413653umeral(Code_numeral_3) != zero_z126310315umeral) # label(fact_4111_code__numeral_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3921 (all Code_numeral_2 zero_z126310315umeral != code_S1047413653umeral(Code_numeral_2)) # label(fact_4112_code__numeral_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3922 (all X all Y hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_complex_real(re,X)),hAPP_complex_real(re,Y))) # label(fact_4116_Re_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3923 (all X all Y hAPP_complex_real(im,hAPP_complex_complex(hAPP_c172932010omplex(plus_plus_complex,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_complex_real(im,X)),hAPP_complex_real(im,Y))) # label(fact_4117_Im_Oadd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3924 (all V_2 hAPP_complex_real(im,hAPP_int_complex(number528085621omplex,V_2)) = zero_zero_real) # label(fact_4119_complex__Im__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3925 (all X hAPP_complex_real(re,hAPP_complex_complex(uminus473333897omplex,X)) = hAPP_real_real(uminus_uminus_real,hAPP_complex_real(re,X))) # label(fact_4120_Re_Ominus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3926 (all V_2 hAPP_complex_real(re,hAPP_int_complex(number528085621omplex,V_2)) = hAPP_int_real(number267125858f_real,V_2)) # label(fact_4121_complex__Re__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3927 (all X hAPP_complex_real(im,hAPP_complex_complex(uminus473333897omplex,X)) = hAPP_real_real(uminus_uminus_real,hAPP_complex_real(im,X))) # label(fact_4122_Im_Ominus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3928 (all X all Y hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_complex_real(re,X)),hAPP_complex_real(re,Y))) # label(fact_4123_Re_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3929 (all X all Y hAPP_complex_real(im,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_complex_real(im,X)),hAPP_complex_real(im,Y))) # label(fact_4124_Im_Odiff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3930 (all X all Y hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,X),Y) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(re,X)),hAPP_complex_real(re,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(im,X)),hAPP_complex_real(im,Y)))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(re,X)),hAPP_complex_real(im,Y))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(im,X)),hAPP_complex_real(re,Y))))) # label(fact_4125_complex__mult__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3931 (all N_1 hAPP_complex_real(im,hAPP_nat_complex(semiri2020571505omplex,N_1)) = zero_zero_real) # label(fact_4126_complex__Im__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3932 (all N_1 hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N_1)) = hAPP_nat_real(semiri132038758t_real,N_1)) # label(fact_4127_complex__Re__of__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3933 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_complex_real(re,X))),hAPP_complex_real(norm_norm_complex,X)))) # label(fact_4128_abs__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3934 (all X hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_complex_real(im,X))),hAPP_complex_real(norm_norm_complex,X)))) # label(fact_4129_abs__Im__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3935 (all Z_1 hAPP_complex_real(im,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1))) = zero_zero_real) # label(fact_4130_complex__In__mult__cnj__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3936 (all Z_1 hAPP_complex_real(re,hAPP_complex_complex(sgn_sgn_complex,Z_1)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_complex_real(re,Z_1)),hAPP_complex_real(norm_norm_complex,Z_1))) # label(fact_4131_Re__sgn) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3937 (all Z_1 hAPP_complex_real(im,hAPP_complex_complex(sgn_sgn_complex,Z_1)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_complex_real(im,Z_1)),hAPP_complex_real(norm_norm_complex,Z_1))) # label(fact_4132_Im__sgn) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3938 (all Z_1 hAPP_complex_real(norm_norm_complex,Z_1) = hAPP_real_real(sqrt,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(re,Z_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(im,Z_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_4133_cmod__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3939 (all X hAPP_complex_real(re,hAPP_complex_complex(invers1449016382omplex,X)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_complex_real(re,X)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(re,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(im,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_4134_complex__Re__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3940 (all N_1 hAPP_C498520661umeral(hAPP_C1594335432umeral(minus_1690775515umeral,code_S1047413653umeral(N_1)),one_on1645066479umeral) = N_1) # label(fact_4135_Suc__code__numeral__minus__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3941 (all X hAPP_complex_real(im,hAPP_complex_complex(invers1449016382omplex,X)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(uminus_uminus_real,hAPP_complex_real(im,X))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(re,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(im,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_4136_complex__Im__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3942 (all Z_1 hAPP_complex_real(norm_norm_complex,Z_1) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1))))) # label(fact_4137_complex__mod__sqrt__Re__mult__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3943 (all Z_1 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1)) = of_real_complex(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(re,Z_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(im,Z_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_4138_complex__mult__cnj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3944 (all X hAPP_complex_complex(invers1449016382omplex,X) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_complex_real(re,X)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(re,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(im,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(uminus_uminus_real,hAPP_complex_real(im,X))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(re,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_complex_real(im,X)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_4139_complex__inverse__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3945 (exists K_4 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),K_4)) & (all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(norm_norm_real,hAPP_complex_real(im,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))))) # label(fact_4140_Im_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3946 (exists K_4 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),K_4)) & (all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(norm_norm_real,hAPP_complex_real(re,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))))) # label(fact_4141_Re_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3947 (exists K_4 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),K_4)) & (all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(norm_norm_real,hAPP_complex_real(im,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))))) # label(fact_4142_Im_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3948 (exists K_4 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),K_4)) & (all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(norm_norm_real,hAPP_complex_real(re,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))))) # label(fact_4143_Re_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3949 (exists K_4 all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(norm_norm_real,hAPP_complex_real(im,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))) # label(fact_4144_Im_Obounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3950 (exists K_4 all X_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(norm_norm_real,hAPP_complex_real(re,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_complex_real(norm_norm_complex,X_2)),K_4)))) # label(fact_4145_Re_Obounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3951 (all Code_numeral_1 hAPP_C2129356693al_nat(size_s945831648umeral,code_S1047413653umeral(Code_numeral_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_C2129356693al_nat(size_s945831648umeral,Code_numeral_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_4146_code__numeral_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3952 (all Y (Y != zero_z126310315umeral -> -(all Code_numeral Y != code_S1047413653umeral(Code_numeral)))) # label(fact_4147_code__numeral_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3953 (all Z_1 expi(Z_1) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(hAPP_real_real(exp_real,hAPP_complex_real(re,Z_1)))),cis(hAPP_complex_real(im,Z_1)))) # label(fact_4148_expi__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3954 (all A_2 hAPP_complex_real(re,cis(A_2)) = hAPP_real_real(cos,A_2)) # label(fact_4149_Re__cis) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3955 (all A_2 hAPP_complex_real(im,cis(A_2)) = hAPP_real_real(sin,A_2)) # label(fact_4150_Im__cis) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3956 (all A_2 all B_1 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,cis(A_2)),cis(B_1)) = cis(hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_2),B_1))) # label(fact_4151_cis__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3957 (all A_2 hAPP_complex_complex(invers1449016382omplex,cis(A_2)) = cis(hAPP_real_real(uminus_uminus_real,A_2))) # label(fact_4153_cis__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3958 (all A_2 all B_1 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,cis(A_2)),cis(B_1)) = cis(hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_2),B_1))) # label(fact_4154_cis__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3959 (all A_2 cis(A_2) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(cos,A_2)),hAPP_real_real(sin,A_2))) # label(fact_4155_cis__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3960 (all A_2 all N_1 hAPP_nat_complex(hAPP_c1088319240omplex(power_power_complex,cis(A_2)),N_1) = cis(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),A_2))) # label(fact_4156_DeMoivre) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3961 (all N_1 all A_2 cis(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,hAPP_nat_nat(suc,N_1))),A_2)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,cis(A_2)),cis(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),A_2)))) # label(fact_4157_cis__real__of__nat__Suc__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3962 (all N_1 all A_2 hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),A_2)) = hAPP_complex_real(re,hAPP_nat_complex(hAPP_c1088319240omplex(power_power_complex,cis(A_2)),N_1))) # label(fact_4159_cos__n__Re__cis__pow__n) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3963 (all N_1 all A_2 hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),A_2)) = hAPP_complex_real(im,hAPP_nat_complex(hAPP_c1088319240omplex(power_power_complex,cis(A_2)),N_1))) # label(fact_4160_sin__n__Im__cis__pow__n) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3964 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M_1)) -> M_1 = zero_zero_nat | M_1 = N_1 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_1)),M_1)))) # label(fact_4161_divides__cases) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3965 (all X hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),X))) # label(fact_4162_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3966 (all K_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(suc,zero_zero_nat)),K_2))) # label(fact_4163_dvd__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3967 (all E_1 all B_1 all D_3 all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_3),A_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,E_1),B_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),E_1)))))) # label(fact_4164_coprime__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3968 (all N_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Y),N_1))))) # label(fact_4165_divides__exp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3969 (all A_2 -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),zero_zero_nat)))) # label(fact_4166_gcd__lcm__complete__lattice__nat_Onot__top__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3970 (all A_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),zero_zero_nat))) # label(fact_4167_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3971 (all Aa (Aa != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Aa),zero_zero_nat)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),Aa)))) # label(fact_4168_gcd__lcm__complete__lattice__nat_Oless__top) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3972 (all Aa (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),Aa)) <-> Aa = zero_zero_nat)) # label(fact_4169_gcd__lcm__complete__lattice__nat_Otop__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3973 (all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2)) -> A_2 = zero_zero_nat)) # label(fact_4170_gcd__lcm__complete__lattice__nat_Otop__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3974 (all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat)) -> A_2 = one_one_nat)) # label(fact_4171_gcd__lcm__complete__lattice__nat_Ole__bot) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3975 (all Aa (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Aa),one_one_nat)) <-> Aa = one_one_nat)) # label(fact_4172_gcd__lcm__complete__lattice__nat_Obot__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3976 (all Aa (Aa != one_one_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),Aa)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Aa),one_one_nat)))) # label(fact_4173_gcd__lcm__complete__lattice__nat_Obot__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3977 (all A_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A_2))) # label(fact_4174_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3978 (all A_2 -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A_2)))) # label(fact_4175_gcd__lcm__complete__lattice__nat_Onot__less__bot) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3979 (all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),one_one_nat)) <-> M = one_one_nat)) # label(fact_4176_nat__dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3980 (all C_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),C_1))))) # label(fact_4177_divides__mul__r) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3981 (all C_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_1),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,C_1),B_1))))) # label(fact_4178_divides__mul__l) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3982 (all B_1 all D_3 all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_3),A_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_3),B_1))))) # label(fact_4179_divides__add__revr) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3983 (all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N)))) # label(fact_4180_dvd__reduce) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3984 (all X -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),X)))) # label(fact_4181_dvd_Oless__irrefl) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3985 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)))) # label(fact_4182_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3986 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)) | X_1 = Y_2)) # label(fact_4183_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3987 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & X_1 != Y_2)) # label(fact_4184_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3988 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)))) # label(fact_4185_dvd_Oless__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3989 (all A_2 all B_1 (A_2 != B_1 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),A_2))))) # label(fact_4186_dvd_Oneq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3990 (all X all Y (X = Y -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)))) # label(fact_4187_dvd_Oeq__refl) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3991 (all Y_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_4188_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3992 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) | X = Y)) # label(fact_4189_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3993 (all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) -> (A_2 != B_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),A_2))))) # label(fact_4190_dvd_Ole__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3994 (all C_1 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),C_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),C_1))))) # label(fact_4191_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3995 (all C_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),C_1))))) # label(fact_4192_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3996 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M_1)) -> M_1 = N_1))) # label(fact_4193_dvd__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3997 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> X = Y))) # label(fact_4194_dvd_Oantisym) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3998 (all Z_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Z_1))))) # label(fact_4195_dvd_Oorder__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 3999 (all C_1 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),C_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C_1),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),C_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C_1),A_2))))) # label(fact_4196_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4000 (all Z_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),Z_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z_1),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Z_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z_1),X))))) # label(fact_4197_dvd_Ole__less__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4001 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> X != Y)) # label(fact_4198_dvd_Oless__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4002 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y))))) # label(fact_4199_dvd_Oless__not__sym) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4003 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)))) # label(fact_4200_dvd_Oless__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4004 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y))))) # label(fact_4201_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4005 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> X != Y)) # label(fact_4202_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4006 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> Y != X)) # label(fact_4203_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4007 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) -> hBOOL(P_1)))) # label(fact_4204_dvd_Oless__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4008 (all C_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),A_2)) -> (B_1 = C_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),C_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C_1),A_2))))) # label(fact_4205_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4009 (all Z_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Z_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z_1),X))))) # label(fact_4206_dvd_Oless__le__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4010 (all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),A_2)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),A_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1))))) # label(fact_4207_dvd_Oless__asym_H) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4011 (all Z_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),Z_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z_1),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Z_1)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z_1),X))))) # label(fact_4208_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4012 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y))))) # label(fact_4209_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4013 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_1)) <-> X_1 = Y_2)) # label(fact_4210_divides__antisym) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4014 (all N_1 all K_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)))))) # label(fact_4211_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4015 (all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),hAPP_nat_nat(suc,zero_zero_nat))) <-> M = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_4212_dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4016 (all N_1 all M_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,M_1),N_1)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M_1))))) # label(fact_4213_nat__dvd__not__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4017 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))))) # label(fact_4214_dvd__pos__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4018 (all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1)) -> B_1 = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_1)))) # label(fact_4215_divides__ge) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4019 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) | N_1 = zero_zero_nat)) # label(fact_4216_divides__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4020 (all M all K_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1))) <-> K_1 = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N)))) # label(fact_4217_nat__mult__dvd__cancel__disj_H) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4021 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) <-> K_1 = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N)))) # label(fact_4218_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4022 (all K_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),N_1)))))) # label(fact_4219_dvd__diffD1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4023 (all K_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),M_1)))))) # label(fact_4220_dvd__diffD) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4024 (all A_2 all N_1 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_2),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,B_1),N_1))) -> (N_1 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_1))))) # label(fact_4221_divides__rev) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4025 (all X all Y all N_1 (N_1 != zero_zero_nat -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N_1)),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y))))) # label(fact_4222_divides__exp2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4026 (all Aa all Ba all N (N != zero_zero_nat -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Aa),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Ba),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Aa),Ba))))) # label(fact_4223_pow__divides__eq__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4027 (all N_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Y),hAPP_nat_nat(suc,N_1)))))) # label(fact_4224_divides__rexp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4028 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(fact_fact_nat,N_1)),hAPP_nat_nat(fact_fact_nat,M_1))))) # label(fact_4225_fact__dvd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4029 (all N_1 all M_1 all R_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_1),R_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),R_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),R_3)))))) # label(fact_4226_divides__mul) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4030 (all D_3 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,D_3),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_3),B_1))))) # label(fact_4227_coprime__divprod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4031 (all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,Aa),Ba)) <-> (all D_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_2),Aa)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_2),Ba)) <-> D_2 = one_one_nat)))) # label(fact_4228_coprime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4032 (all K_2 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_1))))) # label(fact_4229_dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4033 (all K_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_1),N_1))))) # label(fact_4230_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4034 (all M all N all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N))))) # label(fact_4231_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4035 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_1),hAPP_nat_nat(fact_fact_nat,N_1)))))) # label(fact_4232_dvd__fact__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4036 (all X all Q_1 all N_1 all R_3 (X = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Q_1),N_1)),R_3) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),R_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,R_3),N_1)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),X)))))) # label(fact_4233_divides__div__not) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4037 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M)),M)) <-> N = one_one_nat))) # label(fact_4234_dvd__mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4038 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N)),M)) <-> N = one_one_nat))) # label(fact_4235_dvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4039 (all I all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,I),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,I),N_1))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),I)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))))) # label(fact_4236_power__dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4040 (all N (hBOOL(hAPP_nat_bool(even_odd_even_nat,N)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N)))) # label(fact_4237_even__dvd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4041 (all X_1 (hBOOL(hAPP_nat_bool(even_odd_even_nat,X_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1)))) # label(fact_4238_nat__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4042 (all N_1 all D_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),D_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_3),N_1)) -> hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,N_1),D_3)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(real_nat,N_1)),hAPP_nat_real(real_nat,D_3))))) # label(fact_4239_real__of__nat__div) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4043 (all N all N_5 all F ((all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,N)),hAPP_nat_nat(F,N_5)))))) # label(fact_4240_dvd_Olift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4044 (all N all M all F ((all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2)))) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2))),hAPP_nat_nat(F,N_2))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,N)),hAPP_nat_nat(F,M))) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))))) # label(fact_4241_dvd_Olift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4045 (all N all N_5 all F ((all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2)))) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2))),hAPP_nat_nat(F,N_2))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,N)),hAPP_nat_nat(F,N_5))) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(F,N_5)),hAPP_nat_nat(F,N)))))) # label(fact_4242_dvd_Olift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4046 (all D_3 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(abs_abs_int,D_3)),D_3))) # label(fact_4243_zdvd__self__abs2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4047 (all D_3 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D_3),hAPP_int_int(abs_abs_int,D_3)))) # label(fact_4244_zdvd__self__abs1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4048 (all N_1 all F_3 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F_3),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F_3),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F_3),hAPP_int_int(div_mod_int(M_1),N_1)))))) # label(fact_4245_zdvd__zmod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4049 (all K_2 all M_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),hAPP_int_int(div_mod_int(M_1),N_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),M_1))))) # label(fact_4246_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4050 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,B_1),A_2)) -> hAPP_int_int(abs_abs_int,A_2) = hAPP_int_int(abs_abs_int,B_1)))) # label(fact_4247_zdvd__antisym__abs) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4051 (all K_2 all M_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,M_1),N_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),M_1))))) # label(fact_4248_zdvd__zdiffD) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4052 (all D all T (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),T)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(uminus_uminus_int,D)),T)))) # label(fact_4249_uminus__dvd__conv_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4053 (all D all T (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),T)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(uminus_uminus_int,T))))) # label(fact_4250_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4054 (all N_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,M_1),N_1)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M_1))))) # label(fact_4251_zdvd__not__zless) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4055 (all N_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_1),N_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M_1)) -> M_1 = N_1))))) # label(fact_4252_zdvd__antisym__nonneg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4056 (all N_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M_1),zero_zero_int)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),M_1)))) # label(fact_4253_zdvd__bounds) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4057 (all M all T all K_1 (K_1 != zero_zero_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),T)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),M)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),T)))))) # label(fact_4254_zdvd__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4058 (all K_2 all M_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),N_1))) -> (K_2 != zero_zero_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_1),N_1))))) # label(fact_4255_zdvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4059 (all C all X_1 all T all Aa all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Aa),D)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_1),T))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),D))),T)))))) # label(fact_4256_zdvd__period) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4060 (all K_1 all N all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),M)))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),N)))) # label(fact_4257_zdvd__reduce) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4061 (all Aa all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),Aa)))) # label(fact_4258_zcong__zero__equiv__div) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4062 (all X_1 all Pa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X_1),zero_zero_int),Pa)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Pa),X_1)))) # label(fact_4259_zcong__eq__zdvd__prop) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4063 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)))) # label(fact_4260_Nat__Transfer_Otransfer__int__nat__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4064 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_2))))) # label(fact_4261_zdvd__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4065 (all A_2 all N_1 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),N_1))) -> (N_1 != zero_zero_nat -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),B_1))))) # label(fact_4262_pow__divides__pow__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4066 (all Aa all Ba all N (N != zero_zero_nat -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Aa),N)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Ba),N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Aa),Ba))))) # label(fact_4263_pow__divides__eq__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4067 (all N_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M_1)) -> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,N_1),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,M_1),N_1)) = M_1)) # label(fact_4264_zdvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4068 (all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_1),one_one_int)) <-> hAPP_int_int(abs_abs_int,X_1) = one_one_int)) # label(fact_4265_zdvd1__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4069 (all Aa all Ba all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba))))) # label(fact_4266_zcong__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4070 (all X_1 all N all Y_2 (hAPP_int_int(div_mod_int(X_1),N) = hAPP_int_int(div_mod_int(Y_2),N) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_1),Y_2))))) # label(fact_4267_zmod__eq__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4071 (all M_1 all N_1 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),M_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),N_1))))) # label(fact_4268_zprime__zdvd__zmult__better) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4072 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Y),X)) -> hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Y)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(abs_abs_int,X)),hAPP_int_int(abs_abs_int,Y)))) # label(fact_4269_abs__div) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4073 (all A_2 all N_1 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),A_2))))) # label(fact_4270_zprime__zdvd__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4074 (all Z_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Z_1),N_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),N_1))))) # label(fact_4271_zdvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4075 (all P_3 all Y all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),N_1)))))) # label(fact_4272_zpower__zdvd__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4076 (all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_1),B_1)) -> hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(A_2),B_1)),M_1) = hAPP_int_int(div_mod_int(A_2),M_1)))) # label(fact_4273_zmod__zdvd__zmod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4077 (all X_1 all Y_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(number_number_of_int,X_1)),hAPP_int_int(number_number_of_int,Y_2))) <-> hAPP_int_int(div_mod_int(hAPP_int_int(number_number_of_int,Y_2)),hAPP_int_int(number_number_of_int,X_1)) = zero_zero_int)) # label(fact_4274_zdvd__iff__zmod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4078 (all D_3 all I (I != zero_zero_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D_3),I)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(abs_abs_int,D_3)),hAPP_int_int(abs_abs_int,I)))))) # label(fact_4275_dvd__imp__le__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4079 (all N_1 all A_2 all B_1 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),B_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,P_3),N_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,P_3),N_1)),A_2)))))) # label(fact_4276_zprime__power__zdvd__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4080 (all N_1 all B_1 all A_2 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,P_3),N_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,P_3),N_1)),B_1)))))) # label(fact_4277_zprime__power__zdvd__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4081 (all Y_2 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_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_int_nat(nat,X_1)),hAPP_int_nat(nat,Y_2))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_1),Y_2)))))) # label(fact_4278_transfer__nat__int__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4082 (all N all M (M != zero_zero_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),N)),M)) <-> hAPP_int_int(abs_abs_int,N) = one_one_int))) # label(fact_4279_zdvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4083 (all N_1 all P_3 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_1)) -> (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),M_1)) | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),N_1)))))) # label(fact_4280_zprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4084 (all N_1 all D_3 (D_3 != zero_zero_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D_3),N_1)) -> hAPP_int_real(real_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,N_1),D_3)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(real_int,N_1)),hAPP_int_real(real_int,D_3))))) # label(fact_4281_real__of__int__div) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4085 (all Z_2 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Z_2),hAPP_nat_int(semiri1621563631at_int,M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,Z_2))),M)))) # label(fact_4282_dvd__int__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4086 (all M all Z_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(semiri1621563631at_int,M)),Z_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,Z_2)))))) # label(fact_4283_int__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4087 (all Y all N_1 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),N_1))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),Y)))))) # label(fact_4284_zpower__zdvd__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4088 (all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),Pa)) & (all M_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_2)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_2),Pa)) -> M_2 = one_one_int | M_2 = Pa)))) # label(fact_4285_zprime__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4089 (all X_1 (hBOOL(hAPP_int_bool(even_odd_even_int,X_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1)))) # label(fact_4286_int__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4090 (all Z_2 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_int_nat(nat,Z_2)),M)) <-> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Z_2),hAPP_nat_int(semiri1621563631at_int,M)))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z_2)) -> M = zero_zero_nat))) # label(fact_4287_nat__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4091 (all X all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,P_3),one_one_int)))),one_one_int),P_3))))) # label(fact_4288_Little__Fermat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4092 (all Y all X all P_3 (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X),zero_zero_int),P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Y),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X),P_3)) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),Y))))) # label(fact_4289_Euler_Oaux____1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4093 (all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) -> (exists P_4 (hBOOL(hAPP_int_bool(zprime,P_4)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_4),A_2)))))) # label(fact_4290_zprime__factor__exists) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4094 (all M_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),M_1))))) # label(fact_4291_prime__dvd__power__two) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4095 (all K_2 ((K_2 = zero_z891286103de_int -> quickcheck_int_of(K_2) = zero_zero_int) & (K_2 != zero_z891286103de_int -> (hAPP_Q1762011733de_int(div_mo231679042de_int(K_2),hAPP_i1732201573de_int(number1226105091de_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_z891286103de_int -> quickcheck_int_of(K_2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),quickcheck_int_of(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,K_2),hAPP_i1732201573de_int(number1226105091de_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) & (hAPP_Q1762011733de_int(div_mo231679042de_int(K_2),hAPP_i1732201573de_int(number1226105091de_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_z891286103de_int -> quickcheck_int_of(K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),quickcheck_int_of(hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,K_2),hAPP_i1732201573de_int(number1226105091de_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),one_one_int))))) # label(fact_4293_Quickcheck__Narrowing_Oint__of__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4096 (all Q_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(prime,Q_1)) -> (P_3 != Q_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,P_3),Q_1)))))) # label(fact_4294_distinct__prime__coprime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4097 (all N all M (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le258702272de_int,N),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,quickcheck_int_of(N)),quickcheck_int_of(M))))) # label(fact_4295_less__eq__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4098 (all N all M (hBOOL(hAPP_Q2096512830t_bool(hAPP_Q1010094925t_bool(ord_le1860547276de_int,N),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,quickcheck_int_of(N)),quickcheck_int_of(M))))) # label(fact_4296_less__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4099 (all K_2 quickcheck_int_of(hAPP_i1732201573de_int(number1226105091de_int,K_2)) = hAPP_int_int(number_number_of_int,K_2)) # label(fact_4299_int__of__number) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4100 (all X_1 all Y_2 (quickcheck_int_of(X_1) = quickcheck_int_of(Y_2) <-> X_1 = Y_2)) # label(fact_4300_code__int_Oint__of__inject) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4101 (all K_1 all L (quickcheck_int_of(K_1) = quickcheck_int_of(L) <-> K_1 = L)) # label(fact_4301_Quickcheck__Narrowing_Oint__of__inject) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4102 (all Q_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(prime,Q_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),Q_1)) -> P_3 = Q_1)))) # label(fact_4302_primes__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4103 (all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),P_3)))) # label(fact_4304_prime__g__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4104 (all Aa all Ba all Pa (hBOOL(hAPP_nat_bool(prime,Pa)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Pa),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Pa),Aa)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Pa),Ba))))) # label(fact_4305_prime__divprod__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4105 (all A_2 all B_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),A_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),B_1))))) # label(fact_4306_prime__divprod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4106 (all M_1 all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),M_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),N_1))))) # label(fact_4307_prime__dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4107 (all P_3 all Q_1 (hBOOL(hAPP_nat_bool(prime,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,P_3),Q_1))) -> P_3 = one_one_nat | Q_1 = one_one_nat)) # label(fact_4308_prime__product) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4108 (all A_2 all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_2),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),A_2))))) # label(fact_4309_prime__dvd__power) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4109 (all X all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),X))))) # label(fact_4310_prime__divexp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4110 (all X all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N_1)))))) # label(fact_4311_prime__divexp__n) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4111 (all Pa all N (hBOOL(hAPP_nat_bool(prime,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Pa),N))) <-> hBOOL(hAPP_nat_bool(prime,Pa)) & N = one_one_nat)) # label(fact_4312_prime__exp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4112 (all P_3 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),B_1)) -> -(hBOOL(hAPP_nat_bool(prime,P_3)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),A_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),B_1))))) # label(fact_4313_coprime__prime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4113 (all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,P_3),N_1)))) # label(fact_4314_prime__coprime__strong) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4114 (all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,Aa),Ba)) <-> (all P_4 -(hBOOL(hAPP_nat_bool(prime,P_4)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_4),Aa)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_4),Ba)))))) # label(fact_4315_coprime__prime__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4115 (all A_2 (hBOOL(hAPP_nat_bool(prime,A_2)) -> hBOOL(hAPP_int_bool(zprime,hAPP_nat_int(semiri1621563631at_int,A_2))))) # label(fact_4316_prime__impl__zprime__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4116 (all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),P_3)))) # label(fact_4318_prime__g__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4117 (all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(suc,zero_zero_nat))))) # label(fact_4319_prime__nd__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4118 (all M_1 all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (N_1 != zero_zero_nat -> (N_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,P_3),M_1) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))))) # label(fact_4320_prime__factor__lt) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4119 (all Pa (hBOOL(hAPP_nat_bool(prime,Pa)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),Pa)) & (all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_2),Pa)) -> M_2 = one_one_nat | M_2 = Pa)))) # label(fact_4321_prime__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4120 (all D all K_1 all Pa (hBOOL(hAPP_nat_bool(prime,Pa)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Pa),K_1))) <-> (exists I_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_1)) & D = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,Pa),I_2)))))) # label(fact_4322_divides__primepow) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4121 (all N_1 all A_2 all B_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),B_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),N_1)),A_2)))))) # label(fact_4323_prime__power__dvd__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4122 (all X all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),P_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,X),P_3)))))) # label(fact_4324_prime__coprime__lt) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4123 (all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> N_1 = one_one_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,P_3),N_1)))) # label(fact_4325_prime__coprime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4124 (all M_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),M_1))))) # label(fact_4327_prime__dvd__square) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4125 (all N_1 all A_2 all B_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),B_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),N_1)),A_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),N_1)),B_1)))))) # label(fact_4328_prime__divprod__pow) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4126 (all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),P_3)))) # label(fact_4329_prime__ge__2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4127 (all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> P_3 = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) | -hBOOL(hAPP_nat_bool(even_odd_even_nat,P_3)))) # label(fact_4330_prime__odd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4128 (all N_1 all M_1 quickc495462417de_int(N_1,M_1) = hAPP_Q1256397320de_int(hAPP_Q952608535de_int(produc1318306967de_int,hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,N_1),M_1)),hAPP_Q1762011733de_int(div_mo231679042de_int(N_1),M_1))) # label(fact_4331_div__mod__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4129 (all I quickcheck_nat_of(I) = hAPP_int_nat(nat,quickcheck_int_of(I))) # label(fact_4332_nat__of__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4130 (all X all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,X),Y)) -> (exists P_4 (hBOOL(hAPP_nat_bool(prime,P_4)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_4),X)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_4),Y)))))) # label(fact_4333_coprime__prime__dvd__ex) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4131 (all X all K_2 all N_1 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (N_1 != zero_zero_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),K_2) -> (exists I_2 X = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),I_2)))))) # label(fact_4334_prime__power__exp) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4132 (all N_1 (N_1 != one_one_nat -> (exists P_4 (hBOOL(hAPP_nat_bool(prime,P_4)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_4),N_1)))))) # label(fact_4335_prime__factor) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4133 (all A_2 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),A_2)) -> (exists X_2 exists Y_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),X_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,P_3),Y_1)),one_one_nat))))) # label(fact_4336_bezout__prime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4134 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) & -hBOOL(hAPP_nat_bool(prime,N_1)) -> (exists M_2 exists K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),K)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),N_1)) & N_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),K))))) # label(fact_4337_not__prime__ex__mk) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4135 (all N_1 exists P_4 (hBOOL(hAPP_nat_bool(prime,P_4)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),P_4)))) # label(fact_4338_euclid) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4136 (all P_1 all A0 (hBOOL(hAPP_int_bool(accp_int(quickc1265749348ro_rel),A0)) -> ((all I_2 (hBOOL(hAPP_int_bool(accp_int(quickc1265749348ro_rel),I_2)) -> ((-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),zero_zero_int)) -> (I_2 != zero_zero_int -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I_2),one_one_int))))) -> hBOOL(hAPP_int_bool(P_1,I_2))))) -> hBOOL(hAPP_int_bool(P_1,A0))))) # label(fact_4339_around__zero_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4137 (all R_3 all A_2 all N_1 hAPP_nat_complex(hAPP_c1088319240omplex(power_power_complex,rcis(R_3,A_2)),N_1) = rcis(hAPP_nat_real(hAPP_r474017924t_real(power_power_real,R_3),N_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N_1)),A_2))) # label(fact_4340_DeMoivre2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4138 (all X ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hAPP_int_int(fact_fact_int,X) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(fact_fact_nat,hAPP_int_nat(nat,X)))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hAPP_int_int(fact_fact_int,X) = zero_zero_int))) # label(fact_4341_fact__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4139 (all M_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M_1),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,M_1)),hAPP_int_int(fact_fact_int,N_1))))) # label(fact_4342_fact__mono__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4140 (all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,M_1),zero_zero_int)) -> hAPP_int_int(fact_fact_int,M_1) = zero_zero_int)) # label(fact_4344_fact__neg__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4141 (all N_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,M_1),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,M_1)),hAPP_int_int(fact_fact_int,N_1)))))) # label(fact_4345_fact__less__mono__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4142 (all M_1 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(fact_fact_int,M_1)))) # label(fact_4346_fact__ge__zero__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4143 (all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_1)) -> hAPP_int_int(fact_fact_int,N_1) != zero_zero_int)) # label(fact_4347_fact__nonzero__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4144 (all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(fact_fact_int,X))))) # label(fact_4348_transfer__nat__int__factorial__closure) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4145 (all X hAPP_int_int(fact_fact_int,hAPP_nat_int(semiri1621563631at_int,X)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(fact_fact_nat,X))) # label(fact_4350_transfer__int__nat__factorial) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4146 (all R_3 rcis(R_3,zero_zero_real) = of_real_complex(R_3)) # label(fact_4351_rcis__zero__arg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4147 (all R_3 all A_2 hAPP_complex_real(norm_norm_complex,rcis(R_3,A_2)) = hAPP_real_real(abs_abs_real,R_3)) # label(fact_4352_complex__mod__rcis) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4148 (all A_2 cis(A_2) = rcis(one_one_real,A_2)) # label(fact_4353_cis__rcis__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.81 4149 (all A_2 rcis(zero_zero_real,A_2) = zero_zero_complex) # label(fact_4354_rcis__zero__mod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4150 (all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(fact_fact_int,N_1))))) # label(fact_4355_fact__gt__zero__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4151 (all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N_1))))) # label(fact_4356_fact__ge__one__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4152 (all M_1 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,M_1)),hAPP_int_int(fact_fact_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_1),K_2)))))) # label(fact_4357_fact__mono__int__aux) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4153 (all N_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M_1),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_1),hAPP_int_int(fact_fact_int,N_1)))))) # label(fact_4358_dvd__fact__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4154 (all R_3 all A_2 hAPP_complex_real(re,rcis(R_3,A_2)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_real_real(cos,A_2))) # label(fact_4359_Re__rcis) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4155 (all R_3 all A_2 hAPP_complex_real(im,rcis(R_3,A_2)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_real_real(sin,A_2))) # label(fact_4360_Im__rcis) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4156 (all R1 all A_2 all R2 all B_1 hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,rcis(R1,A_2)),rcis(R2,B_1)) = rcis(hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R1),R2),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_2),B_1))) # label(fact_4361_rcis__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4157 (all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> hAPP_nat_nat(fact_fact_nat,hAPP_int_nat(nat,X)) = hAPP_int_nat(nat,hAPP_int_int(fact_fact_int,X)))) # label(fact_4362_transfer__nat__int__factorial) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4158 (all R1 all A_2 all R2 all B_1 hAPP_complex_complex(hAPP_c172932010omplex(invers1025623611omplex,rcis(R1,A_2)),rcis(R2,B_1)) = rcis(hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,R1),R2),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_2),B_1))) # label(fact_4363_rcis__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4159 (all R_3 all A_2 rcis(R_3,A_2) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,of_real_complex(R_3)),cis(A_2))) # label(fact_4364_rcis__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4160 (all M_1 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(fact_fact_int,M_1)),hAPP_int_int(fact_fact_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_1),one_one_int)),K_2))))))) # label(fact_4365_fact__less__mono__int__aux) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4161 (all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_1)) -> hAPP_int_int(fact_fact_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_1),one_one_int)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_1),one_one_int)),hAPP_int_int(fact_fact_int,N_1)))) # label(fact_4366_fact__plus__one__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4162 (all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> hAPP_int_int(fact_fact_int,N_1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,N_1),hAPP_int_int(fact_fact_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,N_1),one_one_int))))) # label(fact_4367_fact__reduce__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4163 (all R_3 all A_2 hAPP_complex_complex(invers1449016382omplex,rcis(R_3,A_2)) = rcis(hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),R_3),hAPP_real_real(uminus_uminus_real,A_2))) # label(fact_4368_rcis__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4164 (all I (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),I)) -> hAPP_list_int_nat(size_size_list_int,quickc666637781d_zero(I)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_int_nat(nat,I))),one_one_nat))) # label(fact_4369_length__around__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4165 (all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Pa)) -> hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(bnorRset(Aa),Pa)) = hAPP_int_nat(nat,Aa)))) # label(fact_4370_Bnor__prime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4166 (all Ba all Aa all M (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(bnorRset(Aa),M))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa)))) # label(fact_4371_Bnor__mem__zle) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4167 (all M all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) -> -hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(bnorRset(Aa),M))))) # label(fact_4372_Bnor__mem__zle__swap) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4168 (all Aa all M hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(bnorRset(Aa),M)))) # label(fact_4373_Bnor__fin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4169 (all Ba all Aa all M (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(bnorRset(Aa),M))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)))) # label(fact_4374_Bnor__mem__zg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4170 (all Aa all Ba all P_1 ((all A_1 all B_3 all C_3 (hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))) & hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,B_3),C_3))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),B_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_3),C_3)) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),C_3))))) -> ((all X_2 exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all A_1 all B_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),B_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_3),A_1)),D_2)) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))))))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,Aa),Ba))))))) # label(fact_4375_lemma__BOLZANO) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4171 (all P_1 ((all A_1 all B_3 all C_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),B_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_3),C_3)) & hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))) & hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,B_3),C_3))) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),C_3))))) & (all X_2 exists D_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D_2)) & (all A_1 all B_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),B_3)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,B_3),A_1)),D_2)) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))))))) -> (all A_1 all B_3 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_1),B_3)) -> hBOOL(hAPP_P1333854989l_bool(P_1,hAPP_r1195171167l_real(hAPP_r2019696015l_real(produc865579683l_real,A_1),B_3))))))) # label(fact_4376_lemma__BOLZANO2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4172 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_P1175774780nt_int(product_fst_int_int,bezw(X,Y))),hAPP_nat_int(semiri1621563631at_int,X))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_P1175774780nt_int(product_snd_int_int,bezw(X,Y))),hAPP_nat_int(semiri1621563631at_int,Y))) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y))) # label(fact_4377_bezw__aux) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4173 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)),N_1))) # label(fact_4378_gcd__dvd2__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4174 (all M_1 all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)),M_1))) # label(fact_4379_gcd__dvd1__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4175 (all M_1 all N_1 all K_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1)))) # label(fact_4380_gcd__dvd__prod__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4176 (all N_1 all M_1 all A_2 all B_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1) = one_one_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_2),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,B_1),M_1)) = one_one_nat)) # label(fact_4381_coprime__exp2__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4177 (all A_2 all B_1 (B_1 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),B_1)))) # label(fact_4382_gcd__le2__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4178 (all B_1 all A_2 (A_2 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),A_2)))) # label(fact_4383_gcd__le1__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4179 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),hAPP_nat_nat(suc,zero_zero_nat)) = hAPP_nat_nat(suc,zero_zero_nat)) # label(fact_4384_gcd__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4180 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M),N))) <-> M != zero_zero_nat | N != zero_zero_nat)) # label(fact_4385_gcd__pos__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4181 (all A_2 all N_1 all B_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_2),N_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,B_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),N_1)) # label(fact_4386_gcd__exp__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4182 (all A_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),A_2) = A_2) # label(fact_4387_gcd__semilattice__nat_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4183 (all X hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),X) = X) # label(fact_4388_gcd__idem__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4184 (all A_2 all B_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,B_1),A_2)) # label(fact_4389_gcd__commute__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4185 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),X)) # label(fact_4390_gcd__semilattice__nat_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4186 (all A_2 all B_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)) # label(fact_4391_gcd__semilattice__nat_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4187 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y)) # label(fact_4392_gcd__semilattice__nat_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4188 (all B_1 all A_2 all C_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,B_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),C_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,B_1),C_1))) # label(fact_4393_gcd__left__commute__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4189 (all X all Y all Z_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),Z_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Z_1))) # label(fact_4394_gcd__semilattice__nat_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4190 (all A_2 all B_1 all C_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),C_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,B_1),C_1))) # label(fact_4395_gcd__assoc__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4191 (all X all Y all Z_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y)),Z_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),Z_1))) # label(fact_4396_gcd__semilattice__nat_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4192 (all K_2 all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_1))) # label(fact_4397_gcd__mult__distrib__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4193 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)) # label(fact_4398_gcd__add1__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4194 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)) # label(fact_4399_gcd__add2__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4195 (all A_2 all B_1 all X (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1))))) # label(fact_4400_gcd__semilattice__nat_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4196 (all B_1 all A_2 all X (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),A_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),X)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1))))) # label(fact_4401_gcd__semilattice__nat_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4197 (all X all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1))) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),A_2)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),B_1))))) # label(fact_4402_gcd__semilattice__nat_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4198 (all K_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),N_1)))) # label(fact_4403_dvd__gcd__D2__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4199 (all K_2 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),M_1)))) # label(fact_4404_dvd__gcd__D1__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4200 (all B_1 all D_3 all A_2 all C_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),C_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),D_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,C_1),D_3)))))) # label(fact_4405_gcd__semilattice__nat_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4201 (all Z_1 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),Z_1)))))) # label(fact_4406_gcd__semilattice__nat_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4202 (all B_1 all X all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),A_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),B_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)))))) # label(fact_4407_gcd__semilattice__nat_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4203 (all N_1 all K_2 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)))))) # label(fact_4408_gcd__greatest__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4204 (all Y all X (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y),X)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = Y)) # label(fact_4409_gcd__proj2__if__dvd__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4205 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),Y)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = X)) # label(fact_4410_gcd__proj1__if__dvd__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4206 (all A_2 all B_1 all X (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_1),X)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),X)))) # label(fact_4411_gcd__semilattice__nat_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4207 (all B_1 all A_2 all X (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),X)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)),X)))) # label(fact_4412_gcd__semilattice__nat_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4208 (all Ba all D all Aa (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D),Aa)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D),Ba)) & (all E (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,E),Aa)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,E),Ba)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,E),D)))) <-> D = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Aa),Ba))) # label(fact_4413_gcd__unique__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4209 (all X_1 all Y_2 all Z_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y_2),Z_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z_2)))) # label(fact_4414_gcd__semilattice__nat_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4210 (all K_1 all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N)))) # label(fact_4415_gcd__greatest__iff__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4211 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_2)) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X_1),Y_2) = X_1)) # label(fact_4416_gcd__semilattice__nat_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4212 (all X all Y hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y)),Y))) # label(fact_4417_gcd__semilattice__nat_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4213 (all X all Y hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y)),X))) # label(fact_4418_gcd__semilattice__nat_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4214 (all X hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,one_one_nat),X) = one_one_nat) # label(fact_4419_gcd__lcm__complete__lattice__nat_Oinf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4215 (all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),one_one_nat) = one_one_nat) # label(fact_4420_gcd__1__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4216 (all X hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),one_one_nat) = one_one_nat) # label(fact_4421_gcd__lcm__complete__lattice__nat_Oinf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4217 (all X_1 all Y_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X_1),Y_2) = zero_zero_nat <-> X_1 = zero_zero_nat & Y_2 = zero_zero_nat)) # label(fact_4422_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4218 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M),N) = zero_zero_nat <-> M = zero_zero_nat & N = zero_zero_nat)) # label(fact_4423_gcd__zero__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4219 (all X hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),zero_zero_nat) = X) # label(fact_4424_gcd__0__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4220 (all X hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,zero_zero_nat),X) = X) # label(fact_4425_gcd__0__left__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4221 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),hAPP_nat_nat(div_mod_nat(X),Y))) # label(fact_4426_gcd__red__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4222 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(suc,N_1)),N_1) = one_one_nat) # label(fact_4427_coprime__Suc__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4223 (all M_1 all K_2 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1)) # label(fact_4428_gcd__add__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4224 (all X all A_2 all B_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1) = one_one_nat -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),A_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X),B_1)) -> X = one_one_nat)))) # label(fact_4429_coprime__common__divisor__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4225 (all Aa all Ba (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Aa),Ba) = one_one_nat <-> (all D_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_2),Aa)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_2),Ba)) <-> D_2 = one_one_nat)))) # label(fact_4430_coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4226 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)),N_1) = one_one_nat) # label(fact_4431_coprime__plus__one__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4227 (all D_3 all A_2 all B_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1)) = one_one_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),B_1) = one_one_nat)) # label(fact_4432_coprime__rmult__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4228 (all D_3 all A_2 all B_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1)) = one_one_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),A_2) = one_one_nat)) # label(fact_4433_coprime__lmult__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4229 (all Ba all C all Aa all D (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Aa),D) = one_one_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Ba),C) = one_one_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),C) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Ba),D) <-> Aa = Ba & C = D)))) # label(fact_4434_coprime__crossproduct__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4230 (all B_1 all D_3 all A_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),A_2) = one_one_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),B_1) = one_one_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1)) = one_one_nat))) # label(fact_4435_coprime__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4231 (all M_1 all K_2 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,K_2),N_1) = one_one_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1))) # label(fact_4436_gcd__mult__cancel__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4232 (all D all Aa all Ba (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Aa),Ba)) = one_one_nat <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D),Aa) = one_one_nat & hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D),Ba) = one_one_nat)) # label(fact_4437_coprime__mul__eq__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4233 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1))) # label(fact_4438_gcd__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4234 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M_1)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1))) # label(fact_4439_gcd__diff2__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4235 (all X all Y ((Y = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = X) & (Y != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),hAPP_nat_nat(div_mod_nat(X),Y))))) # label(fact_4440_gcd__nat_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4236 (all X all Y (Y != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Y),hAPP_nat_nat(div_mod_nat(X),Y)))) # label(fact_4441_gcd__non__0__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4237 (all N_1 all D_3 all A_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),A_2) = one_one_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,D_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_2),N_1)) = one_one_nat)) # label(fact_4442_coprime__exp__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4238 (all B_4 all A_4 all A_2 all B_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1) != zero_zero_nat -> (A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)) -> (B_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_4),B_4) = one_one_nat)))) # label(fact_4443_gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4239 (all N_1 (N_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)),N_1) = one_one_nat)) # label(fact_4444_coprime__minus__one__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4240 (all N_1 all M_1 all R_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M_1),R_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),R_3)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_1),N_1) = one_one_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1)),R_3)))))) # label(fact_4445_divides__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4241 (all M all K_1 all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,K_1),N) = one_one_nat -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M))))) # label(fact_4446_coprime__dvd__mult__iff__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4242 (all M_1 all K_2 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,K_2),N_1) = one_one_nat -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_2),M_1))))) # label(fact_4447_coprime__dvd__mult__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4243 (all B_1 all A_2 (A_2 != zero_zero_nat | B_1 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,A_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,B_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1))) = one_one_nat)) # label(fact_4448_div__gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4244 (all X all Y all M_1 (hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y)),M_1) = one_one_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),M_1) = one_one_nat)) # label(fact_4449_invertible__coprime__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4245 (all Aa all Ba (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,Aa),Ba) = one_one_nat <-> (all D_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_2),Aa)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_2),Ba)) <-> D_2 = hAPP_nat_nat(suc,zero_zero_nat))))) # label(fact_4450_coprime__Suc__0__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4246 (all A_2 all B_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1) != zero_zero_nat -> (exists A_3 exists B_2 (A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)) & B_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1)) & hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_3),B_2) = one_one_nat)))) # label(fact_4451_gcd__coprime__exists__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4247 (all B_1 all A_2 (A_2 != zero_zero_nat -> (exists X_2 exists Y_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),X_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,B_1),Y_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,A_2),B_1))))) # label(fact_4452_bezout__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4248 (all X_3 (hBOOL(cauchy_real(X_3)) <-> (all J_1 exists M_4 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),M_2)) -> (all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_nat_real(X_3,M_2)),hAPP_nat_real(X_3,N_2)))),hAPP_real_real(inverse_inverse_real,hAPP_nat_real(real_nat,hAPP_nat_nat(suc,J_1))))))))))) # label(fact_4453_Cauchy__iff2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4249 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(ln,X)),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),A_2)))))) # label(fact_4454_ln__powr__bound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4250 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(powr,hAPP_real_real(ln,X)),A_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(powr,A_2),A_2)),X)))))) # label(fact_4455_ln__powr__bound2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4251 (all A_2 hAPP_real_real(hAPP_r1250527377l_real(powr,one_one_real),A_2) = one_one_real) # label(fact_4456_powr__one__eq__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4252 (all X all A_2 hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2) != zero_zero_real) # label(fact_4457_powr__not__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4253 (all X all A_2 all B_1 hAPP_real_real(hAPP_r1250527377l_real(powr,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),B_1) = hAPP_real_real(hAPP_r1250527377l_real(powr,hAPP_real_real(hAPP_r1250527377l_real(powr,X),B_1)),A_2)) # label(fact_4458_powr__powr__swap) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4254 (all X all A_2 all B_1 hAPP_real_real(hAPP_r1250527377l_real(powr,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),B_1) = hAPP_real_real(hAPP_r1250527377l_real(powr,X),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_2),B_1))) # label(fact_4459_powr__powr) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4255 (all X all Y hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(powr,X),Y)))) # label(fact_4460_powr__ge__pzero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4256 (all Y all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),zero_zero_real)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(powr,Y),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2))))))) # label(fact_4461_powr__less__mono2__neg) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4257 (all Y all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,Y),A_2))))))) # label(fact_4462_powr__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4258 (all X all A_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)))) # label(fact_4463_powr__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4259 (all X all A_2 all B_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),B_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,X),B_1)))))) # label(fact_4464_powr__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4260 (all X hAPP_real_real(hAPP_r1250527377l_real(powr,X),zero_zero_real) = one_one_real) # label(fact_4465_powr__zero__eq__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4261 (all X all A_2 all B_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,X),B_1))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_1))))) # label(fact_4466_powr__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4262 (all X all A_2 all B_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,X),B_1)))))) # label(fact_4467_powr__less__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4263 (all Aa all Ba all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X_1),Aa)),hAPP_real_real(hAPP_r1250527377l_real(powr,X_1),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba))))) # label(fact_4468_powr__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4264 (all X all A_2 all B_1 hAPP_real_real(hAPP_r1250527377l_real(powr,X),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,A_2),B_1)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,X),B_1))) # label(fact_4469_powr__add) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4265 (all X all A_2 all B_1 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,X),B_1)) = hAPP_real_real(hAPP_r1250527377l_real(powr,X),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,A_2),B_1))) # label(fact_4470_powr__divide2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4266 (all X all A_2 hAPP_real_real(hAPP_r1250527377l_real(powr,X),hAPP_real_real(uminus_uminus_real,A_2)) = hAPP_real_real(inverse_inverse_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2))) # label(fact_4471_powr__minus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4267 (all Y all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X),Y)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,Y),A_2))))))) # label(fact_4472_powr__mono2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4268 (all A_2 all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(hAPP_r1250527377l_real(powr,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,X),Y)),A_2) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,Y),A_2))))) # label(fact_4473_powr__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4269 (all A_2 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)))))) # label(fact_4474_ge__one__powr__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4270 (all Aa all Ba all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X_1),Aa)),hAPP_real_real(hAPP_r1250527377l_real(powr,X_1),Ba))) <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba))))) # label(fact_4475_powr__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4271 (all X_1 (hAPP_real_real(hAPP_r1250527377l_real(powr,X_1),one_one_real) = X_1 <-> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)))) # label(fact_4476_powr__one__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4272 (all A_2 all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(hAPP_r1250527377l_real(powr,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,X),Y)),A_2) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2)),hAPP_real_real(hAPP_r1250527377l_real(powr,Y),A_2))))) # label(fact_4477_powr__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4273 (all X all A_2 hAPP_real_real(hAPP_r1250527377l_real(powr,X),hAPP_real_real(uminus_uminus_real,A_2)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2))) # label(fact_4478_powr__minus__divide) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4274 (all X all A_2 hAPP_real_real(hAPP_r1250527377l_real(powr,X),A_2) = hAPP_real_real(exp_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_2),hAPP_real_real(ln,X)))) # label(fact_4479_powr__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4275 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(hAPP_r1250527377l_real(powr,X),hAPP_nat_real(real_nat,N_1)) = hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1))) # label(fact_4480_powr__realpow) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4276 (all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) -> hAPP_real_real(ln,hAPP_real_real(hAPP_r1250527377l_real(powr,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y),hAPP_real_real(ln,X))))) # label(fact_4481_ln__powr) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4277 (all Y all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (A_2 != one_one_real -> hAPP_real_real(log(A_2),hAPP_real_real(hAPP_r1250527377l_real(powr,A_2),Y)) = Y))) # label(fact_4482_log__powr__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4278 (all X all A_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_2)) -> (A_2 != one_one_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> hAPP_real_real(hAPP_r1250527377l_real(powr,A_2),hAPP_real_real(log(A_2),X)) = X)))) # label(fact_4483_powr__log__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4279 (all B_1 all Y all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y)) -> hAPP_real_real(log(B_1),hAPP_real_real(hAPP_r1250527377l_real(powr,X),Y)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,Y),hAPP_real_real(log(B_1),X))))) # label(fact_4484_log__powr) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4280 (all N_1 all X (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) -> (X = zero_zero_real -> hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1) = zero_zero_real) & (X != zero_zero_real -> hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X),N_1) = hAPP_real_real(hAPP_r1250527377l_real(powr,X),hAPP_nat_real(real_nat,N_1)))))) # label(fact_4485_powr__realpow2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4281 (all C_1 all N_1 all A_2 all B_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(coprime,A_2),B_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_2),B_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,C_1),N_1) -> (exists R_1 exists S_3 (A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,R_1),N_1) & B_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,S_3),N_1)))))) # label(fact_4486_coprime__pow) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4282 (all X all Y all K_2 all P_3 (hBOOL(hAPP_nat_bool(prime,P_3)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),K_2) -> (exists I_2 exists J_1 (X = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),I_2) & Y = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,P_3),J_1)))))) # label(fact_4487_prime__power__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4283 (all X all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (hAPP_int_int(legacy_zgcd(X),M_1) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),phi(M_1))),one_one_int),M_1))))) # label(fact_4488_Euler__Fermat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4284 (all I all J_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(legacy_zgcd(I),J_2)),J_2))) # label(fact_4489_zgcd__zdvd2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4285 (all I all J_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(legacy_zgcd(I),J_2)),I))) # label(fact_4490_zgcd__zdvd1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4286 (all K_2 all M_1 all N_1 hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,K_2)),hAPP_int_int(legacy_zgcd(M_1),N_1))) # label(fact_4491_zgcd__zmult__distrib2__abs) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4287 (all I all J_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(legacy_zgcd(I),J_2)))) # label(fact_4492_zgcd__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4288 (all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_1)) -> hAPP_int_int(legacy_zgcd(M_1),M_1) = M_1)) # label(fact_4493_zgcd__self) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4289 (all X all Y hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(legacy_zgcd(X),Y)))) # label(fact_4494_zgcd__geq__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4290 (all M_1 hAPP_int_int(legacy_zgcd(M_1),zero_zero_int) = hAPP_int_int(abs_abs_int,M_1)) # label(fact_4495_zgcd__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4291 (all M_1 hAPP_int_int(legacy_zgcd(zero_zero_int),M_1) = hAPP_int_int(abs_abs_int,M_1)) # label(fact_4496_zgcd__0__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4292 (all M_1 all N_1 all K_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(legacy_zgcd(M_1),N_1)),hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),N_1)))) # label(fact_4497_zgcd__zdvd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4293 (all N_1 all A_2 all B_1 (hAPP_int_int(legacy_zgcd(A_2),B_1) = one_one_int -> hAPP_int_int(legacy_zgcd(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1)),B_1) = one_one_int)) # label(fact_4498_zgcd__1__power__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4294 (all N_1 all A_2 all B_1 (hAPP_int_int(legacy_zgcd(A_2),B_1) = one_one_int -> hAPP_int_int(legacy_zgcd(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),N_1)) = one_one_int)) # label(fact_4499_zgcd__1__power__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4295 (all A_2 all B_1 all N_1 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(legacy_zgcd(A_2),B_1)),N_1) = hAPP_int_int(legacy_zgcd(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),N_1))) # label(fact_4500_zgcd__power__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4296 (all I all J_2 hAPP_int_int(legacy_zgcd(I),J_2) = hAPP_int_int(legacy_zgcd(J_2),I)) # label(fact_4501_zgcd__commute) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4297 (all K_2 all M_1 all N_1 hAPP_int_int(legacy_zgcd(K_2),hAPP_int_int(legacy_zgcd(M_1),N_1)) = hAPP_int_int(legacy_zgcd(M_1),hAPP_int_int(legacy_zgcd(K_2),N_1))) # label(fact_4502_zgcd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4298 (all K_2 all M_1 all N_1 hAPP_int_int(legacy_zgcd(hAPP_int_int(legacy_zgcd(K_2),M_1)),N_1) = hAPP_int_int(legacy_zgcd(K_2),hAPP_int_int(legacy_zgcd(M_1),N_1))) # label(fact_4503_zgcd__assoc) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4299 (all I all J_2 hAPP_int_int(legacy_zgcd(I),hAPP_int_int(uminus_uminus_int,J_2)) = hAPP_int_int(legacy_zgcd(I),J_2)) # label(fact_4504_zgcd__zminus2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4300 (all I all J_2 hAPP_int_int(legacy_zgcd(hAPP_int_int(uminus_uminus_int,I)),J_2) = hAPP_int_int(legacy_zgcd(I),J_2)) # label(fact_4505_zgcd__zminus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4301 (all M_1 all N_1 all K_2 hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,N_1),K_2))),N_1) = hAPP_int_int(legacy_zgcd(M_1),N_1)) # label(fact_4506_zgcd__zadd__zmult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4302 (all N_1 all K_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),hAPP_int_int(legacy_zgcd(M_1),N_1)))))) # label(fact_4507_zgcd__greatest) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4303 (all K_1 all M all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(legacy_zgcd(M),N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),M)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),N)))) # label(fact_4508_zgcd__greatest__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4304 (all N_1 all K_2 all M_1 (hAPP_int_int(legacy_zgcd(K_2),M_1) = one_one_int -> (hAPP_int_int(legacy_zgcd(N_1),M_1) = one_one_int -> hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),N_1)),M_1) = one_one_int))) # label(fact_4509_zgcd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4305 (all M_1 all K_2 all N_1 (hAPP_int_int(legacy_zgcd(K_2),N_1) = one_one_int -> hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),N_1) = hAPP_int_int(legacy_zgcd(M_1),N_1))) # label(fact_4510_zgcd__zmult__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4306 (all M_1 hAPP_int_int(legacy_zgcd(M_1),one_one_int) = one_one_int) # label(fact_4511_zgcd__1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4307 (all M_1 hAPP_int_int(legacy_zgcd(one_one_int),M_1) = one_one_int) # label(fact_4512_zgcd__1__left) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4308 (all I_1 all J (hAPP_int_int(legacy_zgcd(I_1),J) = zero_zero_int <-> I_1 = zero_zero_int & J = zero_zero_int)) # label(fact_4513_zgcd0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4309 (all M_1 all N_1 hAPP_int_int(legacy_zgcd(M_1),N_1) = hAPP_int_int(legacy_zgcd(N_1),hAPP_int_int(div_mod_int(M_1),N_1))) # label(fact_4514_zgcd__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4310 (all N_1 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),N_1)),K_2) = K_2)) # label(fact_4515_zgcd__zmult__eq__self2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4311 (all M_1 all N_1 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),hAPP_int_int(legacy_zgcd(M_1),N_1)) = hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),N_1)))) # label(fact_4516_zgcd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4312 (all N_1 all K_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_2)) -> hAPP_int_int(legacy_zgcd(K_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),N_1)) = K_2)) # label(fact_4517_zgcd__zmult__eq__self) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4313 (all N all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),N)) <-> hAPP_int_int(legacy_zgcd(N),M) = M))) # label(fact_4518_zdvd__iff__zgcd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4314 (all M_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> hAPP_int_int(legacy_zgcd(M_1),N_1) = hAPP_int_int(legacy_zgcd(N_1),hAPP_int_int(div_mod_int(M_1),N_1)))) # label(fact_4519_zgcd__non__0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4315 (all B_1 all A_2 (A_2 != zero_zero_int | B_1 != zero_zero_int -> hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(legacy_zgcd(A_2),B_1))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),hAPP_int_int(legacy_zgcd(A_2),B_1))) = one_one_int)) # label(fact_4520_div__zgcd__relprime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4316 (all N_1 all A_2 all B_1 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),N_1)) -> (hAPP_int_int(legacy_zgcd(M_1),N_1) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1))))))) # label(fact_4521_zcong__zgcd__zmult__zmod) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4317 (all M (hAPP_int_int(legacy_zgcd(zero_zero_int),M) = one_one_int <-> hAPP_int_int(abs_abs_int,M) = one_one_int)) # label(fact_4522_zgcd__0__1__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4318 (all M_1 all K_2 all N_1 (hAPP_int_int(legacy_zgcd(K_2),N_1) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(legacy_zgcd(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),N_1)),hAPP_int_int(legacy_zgcd(M_1),N_1))))) # label(fact_4523_zgcd__zmult__zdvd__zgcd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4319 (all M_1 all N_1 all K_2 (hAPP_int_int(legacy_zgcd(N_1),K_2) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),M_1))))) # label(fact_4524_zrelprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4320 (all K_2 all I all J_2 (hAPP_int_int(legacy_zgcd(I),J_2) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,I),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),J_2))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,I),K_2))))) # label(fact_4525_zrelprime__dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4321 (all K_1 all L hAPP_int_int(legacy_zgcd(K_1),L) = hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,L),zero_zero_int)),K_1),hAPP_int_int(legacy_zgcd(L),hAPP_int_int(div_mod_int(hAPP_int_int(abs_abs_int,K_1)),hAPP_int_int(abs_abs_int,L)))))) # label(fact_4526_zgcd__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4322 (all N_1 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),N_1)) -> hAPP_int_int(legacy_zgcd(N_1),P_3) = one_one_int))) # label(fact_4527_zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4323 (all Aa all Ba (hAPP_int_int(legacy_zgcd(Aa),Ba) = one_one_int <-> -(exists P_4 (hBOOL(hAPP_int_bool(zprime,P_4)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_4),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_4),Ba)))))) # label(fact_4528_zgcd1__iff__no__common__primedivisor) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4324 (all B_1 all A_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M_1)) -> (hAPP_int_int(legacy_zgcd(A_2),M_1) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(A_2),B_1),M_1)) -> hAPP_int_int(legacy_zgcd(B_1),M_1) = one_one_int)))) # label(fact_4529_zgcd__zcong__zgcd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4325 (all N_1 all P_3 (hBOOL(hAPP_int_bool(zprime,P_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,N_1),P_3)) -> hAPP_int_int(legacy_zgcd(N_1),P_3) = one_one_int)))) # label(fact_4530_zless__zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4326 (all Aa all Ba all K_1 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M)) -> (hAPP_int_int(legacy_zgcd(K_1),M) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),Aa)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),Ba)),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)))))) # label(fact_4531_zcong__cancel2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4327 (all Aa all Ba all K_1 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M)) -> (hAPP_int_int(legacy_zgcd(K_1),M) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),K_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),K_1)),M)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)))))) # label(fact_4532_zcong__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4328 (all M_1 all N_1 all K_2 (hAPP_int_int(legacy_zgcd(N_1),K_2) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),M_1)))))) # label(fact_4533_zrelprime__zdvd__zmult__aux) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4329 (all Aa all Ba all M (hAPP_int_int(legacy_zgcd(Ba),M) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),hAPP_i1948725293t_bool(bnorRset(Aa),M))))))) # label(fact_4534_Bnor__mem__if) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4330 (all Aa all Ba all C all X_1 (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),Ba) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,C),hAPP_int_nat(nat,X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_int_nat(nat,X_1))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (hAPP_int_int(legacy_zgcd(Aa),Ba) = one_one_int -> (exists K Aa = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,K),hAPP_int_nat(nat,X_1)))))))) # label(fact_4535_int__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4331 (all M all K_1 all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N)) -> (hAPP_int_int(legacy_zgcd(M),N) = K_1 <-> (exists S_3 exists T_1 xzgcd(M,N) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,K_1),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,S_3),T_1)))))) # label(fact_4536_xzgcd__correct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4332 (all A_2 all B_1 all C_1 all N_1 (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,C_1),N_1) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_1)) -> (hAPP_int_int(legacy_zgcd(A_2),B_1) = one_one_int -> (exists K hAPP_int_int(abs_abs_int,A_2) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,K),N_1)))))) # label(fact_4537_int__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4333 (all M_1 all N_1 all R_5 all R_3 all S_4 all S_2 all T_3 all T_2 all K_2 ((exists Sn exists Tn xzgcda(M_1,N_1,R_5,R_3,S_4,S_2,T_3,T_2) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,K_2),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Sn),Tn))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),R_3)) -> hAPP_int_int(legacy_zgcd(R_5),R_3) = K_2))) # label(fact_4538_xzgcd__correct__aux2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4334 (all B_1 all A_2 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> (hAPP_int_int(legacy_zgcd(A_2),N_1) = one_one_int -> (exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),N_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),X_2)),B_1),N_1)) & (all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),N_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),Y_1)),B_1),N_1)) -> Y_1 = X_2))))))) # label(fact_4539_zcong__lineq__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4335 (all A_2 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> (hAPP_int_int(legacy_zgcd(A_2),N_1) = one_one_int -> (exists X_2 hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),X_2)),one_one_int),N_1)))))) # label(fact_4540_zcong__lineq__ex) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4336 (all M_1 all N_1 all S_4 all S_2 all T_3 all T_2 all R_5 all R_3 all K_2 (hAPP_int_int(legacy_zgcd(R_5),R_3) = K_2 -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),R_3)) -> (exists Sn exists Tn xzgcda(M_1,N_1,R_5,R_3,S_4,S_2,T_3,T_2) = hAPP_P408881810nt_int(hAPP_i1730167831nt_int(produc282740534nt_int,K_2),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Sn),Tn)))))) # label(fact_4541_xzgcd__correct__aux1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4337 (all Aa all Ba all C all D all X_1 (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),Ba)),C) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,D),hAPP_int_nat(nat,X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_int_nat(nat,X_1))) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),zOdd)) -> (hAPP_int_int(legacy_zgcd(Aa),Ba) = one_one_int -> (hAPP_int_int(legacy_zgcd(Ba),C) = one_one_int -> (hAPP_int_int(legacy_zgcd(C),Aa) = one_one_int -> (exists K exists L_1 exists M_2 (Aa = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,K),hAPP_int_nat(nat,X_1)) & Ba = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,L_1),hAPP_int_nat(nat,X_1)) & C = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,M_2),hAPP_int_nat(nat,X_1))))))))))) # label(fact_4542_int__triple__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4338 (all M_1 all K_2 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) -> (hAPP_int_int(legacy_zgcd(M_1),N_1) = K_2 -> (exists S_3 exists T_1 K_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,S_3),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,T_1),N_1)))))) # label(fact_4543_zgcd__ex__linear) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4339 (all A_2 all B_1 all C_1 all D_3 all N_1 (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)),C_1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,D_3),N_1) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),N_1)) -> (hAPP_int_int(legacy_zgcd(A_2),B_1) = one_one_int -> (hAPP_int_int(legacy_zgcd(B_1),C_1) = one_one_int -> (hAPP_int_int(legacy_zgcd(C_1),A_2) = one_one_int -> (exists K exists L_1 exists M_2 (hAPP_int_int(abs_abs_int,A_2) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,K),N_1) & hAPP_int_int(abs_abs_int,B_1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,L_1),N_1) & hAPP_int_int(abs_abs_int,C_1) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,M_2),N_1))))))))) # label(fact_4544_int__triple__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4340 (all B_1 all A_2 (A_2 != zero_zero_int | B_1 != zero_zero_int -> (exists C_3 exists D_2 (A_2 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(legacy_zgcd(A_2),B_1)),C_3) & B_1 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(legacy_zgcd(A_2),B_1)),D_2) & hAPP_int_int(legacy_zgcd(C_3),D_2) = one_one_int)))) # label(fact_4545_make__zrelprime) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4341 (all Y all X exists R_1 exists A_1 (X = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_1),hAPP_real_real(cos,A_1)) & Y = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_1),hAPP_real_real(sin,A_1)))) # label(fact_4546_polar__Ex) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4342 (all X all Y hAPP_real_real(dist_dist_real(X),Y) = hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X),Y))) # label(fact_4547_dist__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4343 (all X all Y hAPP_complex_real(dist_dist_complex(X),Y) = hAPP_complex_real(norm_norm_complex,hAPP_complex_complex(hAPP_c172932010omplex(minus_minus_complex,X),Y))) # label(fact_4548_dist__complex__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4344 (all Z_2 all P_1 ((all N_2 hBOOL(hAPP_int_bool(P_1,hAPP_nat_int(semiri1621563631at_int,N_2)))) -> ((all N_2 hBOOL(hAPP_int_bool(P_1,hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_2)))))) -> hBOOL(hAPP_int_bool(P_1,Z_2))))) # label(fact_4549_int__of__nat__induct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4345 (all Z_1 ((all N_2 Z_1 != hAPP_nat_int(semiri1621563631at_int,N_2)) -> -(all N_2 Z_1 != hAPP_int_int(uminus_uminus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_2)))))) # label(fact_4550_int__cases) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4346 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> (exists Y_1 (hBOOL(hAPP_real_bool(deriv_real(F,X_2),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_1)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(F,Aa)),hAPP_real_real(F,Ba)))))) # label(fact_4551_DERIV__nonneg__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4347 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> (exists Y_1 (hBOOL(hAPP_real_bool(deriv_real(F,X_2),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_1),zero_zero_real)))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(F,Ba)),hAPP_real_real(F,Aa)))))) # label(fact_4552_DERIV__nonpos__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4348 (all M all N all P_1 ((all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,M_2),zero_zero_nat))) -> ((all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_2),hAPP_nat_nat(div_mod_nat(M_2),N_2))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,M_2),N_2))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,M),N))))) # label(fact_4553_gcd__nat__induct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4349 (all N_1 all P_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),P_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,P_3),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,P_3),hAPP_nat_nat(fact,N_1)))))) # label(fact_4554_divides__fact) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4350 (all N_1 all M_1 hAPP_Q1762011733de_int(div_mo231679042de_int(N_1),M_1) = hAPP_i1732201573de_int(quickcheck_of_int,hAPP_int_int(div_mod_int(quickcheck_int_of(N_1)),quickcheck_int_of(M_1)))) # label(fact_4555_mod__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4351 (all N all M (hAPP_i1732201573de_int(quickcheck_of_int,N) = hAPP_i1732201573de_int(quickcheck_of_int,M) <-> N = M)) # label(fact_4556_Quickcheck__Narrowing_Oof__int__inject) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4352 (all X hAPP_i1732201573de_int(quickcheck_of_int,quickcheck_int_of(X)) = X) # label(fact_4557_int__of__inverse) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4353 (all K_2 hAPP_i1732201573de_int(quickcheck_of_int,quickcheck_int_of(K_2)) = K_2) # label(fact_4558_of__int__int__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4354 (all N_1 quickcheck_int_of(hAPP_i1732201573de_int(quickcheck_of_int,N_1)) = N_1) # label(fact_4559_int__of__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4355 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(fact,M_1)),hAPP_nat_nat(fact,N_1))))) # label(fact_4561_fact__mono) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4356 (all N_1 all M_1 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(times_123202395de_int,N_1),M_1) = hAPP_i1732201573de_int(quickcheck_of_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,quickcheck_int_of(N_1)),quickcheck_int_of(M_1)))) # label(fact_4562_times__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4357 (all N_1 all M_1 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(plus_p1446045655de_int,N_1),M_1) = hAPP_i1732201573de_int(quickcheck_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,quickcheck_int_of(N_1)),quickcheck_int_of(M_1)))) # label(fact_4563_plus__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4358 (all N_1 all M_1 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(minus_534354567de_int,N_1),M_1) = hAPP_i1732201573de_int(quickcheck_of_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,quickcheck_int_of(N_1)),quickcheck_int_of(M_1)))) # label(fact_4564_minus__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4359 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(fact,N_1)))) # label(fact_4566_fact__lt) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4360 (all N_1 hAPP_nat_nat(fact,hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,N_1)),hAPP_nat_nat(fact,N_1))) # label(fact_4568_fact_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4361 (all N_1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(fact,N_1)))) # label(fact_4569_fact__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4362 (all N_1 all M_1 hAPP_Q1762011733de_int(hAPP_Q1729056540de_int(div_di1430059507de_int,N_1),M_1) = hAPP_i1732201573de_int(quickcheck_of_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,quickcheck_int_of(N_1)),quickcheck_int_of(M_1)))) # label(fact_4571_div__code__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4363 (all N_1 exists P_4 (hBOOL(hAPP_nat_bool(prime,P_4)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),P_4)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,P_4),hAPP_nat_nat(suc,hAPP_nat_nat(fact,N_1)))))) # label(fact_4572_euclid__bound) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4364 (all F ((all I_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I_2))),hAPP_nat_nat(F,I_2)))) -> (exists I_2 all K hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)) = hAPP_nat_nat(F,I_2)))) # label(fact_4573_weak__decr__stable) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4365 (all P_1 all A0 all A1 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(norm_frac_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A0),A1))) -> ((all A_1 all B_3 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(norm_frac_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_1),B_3))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_3),zero_zero_int)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,hAPP_int_int(uminus_uminus_int,A_1)),hAPP_int_int(uminus_uminus_int,B_3)))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A_1),B_3))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A0),A1))))) # label(fact_4574_norm__frac_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4366 (all P_1 all A0 all A1 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(upto_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A0),A1))) -> ((all I_2 all J_1 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(upto_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,I_2),J_1))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),J_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)),J_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,I_2),J_1))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A0),A1))))) # label(fact_4575_upto_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4367 (all P_1 all A0 all A1 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(lazy_small_lazy_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A0),A1))) -> ((all D_2 all I_2 (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(lazy_small_lazy_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,D_2),I_2))) -> ((-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,D_2),I_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,D_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_2),one_one_int)))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,D_2),I_2))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(P_1,A0),A1))))) # label(fact_4576_small__lazy_H_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4368 (all M hAPP_i1948725293t_bool(norRRset,M) = hAPP_i1948725293t_bool(bnorRset(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,M),one_one_int)),M)) # label(fact_4577_norRRset__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4369 (all N_1 hAPP_int_int(ring_1_of_int_int,hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,N_1)) # label(fact_4578_of__int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4370 (all Z_1 hAPP_complex_complex(cnj,hAPP_int_complex(ring_11397209091omplex,Z_1)) = hAPP_int_complex(ring_11397209091omplex,Z_1)) # label(fact_4581_complex__cnj__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4371 (all Z_1 hAPP_complex_real(re,hAPP_int_complex(ring_11397209091omplex,Z_1)) = hAPP_int_real(ring_1_of_int_real,Z_1)) # label(fact_4582_complex__Re__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4372 (all W hAPP_int_complex(number528085621omplex,W) = hAPP_int_complex(ring_11397209091omplex,W)) # label(fact_4583_complex__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4373 (all W hAPP_int_int(number_number_of_int,W) = hAPP_int_int(ring_1_of_int_int,W)) # label(fact_4584_int__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4374 (all X hAPP_int_real(number267125858f_real,X) = hAPP_int_real(ring_1_of_int_real,X)) # label(fact_4585_number__of__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4375 (all Z_1 hAPP_complex_real(im,hAPP_int_complex(ring_11397209091omplex,Z_1)) = zero_zero_real) # label(fact_4586_complex__Im__of__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4376 (all M phi(M) = hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(norRRset,M))) # label(fact_4587_phi__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4377 (all Aa all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) -> (hAPP_int_int(legacy_zgcd(Aa),M) = one_one_int -> (exists X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),X_2),M)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),hAPP_i1948725293t_bool(norRRset,M))) & (all Y_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Y_1),M)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_1),hAPP_i1948725293t_bool(norRRset,M))) -> Y_1 = X_2))))))) # label(fact_4588_norR__mem__unique) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4378 (all X_1 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hAPP_int_int(legacy_zgcd(X_1),M) = one_one_int -> hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(noXRRset(M),X_1)) = hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(norRRset,M))))) # label(fact_4589_card__nor__eq__noX) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4379 (all X_1 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hAPP_int_int(legacy_zgcd(X_1),M) = one_one_int -> hBOOL(hAPP_int_bool(is_RRset(hAPP_i1948725293t_bool(noXRRset(M),X_1)),M))))) # label(fact_4590_noX__is__RRset) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4380 (all Aa all A all M (hBOOL(hAPP_int_bool(is_RRset(A),M)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) -> hAPP_int_int(legacy_zgcd(Aa),M) = one_one_int))) # label(fact_4591_RRset__gcd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4381 (all Aa all Ba all A all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) -> (hBOOL(hAPP_int_bool(is_RRset(A),M)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),Ba),M)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),A)) -> Aa = Ba)))))) # label(fact_4592_RRset__zcong__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4382 (all Aa all A all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) -> (hBOOL(hAPP_int_bool(is_RRset(A),M)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),hAPP_int_int(rRset2norRR(A,M),Aa)),M)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(rRset2norRR(A,M),Aa)),hAPP_i1948725293t_bool(norRRset,M))))))) # label(fact_4593_RRset2norRR__correct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4383 (all Aa all A all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) -> (hBOOL(hAPP_int_bool(is_RRset(A),M)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) -> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(rRset2norRR(A,M),Aa)),hAPP_i1948725293t_bool(norRRset,M))))))) # label(fact_4594_RRset2norRR__correct2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4384 (all Aa all A all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) -> (hBOOL(hAPP_int_bool(is_RRset(A),M)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),hAPP_int_int(rRset2norRR(A,M),Aa)),M)))))) # label(fact_4595_RRset2norRR__correct1) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4385 (all A all M (hBOOL(hAPP_int_bool(is_RRset(A),M)) <-> hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,A),rsetR(M))) & hAPP_f957591787ol_nat(finite_card_int,A) = phi(M))) # label(fact_4596_is__RRset__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4386 (all A all M (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,A),rsetR(M))) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)))) # label(fact_4597_RsetR__fin) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4387 (all Aa all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),M)) -> hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,hAPP_i1948725293t_bool(bnorRset(Aa),M)),rsetR(M))))) # label(fact_4598_Bnor__in__RsetR) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4388 (all A all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) -> (hBOOL(hAPP_int_bool(is_RRset(A),M)) -> image_int_int(rRset2norRR(A,M),A) = hAPP_i1948725293t_bool(norRRset,M)))) # label(fact_4599_RRset2norRR__eq__norR) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4389 (all X all Y hAPP_int_int(int_lcm(X),Y) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(nat_lcm(hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,X))),hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,Y))))) # label(fact_4600_Nitpick_Oint__lcm__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4390 (all F all A all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hBOOL(hAPP_f448129468l_bool(resSet(M),A)) -> ((all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) -> (all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),A)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(hAPP_int_int(F,X_2)),hAPP_int_int(F,Xa)),M)) -> X_2 = Xa))))) -> hBOOL(hAPP_f448129468l_bool(resSet(M),image_int_int(F,A))))))) # label(fact_4601_ResSet__image) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4391 (all A (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) <-> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,A))))) # label(fact_4602_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4392 (all A hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,A))) # label(fact_4603_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.82 4393 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X_1)),image_nat_int(semiri1621563631at_int,A))))) # label(fact_4604_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4394 (all A all B (A = B <-> image_nat_int(semiri1621563631at_int,A) = image_nat_int(semiri1621563631at_int,B))) # label(fact_4605_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4395 (all A image_int_nat(nat,image_nat_int(semiri1621563631at_int,A)) = A) # label(fact_4606_transfer__int__nat__set__return__embed) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4396 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))))) # label(fact_4607_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4397 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) <-> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))))) # label(fact_4608_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4398 (all Aa all Pa setS(Aa,Pa) = image_275383677t_bool(multInvPair(Aa,Pa),hAPP_i1948725293t_bool(sRStar,Pa))) # label(fact_4609_SetS__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4399 (all S (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S)) <-> (all M_2 exists N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,N_2),S)))))) # label(fact_4610_infinite__nat__iff__unbounded__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4400 (all S (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S)) <-> (all M_2 exists N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,N_2),S)))))) # label(fact_4611_infinite__nat__iff__unbounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4401 (all X all Y hAPP_nat_nat(nat_lcm(X),Y) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y)),hAPP_nat_nat(nat_gcd(X),Y))) # label(fact_4612_Nitpick_Onat__lcm__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4402 (all B all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> (hBOOL(hAPP_f448129468l_bool(nat_nat_set,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A),B)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,image_int_nat(nat,A)),image_int_nat(nat,B))))))) # label(fact_4613_transfer__int__nat__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4403 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y) = hAPP_nat_nat(nat_gcd(X),Y)) # label(fact_4614_gcd__eq__nitpick__gcd) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4404 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))))) # label(fact_4615_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4405 (all S (hBOOL(hAPP_f448129468l_bool(nat_nat_set,S)) <-> (all X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),S)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)))))) # label(fact_4616_nat__set__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4406 (all C_2 hBOOL(hAPP_f448129468l_bool(nat_nat_set,image_nat_int(semiri1621563631at_int,C_2)))) # label(fact_4617_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4407 (all B all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> (hBOOL(hAPP_f448129468l_bool(nat_nat_set,B)) -> (A = B <-> image_int_nat(nat,A) = image_int_nat(nat,B))))) # label(fact_4618_transfer__int__nat__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4408 (all X all Y ((Y = zero_zero_nat -> hAPP_nat_nat(nat_gcd(X),Y) = X) & (Y != zero_zero_nat -> hAPP_nat_nat(nat_gcd(X),Y) = hAPP_nat_nat(nat_gcd(Y),hAPP_nat_nat(div_mod_nat(X),Y))))) # label(fact_4619_nat__gcd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4409 (all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> image_nat_int(semiri1621563631at_int,image_int_nat(nat,A)) = A)) # label(fact_4620_transfer__nat__int__set__return__embed) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4410 (all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> (hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_int_nat(nat,A)))))) # label(fact_4621_transfer__int__nat__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4411 (all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> hAPP_f957591787ol_nat(finite_card_int,A) = hAPP_f22106695ol_nat(finite_card_nat,image_int_nat(nat,A)))) # label(fact_4622_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4412 (all B all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> (hBOOL(hAPP_f448129468l_bool(nat_nat_set,B)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_int_nat(nat,A)),image_int_nat(nat,B))))))) # label(fact_4623_transfer__int__nat__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4413 (all X_1 all Y_2 (hBOOL(hAPP_P1555980039t_bool(accp_P490777396at_nat(nat_gcd_rel),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_1),Y_2))) -> (Y_2 = zero_zero_nat -> hAPP_nat_nat(nat_gcd(X_1),Y_2) = X_1) & (Y_2 != zero_zero_nat -> hAPP_nat_nat(nat_gcd(X_1),Y_2) = hAPP_nat_nat(nat_gcd(Y_2),hAPP_nat_nat(div_mod_nat(X_1),Y_2))))) # label(fact_4624_nat__gcd_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4414 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(int_gcd,X),Y) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(nat_gcd(hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,X))),hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,Y))))) # label(fact_4625_Nitpick_Oint__gcd__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4415 (all P_1 all A0 all A1 (hBOOL(hAPP_P1555980039t_bool(accp_P490777396at_nat(nat_gcd_rel),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,A0),A1))) -> ((all X_2 all Y_1 (hBOOL(hAPP_P1555980039t_bool(accp_P490777396at_nat(nat_gcd_rel),hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,X_2),Y_1))) -> ((Y_1 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,Y_1),hAPP_nat_nat(div_mod_nat(X_2),Y_1)))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,X_2),Y_1))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,A0),A1))))) # label(fact_4626_nat__gcd_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4416 (all N_4 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_4)) <-> (exists M_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),M_2)))))) # label(fact_4627_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4417 (all N_4 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_4)) <-> (exists M_2 all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),M_2)))))) # label(fact_4628_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4418 (all N all N_4 ((all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),N)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_4)))) # label(fact_4629_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4419 (all L all U hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(ord_gr1297742076an_int(L),U)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,L),one_one_int)))) # label(fact_4630_card__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4420 (all L all U hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(ord_gr1297742076an_int(L),U)))) # label(fact_4631_finite__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4421 (all X_1 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_1),field_1210416355s_real)) -> -(all M_2 all N_2 (N_2 != zero_zero_nat -> (hAPP_real_real(abs_abs_real,X_1) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(real_nat,M_2)),hAPP_nat_real(real_nat,N_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,M_2),N_2) != one_one_nat))))) # label(fact_4632_Rats__abs__nat__div__natE) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4422 (all L all U hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U)))) # label(fact_4633_finite__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4423 (all N hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_nat_real(real_nat,N)),field_1210416355s_real))) # label(fact_4634_Rats__real__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4424 (all L all U hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U),hAPP_nat_nat(suc,L))) # label(fact_4635_card__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4425 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) -> (exists X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),field_1210416355s_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2))))))) # label(fact_4636_Rats__dense__in__nn__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4426 (all F all Y_2 all X_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) -> (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_1),hAPP_r1134773055l_bool(ord_gr788844697n_real(Aa),Ba))) -> (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Y_2),hAPP_r1134773055l_bool(ord_gr788844697n_real(Aa),Ba))) -> ((all X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),hAPP_r1134773055l_bool(ord_gr788844697n_real(Aa),Ba))) -> hBOOL(hAPP_real_bool(deriv_real(F,X_2),zero_zero_real)))) -> hAPP_real_real(F,X_1) = hAPP_real_real(F,Y_2)))))) # label(fact_4637_DERIV__isconst3) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4427 (all K_1 (hBOOL(hAPP_rat_bool(iszero_rat,hAPP_int_rat(number_number_of_rat,K_1))) <-> hBOOL(hAPP_int_bool(iszero_int,hAPP_int_int(number_number_of_int,K_1))))) # label(fact_4638_iszero__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4428 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_2)) -> (exists X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),field_1210416355s_real)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2)))))) # label(fact_4639_Rats__dense__in__real) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4429 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)) -> comple124823625p_real(hAPP_r1134773055l_bool(ord_gr788844697n_real(Y_2),X_1)) = X_1)) # label(fact_4640_Sup__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4430 (all X_1 all X_3 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_1),X_3)) -> ((exists Z all X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),X_3)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Z)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),comple124823625p_real(X_3)))))) # label(fact_4641_Sup__upper__EX) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4431 (all Z_2 all X_1 all X_3 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_1),X_3)) -> ((all X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),X_3)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Z_2)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),comple124823625p_real(X_3)))))) # label(fact_4642_SupInf_OSup__upper) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4432 (all K_2 frct(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,K_2)),one_one_int)) = hAPP_int_rat(number_number_of_rat,K_2)) # label(fact_4643_Frct__code__post_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4433 (all K_2 frct(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,K_2),zero_zero_int)) = zero_zero_rat) # label(fact_4644_Frct__code__post_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4434 (all K_2 frct(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),K_2)) = zero_zero_rat) # label(fact_4645_Frct__code__post_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4435 (all K_2 all L_2 frct(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,K_2)),hAPP_int_int(number_number_of_int,L_2))) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_int_rat(number_number_of_rat,K_2)),hAPP_int_rat(number_number_of_rat,L_2))) # label(fact_4647_Frct__code__post_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4436 (all K_2 frct(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,one_one_int),hAPP_int_int(number_number_of_int,K_2))) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,one_one_rat),hAPP_int_rat(number_number_of_rat,K_2))) # label(fact_4648_Frct__code__post_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4437 (all Z_2 all X_3 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,Z_2),X_3)) -> ((all X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),X_3)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Z_2)))) -> comple124823625p_real(X_3) = Z_2))) # label(fact_4649_Sup__eq__maximum) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4438 (all Z_2 all Y_2 all X_1 all X_3 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_1),X_3)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),X_1)) -> ((all X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),X_3)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Z_2)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),comple124823625p_real(X_3))))))) # label(fact_4650_SupInf_OSup__upper2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4439 (all Q_1 ((hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Q_1),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,Q_1) = hAPP_rat_rat(uminus_uminus_rat,Q_1)) & (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Q_1),zero_zero_rat)) -> hAPP_rat_rat(abs_abs_rat,Q_1) = Q_1))) # label(fact_4651_abs__rat__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4440 (all Q_1 ((Q_1 = zero_zero_rat -> hAPP_rat_rat(sgn_sgn_rat,Q_1) = zero_zero_rat) & (Q_1 != zero_zero_rat -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),Q_1)) -> hAPP_rat_rat(sgn_sgn_rat,Q_1) = one_one_rat) & (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),Q_1)) -> hAPP_rat_rat(sgn_sgn_rat,Q_1) = hAPP_rat_rat(uminus_uminus_rat,one_one_rat))))) # label(fact_4652_sgn__rat__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4441 (all Q_1 all R_3 hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,Q_1),R_3) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,Q_1),hAPP_rat_rat(inverse_inverse_rat,R_3))) # label(fact_4653_divide__rat__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4442 (all P_3 all Q_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Q_1),zero_zero_int)) -> normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1)) = normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(uminus_uminus_int,P_3)),hAPP_int_int(uminus_uminus_int,Q_1))))) # label(fact_4654_normalize__negative) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4443 (all P_3 quotient_of(hAPP_rat_rat(sgn_sgn_rat,P_3)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(sgn_sgn_int,hAPP_P1175774780nt_int(product_fst_int_int,quotient_of(P_3)))),one_one_int)) # label(fact_4655_rat__sgn__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4444 (all Q_1 all R_3 hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,Q_1),R_3) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,Q_1),hAPP_rat_rat(uminus_uminus_rat,R_3))) # label(fact_4656_diff__rat__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4445 (all Aa all Ba (quotient_of(Aa) = quotient_of(Ba) <-> Aa = Ba)) # label(fact_4657_quotient__of__inject__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4446 (all A_2 all B_1 (quotient_of(A_2) = quotient_of(B_1) -> A_2 = B_1)) # label(fact_4658_quotient__of__inject) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4447 (all Z_2 all W_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,Z_2),W_1)) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,Z_2),W_1)) & Z_2 != W_1)) # label(fact_4659_less__rat__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4448 (all R_3 all P_3 all Q_1 (quotient_of(R_3) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Q_1)))) # label(fact_4660_quotient__of__denom__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4449 (all R_3 all P_3 all Q_1 (normalize(R_3) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Q_1)))) # label(fact_4662_normalize__denom__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4450 (all P_3 normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),zero_zero_int)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),one_one_int)) # label(fact_4663_normalize__denom__zero) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4451 (all P_3 all R_3 all S_2 all Q_1 (Q_1 != zero_zero_int -> (S_2 != zero_zero_int -> (normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1)) = normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,R_3),S_2)) -> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,P_3),S_2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,R_3),Q_1))))) # label(fact_4664_normalize__crossproduct) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4452 (all K_2 quotient_of(hAPP_int_rat(number_number_of_rat,K_2)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(number_number_of_int,K_2)),one_one_int)) # label(fact_4666_quotient__of__number_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4453 (all R_3 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),R_3)) -> -(all S_3 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),S_3)) -> (all T_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),T_1)) -> R_3 != hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,S_3),T_1))))))) # label(fact_4667_obtain__pos__sum) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4454 (all X_1 all Y_2 (hBOOL(hAPP_f526364711l_bool(hAPP_P1062890741l_bool(member2143287562nt_int,hAPP_P230595783nt_int(hAPP_P941956607nt_int(produc883642259nt_int,X_1),Y_2)),ratrel)) <-> hAPP_P1175774780nt_int(product_snd_int_int,X_1) != zero_zero_int & hAPP_P1175774780nt_int(product_snd_int_int,Y_2) != zero_zero_int & hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_P1175774780nt_int(product_fst_int_int,X_1)),hAPP_P1175774780nt_int(product_snd_int_int,Y_2)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_P1175774780nt_int(product_fst_int_int,Y_2)),hAPP_P1175774780nt_int(product_snd_int_int,X_1)))) # label(fact_4668_ratrel__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4455 (all K_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,one_one_int),hAPP_int_int(number_number_of_int,K_2)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,one_one_rat),hAPP_int_rat(number_number_of_rat,K_2))) # label(fact_4669_Fract__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4456 (all R_3 all S_2 ratreal(hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_int_rat(number_number_of_rat,R_3)),hAPP_int_rat(number_number_of_rat,S_2))) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(number267125858f_real,R_3)),hAPP_int_real(number267125858f_real,S_2))) # label(fact_4670_Ratreal__number__of__quotient2) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4457 (all A_2 all B_1 all P_3 all Q_1 (quotient_of(hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1) -> hAPP_int_rat(hAPP_int_fun_int_rat(fract,P_3),Q_1) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1))) # label(fact_4671_quotient__of__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4458 (all A_2 all B_1 hAPP_rat_rat(uminus_uminus_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(uminus_uminus_int,A_2)),B_1)) # label(fact_4672_minus__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4459 (all A_2 all B_1 all C_1 all D_3 hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)),hAPP_int_rat(hAPP_int_fun_int_rat(fract,C_1),D_3)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),D_3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),C_1))) # label(fact_4673_divide__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4460 (all K_2 all L_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,K_2),L_2) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_int_rat(ring_1_of_int_rat,K_2)),hAPP_int_rat(ring_1_of_int_rat,L_2))) # label(fact_4674_Fract__of__int__quotient) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4461 (all K_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,K_2),one_one_int) = hAPP_int_rat(ring_1_of_int_rat,K_2)) # label(fact_4675_Fract__of__int__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4462 (all K_2 hAPP_int_rat(ring_1_of_int_rat,K_2) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,K_2),one_one_int)) # label(fact_4676_of__int__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4463 (all K_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,zero_zero_int),K_2) = zero_zero_rat) # label(fact_4677_rat__number__collapse_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4464 (all A_2 all C_1 hAPP_int_rat(hAPP_int_fun_int_rat(fract,zero_zero_int),A_2) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,zero_zero_int),C_1)) # label(fact_4678_eq__rat_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4465 (all K_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,K_2),zero_zero_int) = zero_zero_rat) # label(fact_4679_rat__number__collapse_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4466 (all A_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),zero_zero_int) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,zero_zero_int),one_one_int)) # label(fact_4682_eq__rat_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4467 (all K_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_nat_int(semiri1621563631at_int,K_2)),one_one_int) = hAPP_nat_rat(semiri151668891at_rat,K_2)) # label(fact_4683_Fract__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4468 (all K_2 hAPP_nat_rat(semiri151668891at_rat,K_2) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_nat_int(semiri1621563631at_int,K_2)),one_one_int)) # label(fact_4684_of__nat__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4469 (all W hAPP_int_rat(number_number_of_rat,W) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,W),one_one_int)) # label(fact_4685_rat__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4470 (all X archim1246769320r_real(ratreal(X)) = archim791455193or_rat(X)) # label(fact_4686_real__floor__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4471 (all A_2 all B_1 archim791455193or_rat(hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) = hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)) # label(fact_4687_floor__Fract) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4472 (all A_2 all B_1 hAPP_rat_rat(inverse_inverse_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,B_1),A_2)) # label(fact_4688_inverse__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4473 (all A_2 all B_1 hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(uminus_uminus_int,A_2)),hAPP_int_int(uminus_uminus_int,B_1)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) # label(fact_4689_minus__rat__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4474 (all A_2 all B_1 all C_1 (C_1 != zero_zero_int -> hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_1),A_2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_1),B_1)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1))) # label(fact_4690_mult__rat__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4475 (all Aa all C all D all Ba (Ba != zero_zero_int -> (D != zero_zero_int -> (hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,C),D) <-> hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),D) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba))))) # label(fact_4691_eq__rat_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4476 (all A_2 all B_1 all C_1 all D_3 hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)),hAPP_int_rat(hAPP_int_fun_int_rat(fract,C_1),D_3)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),C_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),D_3))) # label(fact_4692_mult__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4477 (all A_2 all B_1 hAPP_rat_rat(abs_abs_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(abs_abs_int,A_2)),hAPP_int_int(abs_abs_int,B_1))) # label(fact_4693_abs__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4478 (all A_2 all B_1 all P_3 all Q_1 (normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_2),B_1)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1) -> hAPP_int_rat(hAPP_int_fun_int_rat(fract,P_3),Q_1) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1))) # label(fact_4694_normalize__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4479 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,ratreal(X_1)),ratreal(Y_2))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,X_1),Y_2)))) # label(fact_4695_real__less__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4480 (all K_2 hAPP_int_real(number267125858f_real,K_2) = ratreal(hAPP_int_rat(number_number_of_rat,K_2))) # label(fact_4698_number__of__real__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4481 (all K_2 ratreal(hAPP_int_rat(number_number_of_rat,K_2)) = hAPP_int_real(number267125858f_real,K_2)) # label(fact_4699_Ratreal__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4482 (all X_1 all Y_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,ratreal(X_1)),ratreal(Y_2))) <-> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,X_1),Y_2)))) # label(fact_4702_real__less__eq__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4483 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,ratreal(X)),ratreal(Y)) = ratreal(hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,X),Y))) # label(fact_4703_real__plus__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4484 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,ratreal(X)),ratreal(Y)) = ratreal(hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,X),Y))) # label(fact_4704_real__minus__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4485 (all X hAPP_real_real(uminus_uminus_real,ratreal(X)) = ratreal(hAPP_rat_rat(uminus_uminus_rat,X))) # label(fact_4705_real__uminus__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4486 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,ratreal(X)),ratreal(Y)) = ratreal(hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,X),Y))) # label(fact_4706_real__divide__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4487 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(times_times_real,ratreal(X)),ratreal(Y)) = ratreal(hAPP_rat_rat(hAPP_rat_fun_rat_rat(times_times_rat,X),Y))) # label(fact_4707_real__times__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4488 (all X hAPP_real_real(inverse_inverse_real,ratreal(X)) = ratreal(hAPP_rat_rat(inverse_inverse_rat,X))) # label(fact_4708_real__inverse__code) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4489 (all K_2 hAPP_int_rat(number_number_of_rat,K_2) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(number_number_of_int,K_2)),one_one_int)) # label(fact_4710_rat__number__expand_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4490 (all K_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(number_number_of_int,K_2)),one_one_int) = hAPP_int_rat(number_number_of_rat,K_2)) # label(fact_4711_rat__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4491 (all K_2 all L_2 hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(number_number_of_int,K_2)),hAPP_int_int(number_number_of_int,L_2)) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(inverse_divide_rat,hAPP_int_rat(number_number_of_rat,K_2)),hAPP_int_rat(number_number_of_rat,L_2))) # label(fact_4712_Fract__number__of__quotient) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4492 (all A_2 all B_1 quotient_of(hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) = normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,A_2),B_1))) # label(fact_4713_quotient__of__Fract) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4493 (all P_3 frct(P_3) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_P1175774780nt_int(product_fst_int_int,P_3)),hAPP_P1175774780nt_int(product_snd_int_int,P_3))) # label(fact_4714_Frct__def) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4494 (all Aa all C all D all Ba (Ba != zero_zero_int -> (D != zero_zero_int -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba)),hAPP_int_rat(hAPP_int_fun_int_rat(fract,C),D))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),D)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),D))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),D)))))))) # label(fact_4715_less__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4495 (all R_3 all S_2 hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,ratreal(hAPP_int_rat(number_number_of_rat,R_3))),ratreal(hAPP_int_rat(number_number_of_rat,S_2))) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_int_real(number267125858f_real,R_3)),hAPP_int_real(number267125858f_real,S_2))) # label(fact_4716_Ratreal__number__of__quotient) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4496 (all A_2 all B_1 hAPP_rat_rat(sgn_sgn_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) = hAPP_int_rat(ring_1_of_int_rat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(sgn_sgn_int,A_2)),hAPP_int_int(sgn_sgn_int,B_1)))) # label(fact_4717_sgn__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4497 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba)),zero_zero_rat)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int))))) # label(fact_4718_Fract__less__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4498 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa))))) # label(fact_4719_zero__less__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4499 (all Aa all C all D all Ba (Ba != zero_zero_int -> (D != zero_zero_int -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba)),hAPP_int_rat(hAPP_int_fun_int_rat(fract,C),D))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),D)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),D))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C),Ba)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Ba),D)))))))) # label(fact_4720_le__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4500 (all A_2 all C_1 all D_3 all B_1 (B_1 != zero_zero_int -> (D_3 != zero_zero_int -> hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)),hAPP_int_rat(hAPP_int_fun_int_rat(fract,C_1),D_3)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),D_3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_1),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),D_3))))) # label(fact_4721_add__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4501 (all A_2 all C_1 all D_3 all B_1 (B_1 != zero_zero_int -> (D_3 != zero_zero_int -> hAPP_rat_rat(hAPP_rat_fun_rat_rat(minus_minus_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)),hAPP_int_rat(hAPP_int_fun_int_rat(fract,C_1),D_3)) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),D_3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,C_1),B_1))),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),D_3))))) # label(fact_4722_diff__rat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4502 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,one_one_rat),hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),Aa))))) # label(fact_4723_one__less__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4503 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba)),one_one_rat)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba))))) # label(fact_4724_Fract__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4504 (all M_1 all N_1 (N_1 != zero_zero_int -> hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_1),N_1)),N_1) = hAPP_rat_rat(hAPP_rat_fun_rat_rat(plus_plus_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,M_1),N_1)),one_one_rat))) # label(fact_4725_Fract__add__one) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4505 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba)),zero_zero_rat)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),zero_zero_int))))) # label(fact_4726_Fract__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4506 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,zero_zero_rat),hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Aa))))) # label(fact_4727_zero__le__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4507 (all A_2 all B_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(ring_1_of_int_rat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1))),hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1))) & hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)),hAPP_int_rat(ring_1_of_int_rat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),B_1)),one_one_int)))))) # label(fact_4728_rat__floor__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4508 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,one_one_rat),hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Ba),Aa))))) # label(fact_4729_one__le__Fract__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4509 (all Aa all Ba (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(hAPP_int_fun_int_rat(fract,Aa),Ba)),one_one_rat)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Aa),Ba))))) # label(fact_4730_Fract__le__one__iff) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4510 (all Qa all P_1 ((all A_1 all B_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_3)) -> hBOOL(hAPP_rat_bool(P_1,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_1),B_3))))) -> hBOOL(hAPP_rat_bool(P_1,Qa)))) # label(fact_4731_Rat__induct__pos) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4511 (all Ba all Qa all R_2 hAPP_P1975530577nt_int(adjust(Ba),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Qa),R_2)) = hAPP_P1975530577nt_int(hAPP_P1145851913nt_int(hAPP_b40753821nt_int(if_Pro1731782967nt_int,hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,R_2),Ba))),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Qa)),one_one_int)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,R_2),Ba))),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Qa)),R_2))) # label(fact_4732_adjust__eq) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4512 (all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,plus_plus_real),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,plus_plus_real),hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,sin),uminus_uminus_real))),sin))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,minus_minus_real),hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,cos),uminus_uminus_real))),cos))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X_2),zero_zero_real))) # label(fact_4733_lemma__DERIV__sin__cos__minus) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4513 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K_1))))) # label(fact_4734_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4514 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K_1))))) # label(fact_4735_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4515 (all P_1 collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),P_1)) = image_nat_int(semiri1621563631at_int,collect_nat(hAPP_f1154658180t_bool(hAPP_f1361476881t_bool(cOMBB_int_bool_nat,P_1),semiri1621563631at_int)))) # label(fact_4737_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4516 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_f957591787ol_nat(finite_card_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_eq_int),N))))) = N)) # label(fact_4738_int__card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4517 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N)) -> hAPP_f957591787ol_nat(finite_card_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),N)))) = hAPP_int_nat(nat,N))) # label(fact_4739_card__bdd__int__set__l) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4518 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N)) -> hAPP_f957591787ol_nat(finite_card_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_eq_int),N)))) = hAPP_int_nat(nat,N))) # label(fact_4740_card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4519 (all N hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_eq_int),N)))))) # label(fact_4741_bdd__int__set__l__le__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4520 (all N hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),N)))))) # label(fact_4742_bdd__int__set__l__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4521 (all K_1 all Xa_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,cos),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,plus_plus_real),K_1)),Xa_1),hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Xa_1),K_1)))))) # label(fact_4743_DERIV__cos__add) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4522 (all X_2 hAPP_n1699378549t_bool(ord_less_nat,X_2) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_2))) # label(fact_4744_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4523 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),sin)),sin),X_1),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X_1)),hAPP_real_real(sin,X_1))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X_1)),hAPP_real_real(sin,X_1)))))) # label(fact_4745_DERIV__sin__sin__mult) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4524 (all K_1 all Xa_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,sin),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,plus_plus_real),K_1)),Xa_1),hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,Xa_1),K_1))))) # label(fact_4746_DERIV__sin__add) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4525 (all X_1 hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X_1))) = hAPP_nat_nat(suc,X_1)) # label(fact_4747_card__bdd__nat__set__le) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4526 (all N hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),N))) = hAPP_nat_nat(suc,N)) # label(fact_4748_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4527 (all X_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),X_1))))) # label(fact_4749_bdd__nat__set__le__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4528 (all W hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,W)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,W)),hAPP_int_nat(number_number_of_nat,W))) # label(fact_4750_nat__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4529 (all P_1 hBOOL(hAPP_f448129468l_bool(nat_nat_set,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),P_1))))) # label(fact_4751_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4530 (all P_1 collect_nat(P_1) = image_int_nat(nat,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_f1448486952t_bool(hAPP_f696844121t_bool(cOMBB_nat_bool_int,P_1),nat))))) # label(fact_4752_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4531 (all N hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_eq_int),N)))))) # label(fact_4753_bdd__int__set__le__finite) # label(axiom) # label(non_clause). [assumption].
% 4.76/4.83 4532 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),one_one_real)) -> hBOOL(bseq_real(hAPP_r474017924t_real(power_power_real,X_1)))))) # label(fact_4754_Bseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4533 (all Z_2 all Z_3 ((hBOOL(hAPP_int_bool(nat_neg,Z_3)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(nat,Z_2)),hAPP_int_nat(nat,Z_3)) = hAPP_int_nat(nat,Z_2)) & (-hBOOL(hAPP_int_bool(nat_neg,Z_3)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(nat,Z_2)),hAPP_int_nat(nat,Z_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_2),Z_3))),zero_zero_nat),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_2),Z_3)))))) # label(fact_4755_diff__nat__eq__if) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4534 (all M (M != zero_zero_nat -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,dvd_dvd_nat),M)))))) # label(fact_4756_finite__divisors__nat) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4535 (all I_1 (I_1 != zero_zero_int -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,dvd_dvd_int),I_1)))))) # label(fact_4757_finite__divisors__int) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4536 (all X_3 (hBOOL(cauchy_complex(X_3)) -> hBOOL(cauchy_complex(hAPP_f1646117269omplex(hAPP_f1457396693omplex(cOMBB_117013006ex_nat,cnj),X_3))))) # label(fact_4759_cnj_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4537 (all X_3 (hBOOL(cauchy_complex(X_3)) -> hBOOL(cauchy_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,re),X_3))))) # label(fact_4760_Re_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4538 (all X_3 (hBOOL(cauchy_complex(X_3)) -> hBOOL(cauchy_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,im),X_3))))) # label(fact_4761_Im_OCauchy) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4539 (all G all X_1 all M (hBOOL(hAPP_real_bool(deriv_real(G,X_1),M)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,cos),G),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,hAPP_real_real(G,X_1)))),M))))) # label(fact_4762_DERIV__fun__cos) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4540 (all G all X_1 all M (hBOOL(hAPP_real_bool(deriv_real(G,X_1),M)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,sin),G),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,hAPP_real_real(G,X_1))),M))))) # label(fact_4763_DERIV__fun__sin) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4541 (all N hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),N))) = N) # label(fact_4764_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4542 (all X_1 hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X_1))) = X_1) # label(fact_4765_card__bdd__nat__set__l) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4543 (all X_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),X_1))))) # label(fact_4766_bdd__nat__set__l__finite) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4544 (all P_1 all I_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),P_1)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))))) # label(fact_4767_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4545 (all Z_1 all W hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,W))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),hAPP_int_nat(number_number_of_nat,W))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),hAPP_int_nat(number_number_of_nat,W)))) # label(fact_4768_zpower__number__of__even) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4546 (all I_1 all M_3 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(hAPP_f2037783381l_bool(cOMBB_1146692694ol_nat,member_nat),suc)),M_3))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))))) # label(fact_4769_card__less__Suc2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4547 (all I_1 all M_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) != zero_zero_nat)) # label(fact_4770_card__less) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4548 (all I_1 all M_3 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) -> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(hAPP_f2037783381l_bool(cOMBB_1146692694ol_nat,member_nat),suc)),M_3))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))))) # label(fact_4771_card__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4549 (all N hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),N)))))) # label(fact_4772_bdd__int__set__l__l__finite) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4550 (all M all X_1 hAPP_i1948725293t_bool(noXRRset(M),X_1) = image_int_int(hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,times_times_int),X_1),hAPP_i1948725293t_bool(norRRset,M))) # label(fact_4773_noXRRset__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4551 (all N all G all X_1 all M (hBOOL(hAPP_real_bool(deriv_real(G,X_1),M)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),G)),N),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(G,X_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)))),M))))) # label(fact_4774_DERIV__fun__pow) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4552 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N)) -> hAPP_f957591787ol_nat(finite_card_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_eq_int),N)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(nat,N)),one_one_nat))) # label(fact_4775_card__bdd__int__set__le) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4553 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N)) -> hAPP_nat_int(semiri1621563631at_int,hAPP_f957591787ol_nat(finite_card_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),N))))) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,N),one_one_int))) # label(fact_4776_int__card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4554 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N)) -> hAPP_f957591787ol_nat(finite_card_int,collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),N)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(nat,N)),one_one_nat))) # label(fact_4777_card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4555 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),cos)),cos),X_1),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X_1))),hAPP_real_real(cos,X_1))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X_1))),hAPP_real_real(cos,X_1)))))) # label(fact_4778_DERIV__cos__cos__mult) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4556 (all V all N (hAPP_int_nat(number_number_of_nat,V) = hAPP_nat_nat(suc,N) <-> -hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) -> hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V))) = N))) # label(fact_4779_eq__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4557 (all N all V (hAPP_nat_nat(suc,N) = hAPP_int_nat(number_number_of_nat,V) <-> -hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) -> hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V))) = N))) # label(fact_4780_Suc__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4558 (all W ((hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,W))) -> hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,W)) = zero_zero_nat) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,W))) -> hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,W)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_int_nat(number_number_of_nat,W)),hAPP_int_nat(number_number_of_nat,W)))))) # label(fact_4781_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4559 (all N all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,power_power_real),N),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))))))) # label(fact_4782_DERIV__pow) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4560 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),cos)),cos),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,min))),hAPP_real_real(cos,X_1))),hAPP_real_real(sin,X_1))))) # label(fact_4783_DERIV__cos__cos__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4561 (all V all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_nat_nat(suc,N))) <-> (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))),N))))) # label(fact_4784_less__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4562 (all N all V (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,N)),hAPP_int_nat(number_number_of_nat,V))) <-> -hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))))))) # label(fact_4785_less__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4563 (all N all V (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),hAPP_int_nat(number_number_of_nat,V))) <-> -hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) & (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))))))) # label(fact_4786_le__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4564 (all V all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_nat_nat(suc,N))) <-> (-hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))),N))))) # label(fact_4787_le__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4565 (all X_3 all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_int_int(standardRes(M),X_3)),collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),M))))))) # label(fact_4788_SR__pos) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4566 (all X_1 all A all M (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,A),rsetR(M))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) -> (hAPP_int_int(legacy_zgcd(X_1),M) = one_one_int -> hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,image_int_int(hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,times_times_int),X_1),A)),rsetR(M))))))) # label(fact_4789_RsetR__zmult__mono) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4567 (all Z_1 all W ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,W))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z_1),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),hAPP_int_nat(number_number_of_nat,W)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),hAPP_int_nat(number_number_of_nat,W)))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(number_number_of_int,W))) -> hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Z_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit1,W))) = one_one_int))) # label(fact_4790_zpower__number__of__odd) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4568 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),sin)),sin),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(cos,X_1))),hAPP_real_real(sin,X_1))))) # label(fact_4791_DERIV__sin__sin__mult2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4569 (all Ba all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hBOOL(hAPP_real_bool(deriv_real(log(Ba),X_1),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(ln,Ba)),X_1)))))) # label(fact_4792_DERIV__log) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4570 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),cos)),cos),X_1),hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(cos,X_1))),hAPP_real_real(sin,X_1)))))) # label(fact_4793_DERIV__cos__cos__mult3) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4571 (all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,plus_plus_real),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),sin)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),cos)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X_2),zero_zero_real))) # label(fact_4794_DERIV__sin__circle__all__zero) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4572 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),sin)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(cos,X_1))),hAPP_real_real(sin,X_1))))) # label(fact_4795_DERIV__sin__realpow2a) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4573 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),sin)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X_1)),hAPP_real_real(sin,X_1))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(cos,X_1)),hAPP_real_real(sin,X_1)))))) # label(fact_4796_DERIV__sin__realpow2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4574 (all V all V_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_1),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_int_nat(number_number_of_nat,V_1)) = hAPP_int_nat(number_number_of_nat,V)) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_1),pls)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_int_nat(number_number_of_nat,V_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),hAPP_int_int(uminus_uminus_int,V_1))))),zero_zero_nat),hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),hAPP_int_int(uminus_uminus_int,V_1)))))))) # label(fact_4797_diff__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4575 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),cos)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,min))),hAPP_real_real(cos,X_1))),hAPP_real_real(sin,X_1))))) # label(fact_4798_DERIV__cos__realpow2a) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4576 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),cos)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1),hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(cos,X_1))),hAPP_real_real(sin,X_1)))))) # label(fact_4799_DERIV__cos__realpow2b) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4577 (all X_1 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),cos)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),X_1),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X_1))),hAPP_real_real(cos,X_1))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X_1))),hAPP_real_real(cos,X_1)))))) # label(fact_4800_DERIV__cos__realpow2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4578 (all X_1 (hAPP_real_real(cos,X_1) != zero_zero_real -> hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,inverse_divide_real),sin)),cos),X_1),hAPP_real_real(inverse_inverse_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(cos,X_1)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_4801_lemma__DERIV__tan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4579 (all Y_2 all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,plus_plus_real),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,minus_minus_real),hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,sin),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,plus_plus_real),Y_2)))),hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,plus_plus_real),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),sin)),hAPP_real_real(cos,Y_2)))),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),cos)),hAPP_real_real(sin,Y_2)))))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,minus_minus_real),hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,cos),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,plus_plus_real),Y_2)))),hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,minus_minus_real),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),cos)),hAPP_real_real(cos,Y_2)))),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,times_times_real),sin)),hAPP_real_real(sin,Y_2)))))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X_2),zero_zero_real))) # label(fact_4802_lemma__DERIV__sin__cos__add) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4580 (all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,plus_plus_real),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),sin)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,power_power_real),cos)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),X_2),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(cos,X_2))),hAPP_real_real(sin,X_2))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_real_real(cos,X_2))),hAPP_real_real(sin,X_2)))))) # label(fact_4803_DERIV__sin__circle__all) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4581 (all Aa all Ba (hBOOL(hAPP_P603027463t_bool(accp_P2006205492nt_int(norm_frac_rel),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,Aa),Ba))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),zero_zero_int)) -> norm_frac(Aa,Ba) = norm_frac(hAPP_int_int(uminus_uminus_int,Aa),hAPP_int_int(uminus_uminus_int,Ba))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Ba),zero_zero_int)) -> (Aa = zero_zero_int | Ba = zero_zero_int -> norm_frac(Aa,Ba) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),one_one_int)) & (-(Aa = zero_zero_int | Ba = zero_zero_int) -> norm_frac(Aa,Ba) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(int_gcd,Aa),Ba))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,Ba),hAPP_int_int(hAPP_int_fun_int_int(int_gcd,Aa),Ba))))))) # label(fact_4804_norm__frac_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4582 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X_1)),one_one_real)) -> hBOOL(monoseq_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(inverse_divide_real,one_one_real)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))))))) # label(fact_4805_monoseq__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4583 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),one_one_real)) -> hBOOL(monoseq_real(hAPP_r474017924t_real(power_power_real,X_1)))))) # label(fact_4806_monoseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4584 (all A_2 all B_1 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> norm_frac(A_2,B_1) = norm_frac(hAPP_int_int(uminus_uminus_int,A_2),hAPP_int_int(uminus_uminus_int,B_1))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),zero_zero_int)) -> (A_2 = zero_zero_int | B_1 = zero_zero_int -> norm_frac(A_2,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),one_one_int)) & (-(A_2 = zero_zero_int | B_1 = zero_zero_int) -> norm_frac(A_2,B_1) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(int_gcd,A_2),B_1))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),hAPP_int_int(hAPP_int_fun_int_int(int_gcd,A_2),B_1))))))) # label(fact_4807_norm__frac_Osimps) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4585 (all Z_2 arg(Z_2) = hilbert_Eps_real(hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_f1402056515l_bool(hAPP_f824790735l_bool(cOMBB_real_bool_real,hAPP_r1134773055l_bool(fequal_real,hAPP_complex_real(re,hAPP_complex_complex(sgn_sgn_complex,Z_2)))),cos))),hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_f1402056515l_bool(hAPP_f824790735l_bool(cOMBB_real_bool_real,hAPP_r1134773055l_bool(fequal_real,hAPP_complex_real(im,hAPP_complex_complex(sgn_sgn_complex,Z_2)))),sin))),hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,pi)))),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,ord_less_eq_real),pi)))))) # label(fact_4808_arg__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4586 (all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,Pa),Aa)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(big_co1548731110nt_int(cOMBI_int,comple219730294t_bool(setS(Aa,Pa)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,Aa),hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),Pa))))))) # label(fact_4809_Union__SetS__setprod__prop1) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4587 (all Aa big_co1548731110nt_int(cOMBI_int,hAPP_i1948725293t_bool(d22set,Aa)) = hAPP_int_int(zfact,Aa)) # label(fact_4810_d22set__prod__zfact) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4588 (all Aa all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),M)) -> hAPP_int_int(legacy_zgcd(big_co1548731110nt_int(cOMBI_int,hAPP_i1948725293t_bool(bnorRset(Aa),M))),M) = one_one_int)) # label(fact_4811_Bnor__prod__zgcd) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4589 (all Aa all M all X_1 (X_1 != zero_zero_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),M)) -> big_co1548731110nt_int(cOMBI_int,image_int_int(hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,times_times_int),X_1),hAPP_i1948725293t_bool(bnorRset(Aa),M))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,big_co1548731110nt_int(cOMBI_int,hAPP_i1948725293t_bool(bnorRset(Aa),M))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_1),hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(bnorRset(Aa),M))))))) # label(fact_4812_Bnor__prod__power) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4590 (all X_1 all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(quadRes,Pa),Aa)) -> (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),setS(Aa,Pa))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(big_co1548731110nt_int(cOMBI_int,X_1)),Aa),Pa)))))))) # label(fact_4813_SetS__setprod__prop) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4591 (all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(big_co1548731110nt_int(cOMBI_int,hAPP_i1948725293t_bool(wset(Aa),Pa))),one_one_int),Pa)))))) # label(fact_4814_wset__zcong__prod__1) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4592 (all Aa all Pa (hBOOL(hAPP_int_bool(zprime,Pa)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),Pa)) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),zero_zero_int),Pa)) -> big_co1548731110nt_int(cOMBI_int,comple219730294t_bool(setS(Aa,Pa))) = hAPP_int_int(zfact,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Pa),one_one_int)))))) # label(fact_4815_Union__SetS__setprod__prop2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4593 (all F all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(F,X_2))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),big_co1548731110nt_int(F,A)))))) # label(fact_4816_transfer__nat__int__sum__prod__closure_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4594 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X_1)),one_one_real)) -> hAPP_real_real(arctan,X_1) = hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(inverse_divide_real,one_one_real)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))))))) # label(fact_4817_arctan__series) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4595 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,X_1)),one_one_real)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_f1122023986l_real(hAPP_f1786887945l_real(cOMBB_1896127834l_real,suminf_real),hAPP_f1993765077t_real(hAPP_f895854793t_real(cOMBB_1948233853l_real,hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))))),hAPP_f1993765077t_real(hAPP_f895854793t_real(cOMBB_1948233853l_real,hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(inverse_divide_real,one_one_real)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat)))))),hAPP_f1501741374t_real(hAPP_f1135648319t_real(cOMBC_1329014627t_real,hAPP_f1163894827t_real(hAPP_f1998755145t_real(cOMBB_421464275l_real,cOMBB_nat_real_nat),power_power_real)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))))),X_1),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))))) # label(fact_4818_DERIV__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4596 (all X_1 hAPP_real_real(sin,X_1) = hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),sin_coeff)),hAPP_r474017924t_real(power_power_real,X_1)))) # label(fact_4819_sin__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4597 (all X_2 hAPP_real_real(sin,X_2) = hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),sin_coeff)),hAPP_r474017924t_real(power_power_real,X_2)))) # label(fact_4820_lemma__sin__ext) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4598 (all X_1 hAPP_real_real(cos,X_1) = hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),cos_coeff)),hAPP_r474017924t_real(power_power_real,X_1)))) # label(fact_4821_cos__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4599 (all X_2 hAPP_real_real(cos,X_2) = hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),cos_coeff)),hAPP_r474017924t_real(power_power_real,X_2)))) # label(fact_4822_lemma__cos__ext) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4600 (all X_1 hAPP_real_real(uminus_uminus_real,hAPP_real_real(sin,X_1)) = hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,uminus_uminus_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),sin_coeff)),hAPP_r474017924t_real(power_power_real,X_1))))) # label(fact_4823_lemma__sin__minus) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4601 (all X_1 hAPP_real_real(exp_real,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,one_one_real),X_1)),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,fact_fact_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_4824_exp__first__two__terms) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.83 4602 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) -> hAPP_real_real(ln,X_1) = hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(inverse_divide_real,one_one_real)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),one_one_nat)))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),one_one_real))),suc)))))) # label(fact_4826_ln__series) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4603 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X_1)),one_one_real)) -> hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(inverse_divide_real,one_one_real)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat)))))))) # label(fact_4827_summable__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4604 (all F (hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,abs_abs_real),F))) -> hBOOL(summable_real(F)))) # label(fact_4828_summable__rabs__cancel) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4605 (all F all G ((exists N_3 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_3),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_nat_real(F,N_2))),hAPP_nat_real(G,N_2))))) -> (hBOOL(summable_real(G)) -> hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,abs_abs_real),F)))))) # label(fact_4829_summable__rabs__comparison__test) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4606 (all F (hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,abs_abs_real),F))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_f352196356l_real(suminf_real,F))),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,abs_abs_real),F)))))) # label(fact_4830_summable__rabs) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4607 (all X_1 hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),sin_coeff)),hAPP_r474017924t_real(power_power_real,X_1))))) # label(fact_4831_summable__sin) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4608 (all X_1 hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),cos_coeff)),hAPP_r474017924t_real(power_power_real,X_1))))) # label(fact_4832_summable__cos) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4609 (all Pa archim791455193or_rat(Pa) = hAPP_P1175774780nt_int(produc1298267108nt_int(div_div_int),quotient_of(Pa))) # label(fact_4833_rat__floor__code) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4610 (all Pa quotient_of(hAPP_rat_rat(uminus_uminus_rat,Pa)) = hAPP_P1975530577nt_int(produc1518849193nt_int(hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),uminus_uminus_int)),quotient_of(Pa))) # label(fact_4834_rat__uminus__code) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4611 (all X_1 hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,X_1))))) # label(fact_4835_summable__exp) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4612 (all Pa quotient_of(hAPP_rat_rat(abs_abs_rat,Pa)) = hAPP_P1975530577nt_int(produc1518849193nt_int(hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),abs_abs_int)),quotient_of(Pa))) # label(fact_4836_rat__abs__code) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4613 (all Aa all Ba divmod_int_rel(Aa,Ba) = produc93441119t_bool(hAPP_f1048215610t_bool(hAPP_f472159229t_bool(cOMBC_1683390479t_bool,hAPP_f1545556668t_bool(hAPP_f85237525t_bool(cOMBB_389152643ol_int,cOMBS_int_bool_bool),hAPP_f1344929775l_bool(hAPP_f1830214065l_bool(cOMBB_793166024ol_int,hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj)),hAPP_f720654810t_bool(hAPP_f908327869t_bool(cOMBB_1290694363ol_int,hAPP_f1512942609t_bool(cOMBB_int_bool_int,hAPP_i1948725293t_bool(fequal_int,Aa))),hAPP_f1760145644nt_int(hAPP_f1629352853nt_int(cOMBB_1496585939nt_int,plus_plus_int),hAPP_int_fun_int_int(times_times_int,Ba)))))),hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,fimplies(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba))),hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_int),Ba))))),hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,fimplies(hAPP_bool_bool(fNot,hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ba)))),hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_int,Ba))),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,ord_less_eq_int),zero_zero_int))))))) # label(fact_4837_divmod__int__rel__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4614 (all Pa quotient_of(hAPP_rat_rat(inverse_inverse_rat,Pa)) = hAPP_P1975530577nt_int(produc1518849193nt_int(hAPP_f465821005nt_int(hAPP_f1081447804nt_int(cOMBS_1470252563nt_int,hAPP_f400200275nt_int(hAPP_f1731308757nt_int(cOMBB_735549356nt_int,cOMBB_1389251822nt_int),hAPP_P621635040nt_int(hAPP_f1582586579nt_int(cOMBC_707974837nt_int,hAPP_f251264923nt_int(hAPP_f279307923nt_int(cOMBB_662120866nt_int,if_Pro1731782967nt_int),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),zero_zero_int))),hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),one_one_int)))),hAPP_f1574055885nt_int(hAPP_f434654626nt_int(cOMBS_2011279539nt_int,hAPP_f2094497995nt_int(hAPP_f534361363nt_int(cOMBB_1657320178nt_int,cOMBC_1964283556nt_int),hAPP_f2004554147nt_int(hAPP_f1228585167nt_int(cOMBB_1102189010nt_int,hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int)),hAPP_f1760145644nt_int(hAPP_f1629352853nt_int(cOMBB_1496585939nt_int,times_times_int),sgn_sgn_int)))),abs_abs_int))),quotient_of(Pa))) # label(fact_4839_rat__inverse__code) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4615 (all X_1 hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,fact_fact_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))) # label(fact_4840_exp__tail__after__first__two__terms__summable) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4616 (all Ba adjust(Ba) = produc1518849193nt_int(hAPP_f465821005nt_int(hAPP_f1081447804nt_int(cOMBS_1470252563nt_int,hAPP_f617310012nt_int(hAPP_f197974549nt_int(cOMBB_638531587nt_int,cOMBS_1891347093nt_int),hAPP_f55007289nt_int(hAPP_f747475781nt_int(cOMBB_222539774nt_int,hAPP_f1311564564nt_int(cOMBS_1640193733nt_int,hAPP_f251264923nt_int(hAPP_f279307923nt_int(cOMBB_662120866nt_int,if_Pro1731782967nt_int),hAPP_f429935748t_bool(hAPP_f1512942609t_bool(cOMBB_int_bool_int,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,minus_minus_int),Ba))))),hAPP_f1574055885nt_int(hAPP_f960630521nt_int(cOMBC_1805044090nt_int,hAPP_f142232355nt_int(hAPP_f1377453843nt_int(cOMBB_320287386nt_int,cOMBB_1846624359nt_int),hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,hAPP_f1760145644nt_int(hAPP_f1629352853nt_int(cOMBB_1496585939nt_int,plus_plus_int),hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_int)))),hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,minus_minus_int),Ba))))),hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))) # label(fact_4841_adjust__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4617 (all X0 all F all R_4 ((all X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),hAPP_r1134773055l_bool(ord_gr788844697n_real(hAPP_real_real(uminus_uminus_real,R_4)),R_4))) -> hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),F)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),suc)))),hAPP_r474017924t_real(power_power_real,X_2)))))) -> (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X0),hAPP_r1134773055l_bool(ord_gr788844697n_real(hAPP_real_real(uminus_uminus_real,R_4)),R_4))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_4)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_f1122023986l_real(hAPP_f1786887945l_real(cOMBB_1896127834l_real,suminf_real),hAPP_f1993765077t_real(hAPP_f895854793t_real(cOMBB_1948233853l_real,hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),F))),hAPP_f1501741374t_real(hAPP_f1135648319t_real(cOMBC_1329014627t_real,hAPP_f1163894827t_real(hAPP_f1998755145t_real(cOMBB_421464275l_real,cOMBB_nat_real_nat),power_power_real)),suc))),X0),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),F)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),suc)))),hAPP_r474017924t_real(power_power_real,X0))))))))) # label(fact_4842_DERIV__power__series_H) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4618 (all X_3 (hBOOL(summable_complex(X_3)) -> hAPP_complex_complex(cnj,hAPP_f213450978omplex(suminf_complex,X_3)) = hAPP_f213450978omplex(suminf_complex,hAPP_f1646117269omplex(hAPP_f1457396693omplex(cOMBB_117013006ex_nat,cnj),X_3)))) # label(fact_4844_cnj_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4619 (all X_3 (hBOOL(summable_complex(X_3)) -> hBOOL(summable_complex(hAPP_f1646117269omplex(hAPP_f1457396693omplex(cOMBB_117013006ex_nat,cnj),X_3))))) # label(fact_4845_cnj_Osummable) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4620 (all X_3 (hBOOL(summable_complex(X_3)) -> hBOOL(summable_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,re),X_3))))) # label(fact_4846_Re_Osummable) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4621 (all X_3 (hBOOL(summable_complex(X_3)) -> hBOOL(summable_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,im),X_3))))) # label(fact_4847_Im_Osummable) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4622 (all X_3 (hBOOL(summable_complex(X_3)) -> hAPP_complex_real(re,hAPP_f213450978omplex(suminf_complex,X_3)) = hAPP_f352196356l_real(suminf_real,hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,re),X_3)))) # label(fact_4848_Re_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4623 (all X_3 (hBOOL(summable_complex(X_3)) -> hAPP_complex_real(im,hAPP_f213450978omplex(suminf_complex,X_3)) = hAPP_f352196356l_real(suminf_real,hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,im),X_3)))) # label(fact_4849_Im_Osuminf) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4624 (all M all N ((N = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> divmod_nat(M,N) = hAPP_n1289843868at_nat(hAPP_n1865633855at_nat(product_Pair_nat_nat,zero_zero_nat),M)) & (-(N = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))) -> divmod_nat(M,N) = hAPP_P1586233937at_nat(produc1391996073at_nat(hAPP_f837737749at_nat(hAPP_f999082675at_nat(cOMBB_348438404at_nat,product_Pair_nat_nat),suc)),divmod_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N),N))))) # label(fact_4851_divmod__nat__if) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4625 (all P_1 all Aa all Ba all N hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),hAPP_nat_nat(suc,N)) = hAPP_P1860904029l_real(produc595218619l_real(hAPP_f2072293513l_real(hAPP_f1763467369l_real(cOMBS_163651580l_real,hAPP_f1663701695l_real(hAPP_f774948957l_real(cOMBB_3698607l_real,cOMBS_902912708l_real),hAPP_f324002831l_real(hAPP_f677014621l_real(cOMBS_107495110l_real,hAPP_f1161935955l_real(hAPP_f328572565l_real(cOMBB_520243667l_real,cOMBS_794971624l_real),hAPP_f517738447l_real(hAPP_f1879982819l_real(cOMBB_731595089l_real,hAPP_f1076489843l_real(cOMBB_415306361l_real,if_Pro313124157l_real)),hAPP_f1884005689l_bool(hAPP_f172451459l_bool(cOMBB_421479067l_real,hAPP_f940061907l_bool(cOMBB_1795223523l_real,P_1)),hAPP_f320596107l_real(hAPP_f850851693l_real(cOMBS_193881978l_real,hAPP_f1119546819l_real(hAPP_f555557763l_real(cOMBB_422423973l_real,cOMBB_2107848501l_real),produc865579683l_real)),hAPP_r337325687l_real(hAPP_f1644353557l_real(cOMBC_1508019322l_real,hAPP_f1644353557l_real(hAPP_f1874145443l_real(cOMBB_1768400739l_real,cOMBC_real_real_real),hAPP_f1732848529l_real(hAPP_f1310479593l_real(cOMBB_2092576745l_real,hAPP_f1960414057l_real(cOMBB_882763271l_real,inverse_divide_real)),plus_plus_real))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))),hAPP_f1591894897l_real(hAPP_f644105375l_real(cOMBC_467724138l_real,hAPP_f1108539711l_real(hAPP_f1109256153l_real(cOMBB_44084907l_real,cOMBS_511527878l_real),hAPP_f823702159l_real(hAPP_f1040184293l_real(cOMBB_557258983l_real,hAPP_f2114902373l_real(cOMBB_237479429l_real,produc865579683l_real)),hAPP_r337325687l_real(hAPP_f1644353557l_real(cOMBC_1508019322l_real,hAPP_f1644353557l_real(hAPP_f1874145443l_real(cOMBB_1768400739l_real,cOMBC_real_real_real),hAPP_f1732848529l_real(hAPP_f1310479593l_real(cOMBB_2092576745l_real,hAPP_f1960414057l_real(cOMBB_882763271l_real,inverse_divide_real)),plus_plus_real))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),cOMBI_real)))),hAPP_f320596107l_real(hAPP_f850851693l_real(cOMBS_193881978l_real,hAPP_f1119546819l_real(hAPP_f555557763l_real(cOMBB_422423973l_real,cOMBB_2107848501l_real),produc865579683l_real)),hAPP_r337325687l_real(hAPP_f1644353557l_real(cOMBC_1508019322l_real,hAPP_f1644353557l_real(hAPP_f1874145443l_real(cOMBB_1768400739l_real,cOMBC_real_real_real),hAPP_f1732848529l_real(hAPP_f1310479593l_real(cOMBB_2092576745l_real,hAPP_f1960414057l_real(cOMBB_882763271l_real,inverse_divide_real)),plus_plus_real))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N))) # label(fact_4852_Bolzano__bisect_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4626 (all Aa all R_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_2)) -> (hBOOL(summable_real(Aa)) -> (exists N_3 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_3),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_f352196356l_real(suminf_real,hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,Aa),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),N_2))))),R_2))))))) # label(fact_4853_suminf__exist__split) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4627 (all L all K_1 ((K_1 = zero_zero_int -> divmod_int(K_1,L) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),zero_zero_int)) & (K_1 != zero_zero_int -> (L = zero_zero_int -> divmod_int(K_1,L) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),K_1)) & (L != zero_zero_int -> divmod_int(K_1,L) = hAPP_P1975530577nt_int(produc713050258nt_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(sgn_sgn_int,L))),hAPP_P1975530577nt_int(hAPP_P1145851913nt_int(hAPP_b40753821nt_int(if_Pro1731782967nt_int,fdisj(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),L)),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)),hAPP_bool_bool(hAPP_b589554111l_bool(fconj,hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,L),zero_zero_int)),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K_1),zero_zero_int)))),pdivmod(K_1,L)),hAPP_P1975530577nt_int(produc1518849193nt_int(hAPP_f465821005nt_int(hAPP_f1081447804nt_int(cOMBS_1470252563nt_int,hAPP_f617310012nt_int(hAPP_f197974549nt_int(cOMBB_638531587nt_int,cOMBS_1891347093nt_int),hAPP_f1148171384nt_int(hAPP_f334321603nt_int(cOMBB_1484610687nt_int,hAPP_f1582586579nt_int(cOMBC_707974837nt_int,hAPP_f251264923nt_int(hAPP_f279307923nt_int(cOMBB_662120866nt_int,if_Pro1731782967nt_int),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),zero_zero_int)))),hAPP_i1584592887nt_int(hAPP_f465821005nt_int(cOMBC_1964283556nt_int,hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),uminus_uminus_int)),zero_zero_int)))),hAPP_f1574055885nt_int(hAPP_f960630521nt_int(cOMBC_1805044090nt_int,hAPP_f142232355nt_int(hAPP_f1377453843nt_int(cOMBB_320287386nt_int,cOMBB_1846624359nt_int),hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,hAPP_f1760145644nt_int(hAPP_f1629352853nt_int(cOMBB_1496585939nt_int,minus_minus_int),uminus_uminus_int)),one_one_int)))),hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(abs_abs_int,L))))),pdivmod(K_1,L)))))))) # label(fact_4854_divmod__int__pdivmod) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4628 (all L all K_1 ((K_1 = zero_zero_int -> divmod_int(K_1,L) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),zero_zero_int)) & (K_1 != zero_zero_int -> (L = zero_zero_int -> divmod_int(K_1,L) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),K_1)) & (L != zero_zero_int -> divmod_int(K_1,L) = hAPP_P1975530577nt_int(produc713050258nt_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(sgn_sgn_int,L))),hAPP_P1975530577nt_int(hAPP_P1145851913nt_int(hAPP_b40753821nt_int(if_Pro1731782967nt_int,hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,hAPP_int_int(sgn_sgn_int,K_1)),hAPP_int_int(sgn_sgn_int,L))),pdivmod(K_1,L)),hAPP_P1975530577nt_int(produc1518849193nt_int(hAPP_f465821005nt_int(hAPP_f1081447804nt_int(cOMBS_1470252563nt_int,hAPP_f617310012nt_int(hAPP_f197974549nt_int(cOMBB_638531587nt_int,cOMBS_1891347093nt_int),hAPP_f1148171384nt_int(hAPP_f334321603nt_int(cOMBB_1484610687nt_int,hAPP_f1582586579nt_int(cOMBC_707974837nt_int,hAPP_f251264923nt_int(hAPP_f279307923nt_int(cOMBB_662120866nt_int,if_Pro1731782967nt_int),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,fequal_int),zero_zero_int)))),hAPP_i1584592887nt_int(hAPP_f465821005nt_int(cOMBC_1964283556nt_int,hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),uminus_uminus_int)),zero_zero_int)))),hAPP_f1574055885nt_int(hAPP_f960630521nt_int(cOMBC_1805044090nt_int,hAPP_f142232355nt_int(hAPP_f1377453843nt_int(cOMBB_320287386nt_int,cOMBB_1846624359nt_int),hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,product_Pair_int_int),hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,hAPP_f1760145644nt_int(hAPP_f1629352853nt_int(cOMBB_1496585939nt_int,minus_minus_int),uminus_uminus_int)),one_one_int)))),hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(abs_abs_int,L))))),pdivmod(K_1,L)))))))) # label(fact_4856_divmod__int__code) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4629 (all F all G ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_nat_real(F,N_2))),hAPP_nat_real(G,N_2)))) -> (hBOOL(summable_real(G)) -> hBOOL(summable_real(F)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f352196356l_real(suminf_real,F)),hAPP_f352196356l_real(suminf_real,G)))))) # label(fact_4857_summable__le2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4630 (all F (hBOOL(summable_real(F)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(F,N_2)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_f352196356l_real(suminf_real,F)))))) # label(fact_4858_suminf__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4631 (all F (hBOOL(summable_real(F)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(F,N_2)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_f352196356l_real(suminf_real,F)))))) # label(fact_4859_suminf__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4632 (all F ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(F,N_2)))) -> (hBOOL(summable_real(F)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_f352196356l_real(suminf_real,F)))))) # label(fact_4860_suminf__0__le) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4633 (all D int_ge_less_than(D) = collec1347809874nt_int(produc93441119t_bool(hAPP_f428220345t_bool(hAPP_f1878066172t_bool(cOMBS_1720984575t_bool,hAPP_f1315737299t_bool(hAPP_f538565589t_bool(cOMBB_1211207212ol_int,cOMBB_bool_bool_int),hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,D)))),ord_less_int)))) # label(fact_4861_int__ge__less__than__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4634 (all D int_ge_less_than2(D) = collec1347809874nt_int(produc93441119t_bool(hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,D)))),ord_less_int)))) # label(fact_4862_int__ge__less__than2__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4635 (all X_1 hBOOL(hAPP_real_bool(sums_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,fact_fact_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat)))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat)))),hAPP_real_real(sin,X_1)))) # label(fact_4863_sin__paired) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4636 (all X_1 hBOOL(hAPP_real_bool(sums_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),sin_coeff)),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_real_real(sin,X_1)))) # label(fact_4864_sin__converges) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4637 (all X_1 hBOOL(hAPP_real_bool(sums_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),cos_coeff)),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_real_real(cos,X_1)))) # label(fact_4865_cos__converges) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4638 (all X_1 hBOOL(hAPP_real_bool(sums_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_r474017924t_real(power_power_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))) # label(fact_4867_Ln_Oaux2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4639 (all G all X_1 (hBOOL(hAPP_real_bool(sums_real(G),X_1)) -> hBOOL(hAPP_real_bool(sums_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_r195310020l_real(hAPP_f2126667875l_real(cOMBC_746811033l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),zero_zero_real)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,G),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,div_div_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,minus_minus_nat),one_one_nat))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),X_1)))) # label(fact_4868_sums__if_H) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4640 (all F all Y_2 all G all X_1 (hBOOL(hAPP_real_bool(sums_real(G),X_1)) -> (hBOOL(hAPP_real_bool(sums_real(F),Y_2)) -> hBOOL(hAPP_real_bool(sums_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f335634176l_real(cOMBS_337378985l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,F),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,div_div_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,G),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,div_div_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,minus_minus_nat),one_one_nat))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,X_1),Y_2)))))) # label(fact_4869_sums__if) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4641 (all X_1 hBOOL(hAPP_real_bool(sums_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,fact_fact_nat),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_real_real(cos,X_1)))) # label(fact_4870_cos__paired) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4642 (all X_3 all Aa (hBOOL(hAPP_complex_bool(sums_complex(X_3),Aa)) -> hBOOL(hAPP_complex_bool(sums_complex(hAPP_f1646117269omplex(hAPP_f1457396693omplex(cOMBB_117013006ex_nat,cnj),X_3)),hAPP_complex_complex(cnj,Aa))))) # label(fact_4871_cnj_Osums) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4643 (all X_3 all Aa (hBOOL(hAPP_complex_bool(sums_complex(X_3),Aa)) -> hBOOL(hAPP_real_bool(sums_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,re),X_3)),hAPP_complex_real(re,Aa))))) # label(fact_4872_Re_Osums) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4644 (all X_3 all Aa (hBOOL(hAPP_complex_bool(sums_complex(X_3),Aa)) -> hBOOL(hAPP_real_bool(sums_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,im),X_3)),hAPP_complex_real(im,Aa))))) # label(fact_4873_Im_Osums) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4645 (all N hAPP_nat_real(diffs_real(sin_coeff),N) = hAPP_nat_real(cos_coeff,N)) # label(fact_4874_sin__fdiffs2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4646 (all X_2 hAPP_nat_real(diffs_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat))),X_2) = hAPP_real_real(inverse_inverse_real,hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,X_2)))) # label(fact_4876_exp__fdiffs) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4647 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) <-> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M)),N)))) # label(fact_4877_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4648 (all X_2 hAPP_nat_real(diffs_real(cos_coeff),X_2) = hAPP_real_real(uminus_uminus_real,hAPP_nat_real(sin_coeff,X_2))) # label(fact_4878_cos__fdiffs) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4649 (all N hAPP_nat_real(diffs_real(cos_coeff),N) = hAPP_real_real(uminus_uminus_real,hAPP_nat_real(sin_coeff,N))) # label(fact_4879_cos__fdiffs2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4650 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N))) # label(fact_4880_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4651 (all F all G ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(F,N_2)),hAPP_nat_real(G,N_2)))) -> (hBOOL(summable_real(F)) -> (hBOOL(summable_real(G)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f352196356l_real(suminf_real,F)),hAPP_f352196356l_real(suminf_real,G))))))) # label(fact_4881_summable__le) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4652 (all Y_2 hAPP_real_real(arctan,Y_2) = the_real(hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))),hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,ord_less_real),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,hAPP_f1393328161l_bool(hAPP_f1900646853l_bool(cOMBB_430461877l_real,fequal_real),tan)),Y_2))))) # label(fact_4882_arctan__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4653 (all Y_2 hAPP_real_real(arcsin,Y_2) = the_real(hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(uminus_uminus_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))))),hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,ord_less_eq_real),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,pi),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,hAPP_f1393328161l_bool(hAPP_f1900646853l_bool(cOMBB_430461877l_real,fequal_real),sin)),Y_2))))) # label(fact_4883_arcsin__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4654 (all X_1 hAPP_real_real(ln,X_1) = the_real(hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,hAPP_f1393328161l_bool(hAPP_f1900646853l_bool(cOMBB_430461877l_real,fequal_real),exp_real)),X_1))) # label(fact_4884_ln__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4655 (all N all X_1 ((hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hAPP_real_real(hAPP_n546711566l_real(root,N),X_1) = the_real(hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(ord_less_real,zero_zero_real))),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,hAPP_f1393328161l_bool(hAPP_f1900646853l_bool(cOMBB_430461877l_real,fequal_real),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,power_power_real),N))),X_1)))) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)) -> hAPP_real_real(hAPP_n546711566l_real(root,N),X_1) = hAPP_real_real(uminus_uminus_real,the_real(hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(ord_less_real,zero_zero_real))),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,hAPP_f1393328161l_bool(hAPP_f1900646853l_bool(cOMBB_430461877l_real,fequal_real),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,power_power_real),N))),hAPP_real_real(uminus_uminus_real,X_1)))))) & (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)) -> hAPP_real_real(hAPP_n546711566l_real(root,N),X_1) = zero_zero_real)))) # label(fact_4885_root__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4656 (all Y_2 hAPP_real_real(arccos,Y_2) = the_real(hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real))),hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,fconj),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,ord_less_eq_real),pi))),hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,hAPP_f1393328161l_bool(hAPP_f1900646853l_bool(cOMBB_430461877l_real,fequal_real),cos)),Y_2))))) # label(fact_4886_arccos__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4657 (all M all N divmod_nat(M,N) = the_Pr588456374at_nat(divmod_nat_rel(M,N))) # label(fact_4889_divmod__nat__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4658 (all X_1 archim1246769320r_real(X_1) = the_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_r481142414t_bool(hAPP_f1845081853t_bool(cOMBC_int_real_bool,hAPP_f801032407l_bool(hAPP_f499530369l_bool(cOMBB_1317819104ol_int,ord_less_eq_real),ring_1_of_int_real)),X_1))),hAPP_f429384717t_bool(hAPP_f1173902867t_bool(cOMBB_real_bool_int,hAPP_r1134773055l_bool(ord_less_real,X_1)),hAPP_f563293398t_real(hAPP_f134192053t_real(cOMBB_int_real_int,ring_1_of_int_real),hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,plus_plus_int),one_one_int)))))) # label(fact_4890_floor__real__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4659 (all X_1 archim791455193or_rat(X_1) = the_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_r1900510169t_bool(hAPP_f1480506641t_bool(cOMBC_int_rat_bool,hAPP_f601898971t_bool(hAPP_f857296063t_bool(cOMBB_214503962ol_int,ord_less_eq_rat),ring_1_of_int_rat)),X_1))),hAPP_f1241350704t_bool(hAPP_f1131424617t_bool(cOMBB_rat_bool_int,hAPP_r2115560837t_bool(ord_less_rat,X_1)),hAPP_f1900950721nt_rat(hAPP_f1270196437nt_rat(cOMBB_int_rat_int,ring_1_of_int_rat),hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,plus_plus_int),one_one_int)))))) # label(fact_4891_floor__rat__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4660 (all Aa all A all M ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) & hBOOL(hAPP_int_bool(is_RRset(A),M)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) -> hAPP_int_int(rRset2norRR(A,M),Aa) = hilbert_Eps_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,zcong(Aa)),M))),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),hAPP_i1948725293t_bool(norRRset,M))))) & (-(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) & hBOOL(hAPP_int_bool(is_RRset(A),M)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A))) -> hAPP_int_int(rRset2norRR(A,M),Aa) = zero_zero_int))) # label(fact_4892_RRset2norRR__def) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4661 (all Aa all A all M (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),M)) -> (hBOOL(hAPP_int_bool(is_RRset(A),M)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(Aa),hilbert_Eps_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,zcong(Aa)),M))),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),hAPP_i1948725293t_bool(norRRset,M))))),M)) & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hilbert_Eps_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,zcong(Aa)),M))),hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,member_int),hAPP_i1948725293t_bool(norRRset,M))))),hAPP_i1948725293t_bool(norRRset,M))))))) # label(fact_4893_aux__some) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4662 (all X_1 all N hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(sin,X_1)),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_r195310020l_real(hAPP_f2126667875l_real(cOMBC_746811033l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),zero_zero_real)),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,div_div_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,minus_minus_nat),hAPP_nat_nat(suc,zero_zero_nat)))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat))))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(inverse_inverse_real,hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(abs_abs_real,X_1)),N))))) # label(fact_4894_Maclaurin__sin__bound) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4663 (all U all F ((all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(F,N_2)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,ord_less_eq_nat),F)),U)))))) # label(fact_4895_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4664 (all L all U hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U)))) # label(fact_4896_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4665 (all F all N all R_2 hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),R_2)) = hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,minus_minus_real),F)),R_2)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))) # label(fact_4897_sumr__diff__mult__const) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4666 (all K_1 all N_2 all F_2 hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F_2),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),K_1))) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,F_2),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N_2))),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F_2),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),K_1)))) # label(fact_4898_sumr__offset4) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4667 (all K_1 all N all F_2 hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,F_2),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N)) = hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F_2),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1)))),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F_2),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),K_1)))) # label(fact_4899_sumr__offset2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4668 (all F all N hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),F)),hAPP_r474017924t_real(power_power_real,zero_zero_real))),hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,zero_zero_nat)),N)) = zero_zero_real) # label(fact_4900_sumr__one__lb__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4669 (all P_1 all N ((all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) -> hBOOL(hAPP_nat_bool(P_1,M_2)))) <-> (all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))) -> hBOOL(hAPP_nat_bool(P_1,X_2)))))) # label(fact_4901_all__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4670 (all P_1 all N ((exists M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_nat_bool(P_1,M_2)))) <-> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))) & hBOOL(hAPP_nat_bool(P_1,X_2)))))) # label(fact_4902_ex__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4671 (all L all U hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U),L)) # label(fact_4903_card__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4672 (all N all X_1 (X_1 != one_one_real -> hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N)) = hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N)),one_one_real)),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,X_1),one_one_real)))) # label(fact_4904_sumr__geometric) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4673 (all L all U hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U)) # label(fact_4905_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4674 (all K_1 all I_1 all J image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(I_1),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) # label(fact_4906_image__add__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4675 (all I_1 all J image_nat_nat(suc,hAPP_n1699378549t_bool(ord_at4362885an_nat(I_1),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,I_1)),hAPP_nat_nat(suc,J))) # label(fact_4907_image__Suc__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4676 (all Diff all N all X_1 (X_1 = zero_zero_real -> (N != zero_zero_nat -> hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N)) = hAPP_real_real(hAPP_n546711566l_real(Diff,zero_zero_nat),zero_zero_real)))) # label(fact_4908_Maclaurin__zero) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4677 (all A all K_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_n1699378549t_bool(ord_at4362885an_nat(K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),hAPP_f22106695ol_nat(finite_card_nat,A))))) -> A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),hAPP_f22106695ol_nat(finite_card_nat,A))))) # label(fact_4909_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4678 (all F all G all N hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f335634176l_real(cOMBS_337378985l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),F)),G)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N))) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,F),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,G),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N)))) # label(fact_4910_sum__split__even__odd) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4679 (all N hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))),suc)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N))) = zero_zero_real) # label(fact_4911_sumr__minus__one__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4680 (all N hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,hAPP_f451358433l_real(hAPP_f335634176l_real(cOMBS_337378985l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,div_div_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,zero_zero_real)))),zero_zero_real)),hAPP_n1699378549t_bool(ord_at4362885an_nat(one_one_nat),N)) = zero_zero_real) # label(fact_4912_lemma__STAR__cos2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4681 (all N hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,hAPP_f451358433l_real(hAPP_f335634176l_real(cOMBS_337378985l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,div_div_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),zero_zero_real))),hAPP_r474017924t_real(power_power_real,zero_zero_real))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(suc,N))) = one_one_real) # label(fact_4913_sumr__cos__zero__one) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4682 (all N all X_1 exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(sin,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_r195310020l_real(hAPP_f2126667875l_real(cOMBC_746811033l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),zero_zero_real)),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,div_div_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,minus_minus_nat),hAPP_nat_nat(suc,zero_zero_nat)))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat))))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,T_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(real_nat,N))),pi)))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N))))) # label(fact_4914_Maclaurin__sin__expansion2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4683 (all N all X_1 exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(cos,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,hAPP_f451358433l_real(hAPP_f335634176l_real(cOMBS_337378985l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,div_div_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),zero_zero_real))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(cos,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,T_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(real_nat,N))),pi)))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N))))) # label(fact_4915_Maclaurin__cos__expansion) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4684 (all L all U hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(ord_at641636577an_int(L),U)))) # label(fact_4916_finite__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4685 (all U hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(ord_at641636577an_int(zero_zero_int),U)))) # label(fact_4917_finite__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4686 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_2),X_1)) -> comple124823625p_real(hAPP_r1134773055l_bool(ord_at1496968948n_real(Y_2),X_1)) = X_1)) # label(fact_4918_Sup__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4687 (all U hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(ord_at641636577an_int(zero_zero_int),U)) = hAPP_int_nat(nat,U)) # label(fact_4919_card__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4688 (all L all U hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(ord_at641636577an_int(L),U)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U),L))) # label(fact_4920_card__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4689 (all L all U hAPP_i1948725293t_bool(ord_at641636577an_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,L),one_one_int)),U) = hAPP_i1948725293t_bool(ord_gr1297742076an_int(L),U)) # label(fact_4921_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4690 (all L all U image_int_int(hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,plus_plus_int),L),hAPP_i1948725293t_bool(ord_at641636577an_int(zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U),L))) = hAPP_i1948725293t_bool(ord_at641636577an_int(L),U)) # label(fact_4922_image__add__int__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4691 (all X_1 all N exists T_1 hAPP_real_real(sin,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_r195310020l_real(hAPP_f2126667875l_real(cOMBC_746811033l_real,hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,if_real),even_odd_even_nat)),zero_zero_real)),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min))),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,div_div_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,minus_minus_nat),hAPP_nat_nat(suc,zero_zero_nat)))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat))))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(sin,hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,T_1),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,one_one_real),hAPP_int_real(number267125858f_real,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),hAPP_nat_real(real_nat,N))),pi)))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N)))) # label(fact_4923_Maclaurin__sin__expansion) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4692 (all B all K_1 all Diff all H all N ((all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (N = hAPP_nat_nat(suc,K_1) -> (all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,minus_minus_real),hAPP_n546711566l_real(Diff,M_2))),hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,plus_plus_real),hAPP_f2119584768l_real(hAPP_f59594445l_real(cOMBC_2010481033l_real,hAPP_f1523861863l_real(hAPP_f1067681227l_real(cOMBB_1934313333l_real,big_co604158596t_real),hAPP_f1993765077t_real(hAPP_f895854793t_real(cOMBB_1948233853l_real,hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,hAPP_f1904307534l_real(hAPP_f224989205l_real(cOMBB_1419615765al_nat,Diff),hAPP_nat_fun_nat_nat(plus_plus_nat,M_2))),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat))))),power_power_real))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M_2))))),hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,hAPP_r1250527377l_real(times_times_real,B)),hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,inverse_divide_real),hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,power_power_real),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M_2)))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M_2))))))),T_1),hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1)),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,hAPP_f1904307534l_real(hAPP_f224989205l_real(cOMBB_1419615765al_nat,Diff),hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)))),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,T_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,M_2))))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,T_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,M_2)))),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,M_2))))))))))))))) # label(fact_4924_Maclaurin__lemma2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4693 (all N all X_1 (X_1 != zero_zero_real -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(abs_abs_real,T_1))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(exp_real,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(exp_real,T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N)))))))) # label(fact_4925_Maclaurin__exp__lt) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4694 (all N all X_1 exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(exp_real,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(exp_real,T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N))))) # label(fact_4926_Maclaurin__exp__le) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4695 (all K_1 all F (hBOOL(summable_real(F)) -> ((all D_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),D_2)))),hAPP_nat_real(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),D_2)),one_one_nat))))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),K_1))),hAPP_f352196356l_real(suminf_real,F)))))) # label(fact_4927_sumr__pos__lt__pair) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4696 (all F all J all N all H (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H)) -> (exists B_5 hAPP_real_real(F,H) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),J)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,H))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,B_5),hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_nat_real(hAPP_r474017924t_real(power_power_real,H),N)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))))))) # label(fact_4928_Maclaurin__lemma) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4697 (all N all F (hBOOL(summable_real(F)) -> ((all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(F,M_2))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_f352196356l_real(suminf_real,F)))))) # label(fact_4929_series__pos__less) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4698 (all N all F (hBOOL(summable_real(F)) -> ((all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(F,M_2))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_f352196356l_real(suminf_real,F)))))) # label(fact_4930_series__pos__le) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4699 (all N all X_1 all Diff all F (hAPP_n546711566l_real(Diff,zero_zero_nat) = F & (all M_2 all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),X_2),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),X_2)))) & X_1 != zero_zero_real & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(abs_abs_real,T_1))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(F,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N))))))) # label(fact_4931_Maclaurin__all__lt__objl) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4700 (all X_1 all N all Diff all F (hAPP_n546711566l_real(Diff,zero_zero_nat) = F -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (X_1 != zero_zero_real -> ((all M_2 all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),X_2),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),X_2)))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(abs_abs_real,T_1))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(F,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N)))))))))) # label(fact_4932_Maclaurin__all__lt) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4701 (all X_1 all N all Diff all F (hAPP_n546711566l_real(Diff,zero_zero_nat) = F -> ((all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(F,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N)))))))) # label(fact_4933_Maclaurin__bi__le) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4702 (all Diff all F all N all H (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H),zero_zero_real)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hAPP_n546711566l_real(Diff,zero_zero_nat) = F -> ((all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,H),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),zero_zero_real)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,T_1),zero_zero_real)) & hAPP_real_real(F,H) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,H))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,H),N)))))))))) # label(fact_4934_Maclaurin__minus) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4703 (all N all Diff all F all H (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H)) -> (hAPP_n546711566l_real(Diff,zero_zero_nat) = F -> ((all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) & hAPP_real_real(F,H) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,H))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,H),N))))))))) # label(fact_4935_Maclaurin2) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4704 (all Diff all F all N all H (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) & hAPP_n546711566l_real(Diff,zero_zero_nat) = F & (all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,T_1),H)) & hAPP_real_real(F,H) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,H))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,H),N))))))) # label(fact_4936_Maclaurin__objl) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4705 (all N all Diff all F all H (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H)) & hAPP_n546711566l_real(Diff,zero_zero_nat) = F & (all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) & hAPP_real_real(F,H) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,H))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,H),N))))))) # label(fact_4937_Maclaurin2__objl) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4706 (all Diff all F all N all H (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),H)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hAPP_n546711566l_real(Diff,zero_zero_nat) = F -> ((all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),H)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,T_1),H)) & hAPP_real_real(F,H) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,H))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,H),N)))))))))) # label(fact_4938_Maclaurin) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4707 (all Diff all F all N all H (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H),zero_zero_real)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) & hAPP_n546711566l_real(Diff,zero_zero_nat) = F & (all M_2 all T_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,H),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,T_1),zero_zero_real)) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),T_1),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),T_1))))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,H),T_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,T_1),zero_zero_real)) & hAPP_real_real(F,H) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,H))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,H),N))))))) # label(fact_4939_Maclaurin__minus__objl) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4708 (all N all X_1 all Diff all F (hAPP_n546711566l_real(Diff,zero_zero_nat) = F & (all M_2 all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),X_2),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),X_2)))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(F,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N))))))) # label(fact_4940_Maclaurin__all__le__objl) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4709 (all N all X_1 all Diff all F (hAPP_n546711566l_real(Diff,zero_zero_nat) = F -> ((all M_2 all X_2 hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(Diff,M_2),X_2),hAPP_real_real(hAPP_n546711566l_real(Diff,hAPP_nat_nat(suc,M_2)),X_2)))) -> (exists T_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,T_1)),hAPP_real_real(abs_abs_real,X_1))) & hAPP_real_real(F,X_1) = hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,inverse_divide_real),hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,Diff),zero_zero_real))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),fact_fact_nat)))),hAPP_r474017924t_real(power_power_real,X_1))),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_real_real(hAPP_r1250527377l_real(inverse_divide_real,hAPP_real_real(hAPP_n546711566l_real(Diff,N),T_1)),hAPP_nat_real(real_nat,hAPP_nat_nat(fact_fact_nat,N)))),hAPP_nat_real(hAPP_r474017924t_real(power_power_real,X_1),N)))))))) # label(fact_4941_Maclaurin__all__le) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4710 (all F all K_3 all N ((all P_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,P_4),N)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(F,P_4)),K_3)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,hAPP_nat_real(real_nat,N)),K_3))))) # label(fact_4942_real__setsum__nat__ivl__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.83/4.84 4711 (all F all X_1 all F_1 all N all M ((all R_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),R_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,R_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_n546711566l_real(F,R_1),X_1),hAPP_real_real(hAPP_n546711566l_real(F_1,R_1),X_1))))) -> hBOOL(hAPP_real_bool(deriv_real(hAPP_f2119584768l_real(hAPP_f59594445l_real(cOMBC_2010481033l_real,hAPP_f1523861863l_real(hAPP_f1067681227l_real(cOMBB_1934313333l_real,big_co604158596t_real),hAPP_f42270917t_real(cOMBC_nat_real_real,F))),hAPP_n1699378549t_bool(ord_at4362885an_nat(M),N)),X_1),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,F_1),X_1)),hAPP_n1699378549t_bool(ord_at4362885an_nat(M),N)))))) # label(fact_4943_DERIV__sumr) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4712 (all X_1 all F (hBOOL(summable_real(F)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N_2))),X_1))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f352196356l_real(suminf_real,F)),X_1))))) # label(fact_4944_suminf__le) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4713 (all F all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(F,X_2))))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_f1594865479ol_int(hAPP_f1926459811ol_int(big_co230513141nt_int,F),A)))))) # label(fact_4945_transfer__nat__int__sum__prod__closure_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4714 (all X_1 all F ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(F,N_2)))) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,F),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N_2))),X_1))) -> hBOOL(summable_real(F))))) # label(fact_4946_pos__summable) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4715 (all Aa all D all N hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_f659380387ol_int(hAPP_f1599440987ol_int(big_co1024481617at_int,hAPP_f1139079189at_int(hAPP_f1431025877at_int(cOMBB_int_int_nat,hAPP_int_fun_int_int(plus_plus_int,Aa)),hAPP_int_fun_nat_int(hAPP_f1673103573at_int(cOMBC_nat_int_int,hAPP_f1935805932nt_int(hAPP_f125788821nt_int(cOMBB_859312247nt_nat,times_times_int),semiri1621563631at_int)),D))),hAPP_n1699378549t_bool(ord_lessThan_nat,N))) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,N)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat))),D))))) # label(fact_4947_arith__series__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4716 (all K_3 all K_1 all F ((all N_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,K_1),hAPP_nat_real(F,N_2))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(F,N_2)),K_3)))) -> hBOOL(bseq_real(F)))) # label(fact_4948_BseqI2) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4717 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_lessThan_nat,K_1)))) # label(fact_4949_finite__lessThan) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4718 (all U hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(ord_lessThan_nat,U)) = U) # label(fact_4950_card__lessThan) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4719 (all N hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),N) = hAPP_n1699378549t_bool(ord_lessThan_nat,N)) # label(fact_4951_atLeast0LessThan) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4720 (all S (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S)) <-> (exists K hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,S),hAPP_n1699378549t_bool(ord_lessThan_nat,K)))))) # label(fact_4952_finite__nat__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4721 (all Aa all D all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,hAPP_nat_fun_nat_nat(plus_plus_nat,Aa)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),D))),hAPP_n1699378549t_bool(ord_lessThan_nat,N))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)),D))))) # label(fact_4953_arith__series__nat) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4722 (all U (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U)) -> hAPP_i1948725293t_bool(ord_at641636577an_int(zero_zero_int),U) = image_nat_int(semiri1621563631at_int,hAPP_n1699378549t_bool(ord_lessThan_nat,hAPP_int_nat(nat,U))))) # label(fact_4954_image__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4723 (all S (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S)) -> (exists K hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,S),hAPP_n1699378549t_bool(ord_lessThan_nat,K)))))) # label(fact_4955_finite__nat__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4724 (all N all Q_2 all P_1 ((all X_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(Q_2,X_2)),hAPP_nat_nat(P_1,X_2)))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,P_1),hAPP_n1699378549t_bool(ord_lessThan_nat,N))),hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,Q_2),hAPP_n1699378549t_bool(ord_lessThan_nat,N))) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,hAPP_f1914919701at_nat(hAPP_f1408247010at_nat(cOMBS_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,minus_minus_nat),P_1)),Q_2)),hAPP_n1699378549t_bool(ord_lessThan_nat,N)))) # label(fact_4956_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4725 (all X_1 comple124823625p_real(hAPP_r1134773055l_bool(ord_lessThan_real,X_1)) = X_1) # label(fact_4957_Sup__lessThan) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4726 (all P_2 all P_1 ((all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) -> (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_2,X_2))))) -> collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),P_1)) = collect_int(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,fconj),hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int))),P_2)))) # label(fact_4958_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.84 4727 (all P_3 ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_P1175774780nt_int(product_snd_int_int,P_3))) -> normalize(P_3) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_P1175774780nt_int(product_fst_int_int,P_3)),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_P1175774780nt_int(product_fst_int_int,P_3)),hAPP_P1175774780nt_int(product_snd_int_int,P_3)))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_P1175774780nt_int(product_snd_int_int,P_3)),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_P1175774780nt_int(product_fst_int_int,P_3)),hAPP_P1175774780nt_int(product_snd_int_int,P_3))))) & (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_P1175774780nt_int(product_snd_int_int,P_3))) -> (hAPP_P1175774780nt_int(product_snd_int_int,P_3) = zero_zero_int -> normalize(P_3) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,zero_zero_int),one_one_int)) & (hAPP_P1175774780nt_int(product_snd_int_int,P_3) != zero_zero_int -> normalize(P_3) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_P1175774780nt_int(product_fst_int_int,P_3)),hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_P1175774780nt_int(product_fst_int_int,P_3)),hAPP_P1175774780nt_int(product_snd_int_int,P_3))))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,hAPP_P1175774780nt_int(product_snd_int_int,P_3)),hAPP_int_int(uminus_uminus_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_P1175774780nt_int(product_fst_int_int,P_3)),hAPP_P1175774780nt_int(product_snd_int_int,P_3))))))))) # label(fact_4959_normalize__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4728 (all X all Y hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)),X))) # label(fact_4960_gcd__dvd1__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4729 (all X all Y hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)),Y))) # label(fact_4961_gcd__dvd2__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4730 (all N_1 all M_1 all A_2 all B_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),M_1)) = one_one_int)) # label(fact_4962_coprime__exp2__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4731 (all X all Y all M_1 (hAPP_int_int(div_mod_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)),M_1) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),M_1) = one_one_int)) # label(fact_4963_invertible__coprime__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4732 (all M_1 all K_2 all N_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,K_2),N_1) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),M_1))))) # label(fact_4964_coprime__dvd__mult__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4733 (all M all K_1 all N (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,K_1),N) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),M))))) # label(fact_4965_coprime__dvd__mult__iff__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4734 (all N_1 all M_1 all R_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_1),R_3)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),R_3)) -> (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1) = one_one_int -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N_1)),R_3)))))) # label(fact_4966_divides__mult__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4735 (all B_4 all A_4 all A_2 all B_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1) != zero_zero_int -> (A_2 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_4),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)) -> (B_1 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_4),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)) -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_4),B_4) = one_one_int)))) # label(fact_4967_gcd__coprime__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4736 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,X),Y))) # label(fact_4968_transfer__int__nat__gcd_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4737 (all M_1 all K_2 all N_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1)) # label(fact_4969_gcd__add__mult__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4738 (all M_1 all N_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_1),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1)) # label(fact_4970_gcd__add2__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4739 (all M_1 all N_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_1),N_1)),N_1) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1)) # label(fact_4971_gcd__add1__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4740 (all N_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,N_1),one_one_int)),N_1) = one_one_int) # label(fact_4972_coprime__minus__one__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4741 (all N_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,N_1),one_one_int)),N_1) = one_one_int) # label(fact_4973_coprime__plus__one__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4742 (all N_1 all D_3 all A_2 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),A_2) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1)) = one_one_int)) # label(fact_4974_coprime__exp__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4743 (all E_1 all B_1 all D_3 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D_3),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,E_1),B_1)) -> (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),E_1) = one_one_int)))) # label(fact_4975_coprime__divisors__nat) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4744 (all M_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),one_one_int) = one_one_int) # label(fact_4976_gcd__1__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4745 (all M all N (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M),N) = zero_zero_int <-> M = zero_zero_int & N = zero_zero_int)) # label(fact_4977_gcd__zero__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4746 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,Y),hAPP_int_int(div_mod_int(X),Y))) # label(fact_4978_gcd__red__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4747 (all K_1 all M all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M),N))) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),M)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),N)))) # label(fact_4979_gcd__greatest__iff__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4748 (all N_1 all K_2 all M_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),M_1)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),N_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1)))))) # label(fact_4980_gcd__greatest__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4749 (all I all M_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,I),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,I),M_1)))) # label(fact_4981_dvd__gcd__D1__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4750 (all I all M_1 all N_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,I),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,I),N_1)))) # label(fact_4982_dvd__gcd__D2__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4751 (all A_2 all B_1 all C_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)),C_1) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,B_1),C_1))) # label(fact_4983_gcd__assoc__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4752 (all B_1 all A_2 all C_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,B_1),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),C_1)) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,B_1),C_1))) # label(fact_4984_gcd__int_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4753 (all A_2 all B_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,B_1),A_2)) # label(fact_4985_gcd__commute__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4754 (all A_2 all N_1 all B_1 hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_2),N_1)),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,B_1),N_1)) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)),N_1)) # label(fact_4986_gcd__exp__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4755 (all K_2 all M_1 all N_1 hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,K_2)),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1)) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),N_1))) # label(fact_4987_gcd__mult__distrib__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4756 (all X all Y hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)) # label(fact_4988_abs__gcd__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4757 (all X hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),X) = hAPP_int_int(abs_abs_int,X)) # label(fact_4989_gcd__idem__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4758 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(abs_abs_int,X)),hAPP_int_int(abs_abs_int,Y))) # label(fact_4990_gcd__abs__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4759 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),hAPP_int_int(abs_abs_int,Y)) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)) # label(fact_4991_gcd__abs2__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4760 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(abs_abs_int,X)),Y) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)) # label(fact_4992_gcd__abs1__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4761 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),hAPP_int_int(uminus_uminus_int,Y)) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)) # label(fact_4993_gcd__neg2__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4762 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(uminus_uminus_int,X)),Y) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)) # label(fact_4994_gcd__neg1__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4763 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Y),X)) -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y) = hAPP_int_int(abs_abs_int,Y))) # label(fact_4995_gcd__proj2__if__dvd__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4764 (all X all Y (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X),Y)) -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y) = hAPP_int_int(abs_abs_int,X))) # label(fact_4996_gcd__proj1__if__dvd__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4765 (all M all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M),N))) <-> M != zero_zero_int | N != zero_zero_int)) # label(fact_4997_gcd__pos__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4766 (all X hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,zero_zero_int),X) = hAPP_int_int(abs_abs_int,X)) # label(fact_4998_gcd__0__left__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4767 (all X hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),zero_zero_int) = hAPP_int_int(abs_abs_int,X)) # label(fact_4999_gcd__0__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4768 (all D_3 all A_2 all B_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),B_1) = one_one_int)) # label(fact_5000_coprime__rmult__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4769 (all D_3 all A_2 all B_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),A_2) = one_one_int)) # label(fact_5001_coprime__lmult__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4770 (all B_1 all D_3 all A_2 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),A_2) = one_one_int -> (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),B_1) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D_3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_2),B_1)) = one_one_int))) # label(fact_5002_coprime__mult__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4771 (all M_1 all K_2 all N_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,K_2),N_1) = one_one_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),M_1)),N_1) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,M_1),N_1))) # label(fact_5003_gcd__mult__cancel__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4772 (all D all Aa all Ba (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Aa),Ba)) = one_one_int <-> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D),Aa) = one_one_int & hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,D),Ba) = one_one_int)) # label(fact_5004_coprime__mul__eq__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4773 (all A_2 all B_1 hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1))) = hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_2),B_1)) # label(fact_5005_Fract__coprime) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4774 (all B_1 all A_2 (A_2 != zero_zero_int | B_1 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,A_2),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1))),hAPP_int_int(hAPP_int_fun_int_int(div_div_int,B_1),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1))) = one_one_int)) # label(fact_5006_div__gcd__coprime__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4775 (all X all Y (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Y)) -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,Y),hAPP_int_int(div_mod_int(X),Y)))) # label(fact_5007_gcd__non__0__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4776 (all Y all X (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)))))) # label(fact_5008_transfer__nat__int__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4777 (all X all Y hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)))) # label(fact_5009_gcd__ge__0__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4778 (all B_1 all A_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)),A_2)))) # label(fact_5010_gcd__le1__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4779 (all A_2 all B_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)),B_1)))) # label(fact_5011_gcd__le2__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4780 (all Ba all Aa all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),D)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),Ba)) & (all E (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,E),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,E),Ba)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,E),D)))) <-> D = hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,Aa),Ba))) # label(fact_5012_gcd__unique__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4781 (all P_1 all Y_2 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_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X_1),Y_2))))) -> ((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,Y_2),zero_zero_int)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X_1),hAPP_int_int(uminus_uminus_int,Y_2)))))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(uminus_uminus_int,X_1)),Y_2))))) -> ((hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),zero_zero_int)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_2),zero_zero_int)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_int_int(uminus_uminus_int,X_1)),hAPP_int_int(uminus_uminus_int,Y_2)))))) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X_1),Y_2)))))))) # label(fact_5013_gcd__cases__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4782 (all Ba all C all Aa all D (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,Aa),D) = one_one_int -> (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,Ba),C) = one_one_int -> (hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,Aa)),hAPP_int_int(abs_abs_int,C)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(abs_abs_int,Ba)),hAPP_int_int(abs_abs_int,D)) <-> hAPP_int_int(abs_abs_int,Aa) = hAPP_int_int(abs_abs_int,Ba) & hAPP_int_int(abs_abs_int,C) = hAPP_int_int(abs_abs_int,D))))) # label(fact_5014_coprime__crossproduct__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4783 (all K_1 all L hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,K_1),L) = hAPP_int_int(abs_abs_int,hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,L),zero_zero_int)),K_1),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,L),hAPP_int_int(div_mod_int(hAPP_int_int(abs_abs_int,K_1)),hAPP_int_int(abs_abs_int,L)))))) # label(fact_5015_gcd__code__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4784 (all X all A_2 all B_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1) = one_one_int -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X),A_2)) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X),B_1)) -> hAPP_int_int(abs_abs_int,X) = one_one_int)))) # label(fact_5016_coprime__common__divisor__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4785 (all R_3 all P_3 all Q_1 (quotient_of(R_3) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1) -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,P_3),Q_1) = one_one_int)) # label(fact_5017_quotient__of__coprime) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4786 (all R_3 all P_3 all Q_1 (normalize(R_3) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1) -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,P_3),Q_1) = one_one_int)) # label(fact_5018_normalize__coprime) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4787 (all Aa all Ba (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,Aa),Ba) = one_one_int <-> (all D_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),D_2)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D_2),Aa)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D_2),Ba)) <-> D_2 = one_one_int)))) # label(fact_5019_coprime__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4788 (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)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_int_nat(nat,X)),hAPP_int_nat(nat,Y)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y))))) # label(fact_5020_transfer__nat__int__gcd_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4789 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(gcd_gcd_nat,hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,X))),hAPP_int_nat(nat,hAPP_int_int(abs_abs_int,Y))))) # label(fact_5021_gcd__int__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4790 (all P_3 all Q_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Q_1)) -> (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,P_3),Q_1) = one_one_int -> normalize(hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1)) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,P_3),Q_1)))) # label(fact_5022_normalize__stable) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4791 (all X_1 quotient_of(X_1) = the_Pr2103884470nt_int(hAPP_f237669397t_bool(hAPP_f461489489t_bool(cOMBS_400904860l_bool,hAPP_f365317245l_bool(hAPP_f1961001761l_bool(cOMBB_1550063917nt_int,fconj),hAPP_f1084724746t_bool(hAPP_f374502857t_bool(cOMBB_569260360nt_int,hAPP_r2115560837t_bool(fequal_rat,X_1)),hAPP_f1065357839nt_rat(hAPP_f1120137083nt_rat(cOMBS_549334880nt_rat,hAPP_f1547007718nt_rat(hAPP_f382317021nt_rat(cOMBB_170828966nt_int,fract),product_fst_int_int)),product_snd_int_int)))),hAPP_f237669397t_bool(hAPP_f461489489t_bool(cOMBS_400904860l_bool,hAPP_f365317245l_bool(hAPP_f1961001761l_bool(cOMBB_1550063917nt_int,fconj),hAPP_f892584630t_bool(hAPP_f492612297t_bool(cOMBB_798864284nt_int,hAPP_i1948725293t_bool(ord_less_int,zero_zero_int)),product_snd_int_int))),hAPP_i119638232t_bool(hAPP_f2018027565t_bool(cOMBC_33652895t_bool,hAPP_f291087797t_bool(hAPP_f214467655t_bool(cOMBB_182850971nt_int,fequal_int),hAPP_f521271395nt_int(hAPP_f1914742907nt_int(cOMBS_2019229620nt_int,hAPP_f1855025978nt_int(hAPP_f1038672605nt_int(cOMBB_1506897658nt_int,gcd_gcd_int),product_fst_int_int)),product_snd_int_int))),one_one_int))))) # label(fact_5023_quotient__of__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4792 (all R_3 exists X_2 (R_3 = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_P1175774780nt_int(product_fst_int_int,X_2)),hAPP_P1175774780nt_int(product_snd_int_int,X_2)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_P1175774780nt_int(product_snd_int_int,X_2))) & hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_P1175774780nt_int(product_fst_int_int,X_2)),hAPP_P1175774780nt_int(product_snd_int_int,X_2)) = one_one_int & (all Y_1 (R_3 = hAPP_int_rat(hAPP_int_fun_int_rat(fract,hAPP_P1175774780nt_int(product_fst_int_int,Y_1)),hAPP_P1175774780nt_int(product_snd_int_int,Y_1)) & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_P1175774780nt_int(product_snd_int_int,Y_1))) & hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,hAPP_P1175774780nt_int(product_fst_int_int,Y_1)),hAPP_P1175774780nt_int(product_snd_int_int,Y_1)) = one_one_int -> Y_1 = X_2)))) # label(fact_5024_quotient__of__unique) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4793 (all Q_1 ((all A_1 all B_3 (Q_1 = hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_1),B_3) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_3)) -> (A_1 != zero_zero_int -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_1),B_3) != one_one_int)))) -> Q_1 = zero_zero_rat)) # label(fact_5025_Rat__cases__nonzero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4794 (all Qa all P_1 ((all A_1 all B_3 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_3)) -> (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_1),B_3) = one_one_int -> hBOOL(hAPP_rat_bool(P_1,hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_1),B_3)))))) -> hBOOL(hAPP_rat_bool(P_1,Qa)))) # label(fact_5026_Rat__induct) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4795 (all Q_1 -(all A_1 all B_3 (Q_1 = hAPP_int_rat(hAPP_int_fun_int_rat(fract,A_1),B_3) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_3)) -> hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_1),B_3) != one_one_int)))) # label(fact_5027_Rat__cases) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4796 (all N all S (hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,S)) -> ((all X_2 (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_2),S)) -> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X_2)))) -> ((all X_2 (hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_2),S)) -> hAPP_f957591787ol_nat(finite_card_int,X_2) = N)) -> hAPP_f521865025ol_nat(hAPP_f93439879ol_nat(big_co1758102091ol_nat,finite_card_int),S) = hAPP_f521865025ol_nat(hAPP_f93439879ol_nat(big_co1758102091ol_nat,cOMBK_1643584600t_bool(N)),S))))) # label(fact_5028_card__setsum__aux) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4797 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> (hBOOL(monoseq_real(Aa)) -> hBOOL(tendsto_nat_real(hAPP_f292751352t_real(hAPP_f1607377819t_real(cOMBB_1533963633al_nat,hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))),hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,ord_at4362885an_nat(zero_zero_nat)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),sequentially))))) # label(fact_5032_summable__Leibniz_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4798 (all S_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),S_1)) -> hBOOL(tendsto_nat_real(hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,powr),real_nat)),hAPP_real_real(uminus_uminus_real,S_1)),zero_zero_real,sequentially)))) # label(fact_5033_LIMSEQ__neg__powr) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4799 (all R_2 hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(plus_plus_real,R_2)),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,uminus_uminus_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),suc)))),R_2,sequentially))) # label(fact_5034_LIMSEQ__inverse__real__of__nat__add__minus) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4800 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X_1)) -> hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_r474017924t_real(power_power_real,X_1)),zero_zero_real,sequentially)))) # label(fact_5035_LIMSEQ__inverse__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4801 (all Aa all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X_1)) -> hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(inverse_divide_real,Aa)),hAPP_r474017924t_real(power_power_real,X_1)),zero_zero_real,sequentially)))) # label(fact_5036_LIMSEQ__divide__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4802 (all F (hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,abs_abs_real),F),zero_zero_real,sequentially)) <-> hBOOL(tendsto_nat_real(F,zero_zero_real,sequentially)))) # label(fact_5038_LIMSEQ__rabs__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4803 (all F all L (hBOOL(tendsto_nat_real(F,L,sequentially)) -> hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,abs_abs_real),F),hAPP_real_real(abs_abs_real,L),sequentially)))) # label(fact_5039_LIMSEQ__imp__rabs) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4804 (all R_2 hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(plus_plus_real,R_2)),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),suc))),R_2,sequentially))) # label(fact_5040_LIMSEQ__inverse__real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4805 (all C (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,C)),one_one_real)) -> hBOOL(tendsto_nat_real(hAPP_r474017924t_real(power_power_real,C),zero_zero_real,sequentially)))) # label(fact_5041_LIMSEQ__rabs__realpow__zero2) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4806 (all C (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,C)),one_one_real)) -> hBOOL(tendsto_nat_real(hAPP_r474017924t_real(power_power_real,hAPP_real_real(abs_abs_real,C)),zero_zero_real,sequentially)))) # label(fact_5042_LIMSEQ__rabs__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4807 (all X_1 all Aa (hBOOL(monoseq_real(Aa)) -> (hBOOL(tendsto_nat_real(Aa,X_1,sequentially)) -> (all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,N_2)),X_1))) & (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,M_2)),hAPP_nat_real(Aa,N_2))))) | (all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),hAPP_nat_real(Aa,N_2)))) & (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,N_2)),hAPP_nat_real(Aa,M_2)))))))) # label(fact_5043_monoseq__le) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4808 (all Y_3 all Y_2 all X_3 all X_1 (hBOOL(tendsto_nat_real(X_3,X_1,sequentially)) -> (hBOOL(tendsto_nat_real(Y_3,Y_2,sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_3),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(X_3,N_2)),hAPP_nat_real(Y_3,N_2))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_2)))))) # label(fact_5044_LIMSEQ__le) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4809 (all Aa all X_3 all X_1 (hBOOL(tendsto_nat_real(X_3,X_1,sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_3),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(X_3,N_2)),Aa)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Aa))))) # label(fact_5045_LIMSEQ__le__const2) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4810 (all Aa all X_3 all X_1 (hBOOL(tendsto_nat_real(X_3,X_1,sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_3),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),hAPP_nat_real(X_3,N_2))))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_1))))) # label(fact_5046_LIMSEQ__le__const) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4811 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)) -> hBOOL(tendsto_nat_real(hAPP_r474017924t_real(power_power_real,X_1),zero_zero_real,sequentially))))) # label(fact_5047_LIMSEQ__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4812 (all R_2 hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(times_times_real,R_2)),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(plus_plus_real,one_one_real)),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,uminus_uminus_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),suc))))),R_2,sequentially))) # label(fact_5048_LIMSEQ__inverse__real__of__nat__add__minus__mult) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4813 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> (hBOOL(monoseq_real(Aa)) -> hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)))))) # label(fact_5049_summable__Leibniz_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4814 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,X_1)),one_one_real)) -> hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,hAPP_r1250527377l_real(inverse_divide_real,one_one_real)),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,real_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))))),hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,hAPP_r474017924t_real(power_power_real,X_1)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,times_times_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))),zero_zero_real,sequentially)))) # label(fact_5050_zeroseq__arctan__series) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4815 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> (hBOOL(monoseq_real(Aa)) -> hBOOL(tendsto_nat_real(hAPP_f292751352t_real(hAPP_f1607377819t_real(cOMBB_1533963633al_nat,hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))),hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,ord_at4362885an_nat(zero_zero_nat)),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),sequentially))))) # label(fact_5052_summable__Leibniz_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4816 (all N all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(Aa,N_2)))) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,hAPP_nat_nat(suc,N_2))),hAPP_nat_real(Aa,N_2)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N)),one_one_nat))))))))) # label(fact_5053_summable__Leibniz_H_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4817 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(Aa,N_2)))) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,hAPP_nat_nat(suc,N_2))),hAPP_nat_real(Aa,N_2)))) -> hBOOL(tendsto_nat_real(hAPP_f292751352t_real(hAPP_f1607377819t_real(cOMBB_1533963633al_nat,hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))),hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,ord_at4362885an_nat(zero_zero_nat)),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,plus_plus_nat),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),one_one_nat))),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),sequentially)))))) # label(fact_5054_summable__Leibniz_H_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4818 (all X_3 all Aa (hBOOL(tendsto_nat_complex(X_3,Aa,sequentially)) -> hBOOL(tendsto_nat_complex(hAPP_f1646117269omplex(hAPP_f1457396693omplex(cOMBB_117013006ex_nat,cnj),X_3),hAPP_complex_complex(cnj,Aa),sequentially)))) # label(fact_5055_cnj_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4819 (all X_3 all Aa (hBOOL(tendsto_nat_complex(X_3,Aa,sequentially)) -> hBOOL(tendsto_nat_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,re),X_3),hAPP_complex_real(re,Aa),sequentially)))) # label(fact_5056_Re_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4820 (all X_3 all Aa (hBOOL(tendsto_nat_complex(X_3,Aa,sequentially)) -> hBOOL(tendsto_nat_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,im),X_3),hAPP_complex_real(im,Aa),sequentially)))) # label(fact_5057_Im_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4821 (all Y_3 all Ba all X_3 all Aa (hBOOL(tendsto_nat_real(X_3,Aa,sequentially)) -> (hBOOL(tendsto_nat_real(Y_3,Ba,sequentially)) -> hBOOL(tendsto_nat_complex(hAPP_f219720582omplex(hAPP_f1052840010omplex(cOMBS_696648398omplex,hAPP_f23851874omplex(hAPP_f406530075omplex(cOMBB_1714920583ex_nat,complex),X_3)),Y_3),hAPP_real_complex(hAPP_r265291036omplex(complex,Aa),Ba),sequentially))))) # label(fact_5058_LIMSEQ__Complex) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4822 (all P_1 all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),Ba)) -> (hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,minus_minus_real),hAPP_f73570213t_real(hAPP_f918606171t_real(cOMBB_64450052al_nat,produc1935615926l_real),bolzano_bisect(P_1,Aa,Ba)))),hAPP_f73570213t_real(hAPP_f918606171t_real(cOMBB_64450052al_nat,produc556554744l_real),bolzano_bisect(P_1,Aa,Ba))),zero_zero_real,sequentially)) -> (exists L_1 ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_P731461727l_real(produc1935615926l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2))),L_1))) & hBOOL(tendsto_nat_real(hAPP_f73570213t_real(hAPP_f918606171t_real(cOMBB_64450052al_nat,produc1935615926l_real),bolzano_bisect(P_1,Aa,Ba)),L_1,sequentially)) & (all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,L_1),hAPP_P731461727l_real(produc556554744l_real,hAPP_n332733730l_real(bolzano_bisect(P_1,Aa,Ba),N_2))))) & hBOOL(tendsto_nat_real(hAPP_f73570213t_real(hAPP_f918606171t_real(cOMBB_64450052al_nat,produc556554744l_real),bolzano_bisect(P_1,Aa,Ba)),L_1,sequentially))))))))) # label(fact_5059_Bolzano__nest__unique) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4823 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(Aa,N_2)))) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,hAPP_nat_nat(suc,N_2))),hAPP_nat_real(Aa,N_2)))) -> hBOOL(tendsto_nat_real(hAPP_f292751352t_real(hAPP_f1607377819t_real(cOMBB_1533963633al_nat,hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))),hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,ord_at4362885an_nat(zero_zero_nat)),hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),sequentially)))))) # label(fact_5060_summable__Leibniz_H_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4824 (all N all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(Aa,N_2)))) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,hAPP_nat_nat(suc,N_2))),hAPP_nat_real(Aa,N_2)))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N)))),hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)))))))) # label(fact_5061_summable__Leibniz_H_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4825 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> (hBOOL(monoseq_real(Aa)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(Aa,zero_zero_nat)),zero_zero_real)) -> (all N_2 hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))),hAPP_r1134773055l_bool(ord_at1589558736t_real(hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_2)),one_one_nat)))),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_2))))))))))) # label(fact_5062_summable__Leibniz_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4826 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> (hBOOL(monoseq_real(Aa)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(Aa,zero_zero_nat))) -> (all N_2 hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,hAPP_f352196356l_real(suminf_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))),hAPP_r1134773055l_bool(ord_at1589558736t_real(hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_2)))),hAPP_f1406902706l_real(hAPP_f1509287679l_real(big_co604158596t_real,hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa)),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),N_2)),one_one_nat))))))))))) # label(fact_5063_summable__Leibniz_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4827 (all Y_2 all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Y_2),X_1)) -> comple124823625p_real(hAPP_r1134773055l_bool(ord_at1589558736t_real(Y_2),X_1)) = X_1)) # label(fact_5064_Sup__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4828 (all Aa (hBOOL(tendsto_nat_real(Aa,zero_zero_real,sequentially)) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(Aa,N_2)))) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(Aa,hAPP_nat_nat(suc,N_2))),hAPP_nat_real(Aa,N_2)))) -> hBOOL(summable_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,times_times_real),hAPP_r474017924t_real(power_power_real,hAPP_int_real(number267125858f_real,min)))),Aa))))))) # label(fact_5065_summable) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4829 (all L all U hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U)))) # label(fact_5066_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4830 (all L all U hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_i1948725293t_bool(ord_at875362053st_int(L),U)))) # label(fact_5067_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4831 (all P_1 all N ((exists M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) & hBOOL(hAPP_nat_bool(P_1,M_2)))) <-> (exists X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),N))) & hBOOL(hAPP_nat_bool(P_1,X_2)))))) # label(fact_5068_ex__nat__less) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4832 (all P_1 all N ((all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) -> hBOOL(hAPP_nat_bool(P_1,M_2)))) <-> (all X_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),N))) -> hBOOL(hAPP_nat_bool(P_1,X_2)))))) # label(fact_5069_all__nat__less) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4833 (all Y_2 all X_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) -> hBOOL(hAPP_f448129468l_bool(nat_nat_set,hAPP_i1948725293t_bool(ord_at875362053st_int(X_1),Y_2))))) # label(fact_5070_SetInterval_Otransfer__nat__int__set__function__closures) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4834 (all L all U hAPP_n1699378549t_bool(ord_at4362885an_nat(L),hAPP_nat_nat(suc,U)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U)) # label(fact_5071_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4835 (all N hAPP_nat_nat(fact_fact_nat,N) = big_co1705425894at_nat(cOMBI_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(one_one_nat),N))) # label(fact_5072_fact__altdef__nat) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4836 (all K_1 all I_1 all J image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(I_1),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) # label(fact_5073_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4837 (all I_1 all J image_nat_nat(suc,hAPP_n1699378549t_bool(ord_at238088361st_nat(I_1),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,I_1)),hAPP_nat_nat(suc,J))) # label(fact_5074_image__Suc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4838 (all M all N hAPP_n1699378549t_bool(ord_at238088361st_nat(M),N) = image_int_nat(nat,hAPP_i1948725293t_bool(ord_at875362053st_int(hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,N)))) # label(fact_5075_SetInterval_Otransfer__nat__int__set__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4839 (all Aa hBOOL(tendst1507391555omplex(cnj,hAPP_complex_complex(cnj,Aa),at_complex(Aa)))) # label(fact_5076_cnj_Ocont) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4840 (all Aa hBOOL(tendsto_complex_real(re,hAPP_complex_real(re,Aa),at_complex(Aa)))) # label(fact_5077_Re_Ocont) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4841 (all Aa hBOOL(tendsto_complex_real(im,hAPP_complex_real(im,Aa),at_complex(Aa)))) # label(fact_5078_Im_Ocont) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4842 (all L all U hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U)),L)) # label(fact_5079_card__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4843 (all L all U hAPP_i1948725293t_bool(ord_at641636577an_int(L),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U),one_one_int)) = hAPP_i1948725293t_bool(ord_at875362053st_int(L),U)) # label(fact_5080_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4844 (all K_1 all F (hAPP_nat_nat(F,zero_zero_nat) = zero_zero_nat -> hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),K_1)) = hAPP_f22106695ol_nat(hAPP_f782000547ol_nat(big_co387207925at_nat,F),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),K_1)))) # label(fact_5081_setsum__shift__lb__Suc0__0) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4845 (all L all U hAPP_f957591787ol_nat(finite_card_int,hAPP_i1948725293t_bool(ord_at875362053st_int(L),U)) = hAPP_int_nat(nat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U),L)),one_one_int))) # label(fact_5082_card__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4846 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(div_div_nat,hAPP_nat_nat(fact_fact_nat,M)),hAPP_nat_nat(fact_fact_nat,N)) = big_co1705425894at_nat(cOMBI_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)),M)))) # label(fact_5083_fact__div__fact) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4847 (all N (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N)) -> hAPP_int_int(fact_fact_int,N) = big_co1548731110nt_int(cOMBI_int,hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),N)))) # label(fact_5084_fact__altdef__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4848 (all F all L all C (hBOOL(tendsto_real_real(F,L,at_real(C))) -> (L != zero_zero_real -> (exists R_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_1)) & (all X_2 (X_2 != C & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C),X_2))),R_1)) -> hAPP_real_real(F,X_2) != zero_zero_real))))))) # label(fact_5086_LIM__fun__not__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4849 (all F all L all C (hBOOL(tendsto_real_real(F,L,at_real(C))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),L)) -> (exists R_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_1)) & (all X_2 (X_2 != C & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C),X_2))),R_1)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(F,X_2)))))))))) # label(fact_5087_LIM__fun__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4850 (all F all L all C (hBOOL(tendsto_real_real(F,L,at_real(C))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,L),zero_zero_real)) -> (exists R_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_1)) & (all X_2 (X_2 != C & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,C),X_2))),R_1)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,X_2)),zero_zero_real))))))))) # label(fact_5088_LIM__fun__less__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4851 (all T all A all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)))))))) # label(fact_5089_aset_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4852 (all T all A all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,T),one_one_int)),A)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),T)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)),T)))))))) # label(fact_5090_aset_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4853 (all T all B all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,T),one_one_int)),B)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,T),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1))))))))) # label(fact_5091_bset_I8_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4854 (all T all B all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),T)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1)),T))))))) # label(fact_5092_bset_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4855 (all T all B all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,T),one_one_int)),B)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (X_2 = T -> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1) = T)))))) # label(fact_5093_bset_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4856 (all T all A all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,T),one_one_int)),A)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (X_2 = T -> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1) = T)))))) # label(fact_5094_aset_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4857 (all T all A all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,T),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,T),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)))))))) # label(fact_5095_aset_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4858 (all T all B all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),T)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1)),T))))))) # label(fact_5096_bset_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4859 (all T all A all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,T),A)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),T)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)),T)))))))) # label(fact_5097_aset_I5_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4860 (all T all B all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,T),B)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,T),X_2)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,T),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1))))))))) # label(fact_5098_bset_I7_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4861 (all T all A all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,T),A)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (X_2 != T -> hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1) != T)))))) # label(fact_5099_aset_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4862 (all T all B all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,T),B)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (X_2 != T -> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1) != T)))))) # label(fact_5100_bset_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4863 (all P_1 all D (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) -> ((all X_2 all K (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D)))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_1,X1))) <-> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D))) & hBOOL(hAPP_int_bool(P_1,X_2)))))))) # label(fact_5101_periodic__finite__ex) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4864 (all T all A all D all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),T))) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)),T)))))))) # label(fact_5102_aset_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4865 (all T all B all D all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),T))) -> -hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1)),T)))))))) # label(fact_5103_bset_I10_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4866 (all T all B all D all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),T))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1)),T)))))))) # label(fact_5104_bset_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4867 (all T all A all D all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),D_1)) -> (all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),T))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,D),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)),T)))))))) # label(fact_5105_aset_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4868 (all X_3 ((all R_1 exists N_3 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_3),N_2)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,R_1),hAPP_nat_real(X_3,N_2))))) -> hBOOL(tendsto_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,inverse_inverse_real),X_3),zero_zero_real,sequentially)))) # label(fact_5106_LIMSEQ__inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4869 (all R_3 all X hAPP_complex_complex(cnj,hAPP_complex_complex(scaleR1652505878omplex(R_3),X)) = hAPP_complex_complex(scaleR1652505878omplex(R_3),hAPP_complex_complex(cnj,X))) # label(fact_5107_cnj_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4870 (all R_3 all X hAPP_complex_real(re,hAPP_complex_complex(scaleR1652505878omplex(R_3),X)) = hAPP_real_real(scaleR_scaleR_real(R_3),hAPP_complex_real(re,X))) # label(fact_5108_Re_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4871 (all R_3 all X hAPP_complex_real(im,hAPP_complex_complex(scaleR1652505878omplex(R_3),X)) = hAPP_real_real(scaleR_scaleR_real(R_3),hAPP_complex_real(im,X))) # label(fact_5109_Im_OscaleR) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4872 (all A_2 all X hAPP_real_real(scaleR_scaleR_real(A_2),X) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,A_2),X)) # label(fact_5110_real__scaleR__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4873 (all R_3 all A_2 all B_1 hAPP_complex_complex(scaleR1652505878omplex(R_3),hAPP_real_complex(hAPP_r265291036omplex(complex,A_2),B_1)) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),A_2)),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),B_1))) # label(fact_5111_complex__scaleR) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4874 (all R_3 all X hAPP_complex_real(im,hAPP_complex_complex(scaleR1652505878omplex(R_3),X)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_complex_real(im,X))) # label(fact_5112_complex__Im__scaleR) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4875 (all R_3 all X hAPP_complex_real(re,hAPP_complex_complex(scaleR1652505878omplex(R_3),X)) = hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_complex_real(re,X))) # label(fact_5113_complex__Re__scaleR) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4876 (all X hAPP_complex_complex(sgn_sgn_complex,X) = hAPP_complex_complex(scaleR1652505878omplex(hAPP_real_real(inverse_inverse_real,hAPP_complex_real(norm_norm_complex,X))),X)) # label(fact_5114_complex__sgn__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4877 (all R_3 all X hAPP_complex_complex(scaleR1652505878omplex(R_3),X) = hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_complex_real(re,X))),hAPP_real_real(hAPP_r1250527377l_real(times_times_real,R_3),hAPP_complex_real(im,X)))) # label(fact_5115_complex__scaleR__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4878 (all A_2 all B_1 (hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1) != zero_zero_int -> (exists A_3 exists B_2 (A_2 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_3),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)) & B_1 = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_2),B_1)) & hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,A_3),B_2) = one_one_int)))) # label(fact_5118_gcd__coprime__exists__int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4879 (all V all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))),zero_zero_nat),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))),N)))) # label(fact_5119_min__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4880 (all N all V hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,N)),hAPP_int_nat(number_number_of_nat,V)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))),zero_zero_nat),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N),hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V))))))) # label(fact_5120_min__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4881 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_1),N_1))) # label(fact_5121_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4882 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N_1),zero_zero_nat) = zero_zero_nat) # label(fact_5122_min__0R) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4883 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,zero_zero_nat),N_1) = zero_zero_nat) # label(fact_5123_min__0L) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4884 (all M_1 all I all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),I)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_1),N_1)),I)) # label(fact_5124_min__diff) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4885 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,ord_min_nat),N))),M)) # label(fact_5125_min__Suc2) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4886 (all N all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,N)),M) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(ord_min_nat,N))),M)) # label(fact_5126_min__Suc1) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4887 (all Y_3 all X_3 ((exists A_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),A_1)) & (all N_2 hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,hAPP_nat_rat(X_3,N_2))),A_1))))) -> (hBOOL(vanishes(Y_3)) -> hBOOL(vanishes(hAPP_f2062659861at_rat(hAPP_f1131305186at_rat(cOMBS_nat_rat_rat,hAPP_f1830834240at_rat(hAPP_f1073644437at_rat(cOMBB_1926947at_nat,times_times_rat),X_3)),Y_3)))))) # label(fact_5127_vanishes__mult__bounded) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4888 (all N all M (hBOOL(hAPP_int_bool(nat_is_nat,M)) -> (hBOOL(hAPP_int_bool(nat_is_nat,N)) -> hAPP_i1948725293t_bool(ord_at875362053st_int(M),N) = image_nat_int(semiri1621563631at_int,hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_int_nat(nat,M)),hAPP_int_nat(nat,N)))))) # label(fact_5128_SetInterval_Otransfer__int__nat__set__functions) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4889 (all X_1 (hBOOL(hAPP_int_bool(nat_is_nat,X_1)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)))) # label(fact_5129_is__nat__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4890 (all Z_1 hBOOL(hAPP_int_bool(nat_is_nat,hAPP_nat_int(semiri1621563631at_int,Z_1)))) # label(fact_5130_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4891 (all Y all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> (hBOOL(hAPP_int_bool(nat_is_nat,Y)) -> hBOOL(hAPP_int_bool(nat_is_nat,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))))) # label(fact_5131_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4892 (all X_1 all A (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) -> hBOOL(hAPP_int_bool(nat_is_nat,X_1))))) # label(fact_5134_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4893 (all N_1 all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> hBOOL(hAPP_int_bool(nat_is_nat,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X),N_1))))) # label(fact_5135_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4894 (all Y all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> (hBOOL(hAPP_int_bool(nat_is_nat,Y)) -> hBOOL(hAPP_int_bool(nat_is_nat,hAPP_int_int(div_mod_int(X),Y)))))) # label(fact_5136_Divides_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4895 (all Y all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> (hBOOL(hAPP_int_bool(nat_is_nat,Y)) -> hBOOL(hAPP_int_bool(nat_is_nat,hAPP_int_int(hAPP_int_fun_int_int(div_div_int,X),Y)))))) # label(fact_5137_Divides_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4896 (all Y all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> (hBOOL(hAPP_int_bool(nat_is_nat,Y)) -> hBOOL(hAPP_int_bool(nat_is_nat,hAPP_int_int(nat_tsub(X),Y)))))) # label(fact_5138_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4897 (all Y all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> (hBOOL(hAPP_int_bool(nat_is_nat,Y)) -> hBOOL(hAPP_int_bool(nat_is_nat,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)))))) # label(fact_5139_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4898 (all X_3 (hBOOL(vanishes(X_3)) -> hBOOL(vanishes(hAPP_f2062659861at_rat(hAPP_f1082758869at_rat(cOMBB_rat_rat_nat,uminus_uminus_rat),X_3))))) # label(fact_5140_vanishes__minus) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4899 (all C (hBOOL(vanishes(cOMBK_rat_nat(C))) <-> C = zero_zero_rat)) # label(fact_5141_vanishes__const) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4900 (all Y_3 all X_3 (hBOOL(vanishes(X_3)) -> (hBOOL(vanishes(Y_3)) -> hBOOL(vanishes(hAPP_f2062659861at_rat(hAPP_f1131305186at_rat(cOMBS_nat_rat_rat,hAPP_f1830834240at_rat(hAPP_f1073644437at_rat(cOMBB_1926947at_nat,minus_minus_rat),X_3)),Y_3)))))) # label(fact_5142_vanishes__diff) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4901 (all Y_3 all X_3 (hBOOL(vanishes(X_3)) -> (hBOOL(vanishes(Y_3)) -> hBOOL(vanishes(hAPP_f2062659861at_rat(hAPP_f1131305186at_rat(cOMBS_nat_rat_rat,hAPP_f1830834240at_rat(hAPP_f1073644437at_rat(cOMBB_1926947at_nat,plus_plus_rat),X_3)),Y_3)))))) # label(fact_5143_vanishes__add) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4902 (all Y_2 all X_1 (hBOOL(hAPP_int_bool(nat_is_nat,X_1)) -> hBOOL(hAPP_f448129468l_bool(nat_nat_set,hAPP_i1948725293t_bool(ord_at875362053st_int(X_1),Y_2))))) # label(fact_5144_SetInterval_Otransfer__int__nat__set__function__closures) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4903 (all Y all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> (hBOOL(hAPP_int_bool(nat_is_nat,Y)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(gcd_gcd_int,X),Y)))))) # label(fact_5146_transfer__int__nat__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4904 (all X (hBOOL(hAPP_int_bool(nat_is_nat,X)) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(fact_fact_int,X))))) # label(fact_5147_transfer__int__nat__factorial__closure) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4905 (all A all X_1 (hBOOL(hAPP_int_bool(nat_is_nat,X_1)) -> (hBOOL(hAPP_f448129468l_bool(nat_nat_set,A)) -> (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_int_nat(nat,X_1)),image_int_nat(nat,A))))))) # label(fact_5148_transfer__int__nat__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.85 4906 (all R_2 all X_3 (hBOOL(vanishes(X_3)) -> (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),R_2)) -> (exists K all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,hAPP_nat_rat(X_3,N_2))),R_2))))))) # label(fact_5150_vanishesD) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4907 (all X_3 (hBOOL(vanishes(X_3)) <-> (all R_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),R_1)) -> (exists K all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,hAPP_nat_rat(X_3,N_2))),R_1)))))))) # label(fact_5151_vanishes__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4908 (all X_3 ((all R_1 (hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,zero_zero_rat),R_1)) -> (exists K all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N_2)) -> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_rat_rat(abs_abs_rat,hAPP_nat_rat(X_3,N_2))),R_1)))))) -> hBOOL(vanishes(X_3)))) # label(fact_5152_vanishesI) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4909 (all M all X_2 all Xa (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcongm(M),X_2),Xa)) <-> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(X_2),Xa),M)))) # label(fact_5153_zcongm__def) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4910 (all A all P_2 all P_1 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),X_2)) -> (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_2,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),A)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)))))) -> ((all X_2 all K (hBOOL(hAPP_int_bool(P_2,X_2)) <-> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_1,X1))) <-> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) & hBOOL(hAPP_int_bool(P_2,X_2)))) | (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) & (exists Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),A)) & hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Xa),X_2))))))))))))) # label(fact_5154_cppi) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4911 (all A all B all M (hBOOL(hAPP_f1469637905l_bool(hAPP_P1681069257l_bool(member308914164t_bool,hAPP_f538843494t_bool(hAPP_f1418982953t_bool(produc713279741t_bool,A),B)),bijR_int_int(zcongm(M)))) -> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(zcong(big_co1548731110nt_int(cOMBI_int,A)),big_co1548731110nt_int(cOMBI_int,B)),M)))) # label(fact_5155_bijzcong__zcong__prod) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4912 (all B all P_2 all P_1 all D_1 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) -> ((exists Z all X_2 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z)) -> (hBOOL(hAPP_int_bool(P_1,X_2)) <-> hBOOL(hAPP_int_bool(P_2,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) -> (all Xb (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xb),B)) -> X_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xb),Xa))))) -> (hBOOL(hAPP_int_bool(P_1,X_2)) -> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1)))))) -> ((all X_2 all K (hBOOL(hAPP_int_bool(P_2,X_2)) <-> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))))) -> ((exists X1 hBOOL(hAPP_int_bool(P_1,X1))) <-> (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) & hBOOL(hAPP_int_bool(P_2,X_2)))) | (exists X_2 (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),hAPP_i1948725293t_bool(ord_at875362053st_int(one_one_int),D_1))) & (exists Xa (hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Xa),B)) & hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),X_2))))))))))))) # label(fact_5156_cpmi) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4913 (all L all F ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(F,N_2)),hAPP_nat_real(F,hAPP_nat_nat(suc,N_2))))) -> ((all N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(F,N_2)),L))) -> ((all E (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),E)) -> (exists N_2 hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,L),hAPP_real_real(hAPP_r1250527377l_real(plus_plus_real,hAPP_nat_real(F,N_2)),E)))))) -> hBOOL(tendsto_nat_real(F,L,sequentially)))))) # label(fact_5157_increasing__LIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4914 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hBOOL(hAPP_real_bool(isCont_real_real(hAPP_n546711566l_real(root,N)),X_1)))) # label(fact_5158_isCont__real__root) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4915 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hBOOL(hAPP_real_bool(isCont_real_real(ln),X_1)))) # label(fact_5159_isCont__ln) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4916 (all Aa hBOOL(hAPP_real_bool(isCont_real_real(abs_abs_real),Aa))) # label(fact_5160_isCont__abs) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4917 (all Aa hBOOL(hAPP_complex_bool(isCont_complex_real(im),Aa))) # label(fact_5161_Im_OisCont) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4918 (all Aa hBOOL(hAPP_complex_bool(isCont_complex_real(re),Aa))) # label(fact_5162_Re_OisCont) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4919 (all Aa hBOOL(hAPP_complex_bool(isCont156215680omplex(cnj),Aa))) # label(fact_5163_cnj_OisCont) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4920 (all X_1 hBOOL(hAPP_real_bool(isCont_real_real(sqrt),X_1))) # label(fact_5164_isCont__real__sqrt) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4921 (all X_1 hBOOL(hAPP_real_bool(isCont_real_real(cos),X_1))) # label(fact_5165_isCont__cos) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4922 (all X_1 hBOOL(hAPP_real_bool(isCont_real_real(arctan),X_1))) # label(fact_5166_isCont__arctan) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4923 (all X_1 hBOOL(hAPP_real_bool(isCont_real_real(sin),X_1))) # label(fact_5167_isCont__sin) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4924 (all X_1 (hAPP_real_real(cos,X_1) != zero_zero_real -> hBOOL(hAPP_real_bool(isCont_real_real(tan),X_1)))) # label(fact_5168_isCont__tan) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4925 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hBOOL(hAPP_real_bool(isCont_real_real(hAPP_n546711566l_real(root,N)),zero_zero_real)))) # label(fact_5169_isCont__root__zero) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4926 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),zero_zero_real)) -> hBOOL(hAPP_real_bool(isCont_real_real(hAPP_n546711566l_real(root,N)),X_1))))) # label(fact_5170_isCont__root__neg) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4927 (all X_1 all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) -> hBOOL(hAPP_real_bool(isCont_real_real(hAPP_n546711566l_real(root,N)),X_1))))) # label(fact_5171_isCont__root__pos) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4928 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)) -> hBOOL(hAPP_real_bool(isCont_real_real(arccos),X_1))))) # label(fact_5172_isCont__arccos) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4929 (all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,min)),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),one_one_real)) -> hBOOL(hAPP_real_bool(isCont_real_real(arcsin),X_1))))) # label(fact_5173_isCont__arcsin) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4930 (all F all Ba all X_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Ba),X_1)) -> ((all X_2 (hBOOL(hAPP_f1501066425l_bool(hAPP_r1130899993l_bool(member_real,X_2),hAPP_r1134773055l_bool(ord_gr788844697n_real(Ba),X_1))) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(F,X_2))))) -> (hBOOL(hAPP_real_bool(isCont_real_real(F),X_1)) -> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(F,X_1))))))) # label(fact_5174_LIM__less__bound) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4931 (all Ba all Aa all F all G all X_1 all D_1 (hBOOL(hAPP_real_bool(deriv_real(F,hAPP_real_real(G,X_1)),D_1)) -> (D_1 != zero_zero_real -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Ba)) -> ((all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Y_1)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_1),Ba)) -> hAPP_real_real(F,hAPP_real_real(G,Y_1)) = Y_1)) -> (hBOOL(hAPP_real_bool(isCont_real_real(G),X_1)) -> hBOOL(hAPP_real_bool(deriv_real(G,X_1),hAPP_real_real(inverse_inverse_real,D_1)))))))))) # label(fact_5175_DERIV__inverse__function) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4932 (all G all F all X_1 all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hAPP_real_real(G,hAPP_real_real(F,Z)) = Z)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hBOOL(hAPP_real_bool(isCont_real_real(F),Z)))) -> hBOOL(hAPP_real_bool(isCont_real_real(G),hAPP_real_real(F,X_1))))))) # label(fact_5176_isCont__inv__fun) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4933 (all X_1 all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> hBOOL(hAPP_real_bool(isCont_real_real(F),X_2)))) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Ba)) -> hBOOL(hAPP_real_bool(deriv_real(F,X_2),zero_zero_real)))) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_1)) -> (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Ba)) -> hAPP_real_real(F,X_1) = hAPP_real_real(F,Aa))))))) # label(fact_5177_DERIV__isconst2) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4934 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> hBOOL(hAPP_real_bool(isCont_real_real(F),X_2)))) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Ba)) -> hBOOL(hAPP_real_bool(deriv_real(F,X_2),zero_zero_real)))) -> hAPP_real_real(F,Ba) = hAPP_real_real(F,Aa))))) # label(fact_5178_DERIV__isconst__end) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4935 (all F all Aa all Ba (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),Ba)) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> hBOOL(hAPP_real_bool(isCont_real_real(F),X_2)))) -> ((all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Ba)) -> hBOOL(hAPP_real_bool(deriv_real(F,X_2),zero_zero_real)))) -> (all X_2 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Aa),X_2)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Ba)) -> hAPP_real_real(F,X_2) = hAPP_real_real(F,Aa))))))) # label(fact_5179_DERIV__isconst1) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4936 (all G all F all X_1 all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hAPP_real_real(G,hAPP_real_real(F,Z)) = Z)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hBOOL(hAPP_real_bool(isCont_real_real(F),Z)))) -> (exists Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,Z)),hAPP_real_real(F,X_1))))))))) # label(fact_5180_lemma__isCont__inj2) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4937 (all G all F all X_1 all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hAPP_real_real(G,hAPP_real_real(F,Z)) = Z)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hBOOL(hAPP_real_bool(isCont_real_real(F),Z)))) -> (exists E (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),E)) & (all Y_1 (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Y_1),hAPP_real_real(F,X_1))))) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Y_1),hAPP_real_real(F,X_1)))),E)) -> hAPP_real_real(F,hAPP_real_real(G,Y_1)) = Y_1)))))))) # label(fact_5181_isCont__inv__fun__inv) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4938 (all G all F all X_1 all D (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),D)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hAPP_real_real(G,hAPP_real_real(F,Z)) = Z)) -> ((all Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) -> hBOOL(hAPP_real_bool(isCont_real_real(F),Z)))) -> (exists Z (hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(abs_abs_real,hAPP_real_real(hAPP_r1250527377l_real(minus_minus_real,Z),X_1))),D)) & hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(F,X_1)),hAPP_real_real(F,Z))))))))) # label(fact_5182_lemma__isCont__inj) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4939 (all N hAPP_n1699378549t_bool(ord_atMost_nat,N) = image_int_nat(nat,hAPP_i1948725293t_bool(ord_at875362053st_int(zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N)))) # label(fact_5183_SetInterval_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4940 (all V all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_int_nat(number_number_of_nat,V)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,hAPP_int_bool(nat_neg,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))),hAPP_nat_nat(suc,N)),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_int_nat(nat,hAPP_int_int(number_number_of_int,hAPP_int_int(pred,V)))),N)))) # label(fact_5184_max__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4941 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_atMost_nat,K_1)))) # label(fact_5185_finite__atMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4942 (all N hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),N) = hAPP_n1699378549t_bool(ord_atMost_nat,N)) # label(fact_5186_atLeast0AtMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4943 (all U hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(ord_atMost_nat,U)) = hAPP_nat_nat(suc,U)) # label(fact_5187_card__atMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4944 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,M_1),N_1))) # label(fact_5188_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4945 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,N_1),zero_zero_nat) = N_1) # label(fact_5189_max__0R) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4946 (all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,zero_zero_nat),N_1) = N_1) # label(fact_5190_max__0L) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4947 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M_1)),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,N_1),M_1)) # label(fact_5191_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4948 (all N all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(suc,N)),M) = hAPP_nat_nat(nat_case_nat(hAPP_nat_nat(suc,N),hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(ord_max_nat,N))),M)) # label(fact_5192_max__Suc1) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4949 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(nat_case_nat(hAPP_nat_nat(suc,N),hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,suc),hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,ord_max_nat),N))),M)) # label(fact_5193_max__Suc2) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4950 (all K_1 hAPP_n1699378549t_bool(ord_lessThan_nat,hAPP_nat_nat(suc,K_1)) = hAPP_n1699378549t_bool(ord_atMost_nat,K_1)) # label(fact_5194_lessThan__Suc__atMost) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4951 (all S (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,S)) <-> (exists K hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,S),hAPP_n1699378549t_bool(ord_atMost_nat,K)))))) # label(fact_5195_finite__nat__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4952 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4953 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4954 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4955 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4956 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4957 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4958 (all Q all P (-hBOOL(P) | hBOOL(fdisj(P,Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4959 (all P all Q (-hBOOL(Q) | hBOOL(fdisj(P,Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4960 (all P all Q (-hBOOL(fdisj(P,Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4961 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4962 (all Q all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fimplies(P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4963 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(fimplies(P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4964 (all P all Q (-hBOOL(hAPP_bool_bool(fimplies(P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4965 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4966 (all X all Y hAPP_int_int(hAPP_int_fun_int_int(hAPP_b1463609396nt_int(if_int,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4967 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4968 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4969 (all X all Y hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_b992065680at_nat(if_nat,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4970 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4971 (all P all X (-hBOOL(hAPP_int_bool(P,X)) | hBOOL(hAPP_f448129468l_bool(fEx_int,P)))) # label(help_fEx_1_1_fEx_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4972 (all P all X (-hBOOL(hAPP_nat_bool(P,X)) | hBOOL(hAPP_f54304608l_bool(fEx_nat,P)))) # label(help_fEx_1_1_fEx_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4973 (all P hAPP_int_int(cOMBI_int,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4974 (all P hAPP_nat_nat(cOMBI_nat,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4975 (all X all Y (-hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4976 (all X all Y (X != Y | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Int__Oint_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4977 (all X all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4978 (all X all Y (X != Y | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4979 (all X all Y (-hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(fequal_rat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Rat__Orat_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4980 (all X all Y (X != Y | hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(fequal_rat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Rat__Orat_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4981 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(hAPP_b646336293l_real(if_real,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__RealDef__Oreal_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4982 (all X all Y hAPP_real_real(hAPP_r1250527377l_real(hAPP_b646336293l_real(if_real,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__RealDef__Oreal_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4983 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__RealDef__Oreal_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4984 (all P hAPP_real_real(cOMBI_real,P) = P) # label(help_COMBI_1_1_COMBI_000tc__RealDef__Oreal_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4985 (all X all Y (-hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(fequal_real,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__RealDef__Oreal_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4986 (all X all Y (X != Y | hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(fequal_real,X),Y)))) # label(help_fequal_2_1_fequal_000tc__RealDef__Oreal_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4987 (all P all Q hAPP_nat_rat(cOMBK_rat_nat(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Rat__Orat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4988 (all P all Q (is_bool(P) -> hAPP_nat_bool(cOMBK_bool_nat(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4989 (all X all Y hAPP_P1975530577nt_int(hAPP_P1145851913nt_int(hAPP_b40753821nt_int(if_Pro1731782967nt_int,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4990 (all X all Y hAPP_P1975530577nt_int(hAPP_P1145851913nt_int(hAPP_b40753821nt_int(if_Pro1731782967nt_int,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4991 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4992 (all P all Q all R hAPP_int_int(hAPP_f1356864277nt_int(hAPP_f747162069nt_int(cOMBB_int_int_int,P),Q),R) = hAPP_int_int(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Int__Oint_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4993 (all P all Q all R hAPP_nat_int(hAPP_f1139079189at_int(hAPP_f1431025877at_int(cOMBB_int_int_nat,P),Q),R) = hAPP_int_int(P,hAPP_nat_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Int__Oint_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4994 (all P all Q all R hAPP_int_rat(hAPP_f1900950721nt_rat(hAPP_f1270196437nt_rat(cOMBB_int_rat_int,P),Q),R) = hAPP_int_rat(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Rat__Orat_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4995 (all P all Q all R hAPP_nat_nat(hAPP_f1914919701at_nat(hAPP_f1585078997at_nat(cOMBB_nat_nat_nat,P),Q),R) = hAPP_nat_nat(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4996 (all P all Q all R hAPP_nat_rat(hAPP_f2062659861at_rat(hAPP_f1082758869at_rat(cOMBB_rat_rat_nat,P),Q),R) = hAPP_rat_rat(P,hAPP_nat_rat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Rat__Orat_000tc__Rat__Orat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4997 (all P all Q all R hAPP_int_int(hAPP_int_fun_int_int(hAPP_f2135977429nt_int(cOMBC_int_int_int,P),Q),R) = hAPP_int_int(hAPP_int_fun_int_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4998 (all P all Q all R hAPP_int_int(hAPP_nat_fun_int_int(hAPP_f2105620693nt_int(cOMBC_int_nat_int,P),Q),R) = hAPP_nat_int(hAPP_int_fun_nat_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Nat__Onat_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 4999 (all P all Q all R hAPP_nat_int(hAPP_int_fun_nat_int(hAPP_f1673103573at_int(cOMBC_nat_int_int,P),Q),R) = hAPP_int_int(hAPP_nat_fun_int_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5000 (all P all Q all R hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5001 (all P all Q all R hAPP_nat_nat(hAPP_f1914919701at_nat(hAPP_f1408247010at_nat(cOMBS_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),hAPP_nat_nat(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5002 (all P all Q all R hAPP_nat_rat(hAPP_f2062659861at_rat(hAPP_f1131305186at_rat(cOMBS_nat_rat_rat,P),Q),R) = hAPP_rat_rat(hAPP_nat_fun_rat_rat(P,R),hAPP_nat_rat(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__Rat__Orat_000tc__Rat__Orat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5003 (all X all Y hAPP_P1860904029l_real(hAPP_P1982799375l_real(hAPP_b1482221219l_real(if_Pro313124157l_real,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__prod_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5004 (all X all Y hAPP_P1860904029l_real(hAPP_P1982799375l_real(hAPP_b1482221219l_real(if_Pro313124157l_real,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__prod_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5005 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__prod_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_T) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5006 (all P all Q all R hAPP_int_bool(hAPP_f429935748t_bool(hAPP_f1512942609t_bool(cOMBB_int_bool_int,P),Q),R) = hAPP_int_bool(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5007 (all P all Q all R hAPP_nat_bool(hAPP_f1154658180t_bool(hAPP_f1361476881t_bool(cOMBB_int_bool_nat,P),Q),R) = hAPP_int_bool(P,hAPP_nat_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5008 (all P all Q all R hAPP_int_bool(hAPP_f1448486952t_bool(hAPP_f696844121t_bool(cOMBB_nat_bool_int,P),Q),R) = hAPP_nat_bool(P,hAPP_int_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5009 (all P all Q all R hAPP_int_bool(hAPP_f1241350704t_bool(hAPP_f1131424617t_bool(cOMBB_rat_bool_int,P),Q),R) = hAPP_rat_bool(P,hAPP_int_rat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Rat__Orat_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5010 (all P all Q all R hAPP_int_bool(hAPP_i1948725293t_bool(hAPP_f428220345t_bool(cOMBC_int_int_bool,P),Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5011 (all P all Q all R hAPP_int_bool(hAPP_r1900510169t_bool(hAPP_f1480506641t_bool(cOMBC_int_rat_bool,P),Q),R) = hAPP_rat_bool(hAPP_i16292313t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Rat__Orat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5012 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5013 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f627970963t_bool(cOMBB_bool_bool_int,P),Q),R) = hAPP_bool_bool(P,hAPP_int_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5014 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5015 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f727283836t_bool(cOMBS_int_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5016 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5017 (all P all Q all R hAPP_int_real(hAPP_f563293398t_real(hAPP_f134192053t_real(cOMBB_int_real_int,P),Q),R) = hAPP_int_real(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__RealDef__Oreal_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5018 (all P all Q all R hAPP_nat_real(hAPP_f1676298106t_real(hAPP_f1566856189t_real(cOMBB_nat_real_nat,P),Q),R) = hAPP_nat_real(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__RealDef__Oreal_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5019 (all P all Q all R hAPP_int_bool(hAPP_f429384717t_bool(hAPP_f1173902867t_bool(cOMBB_real_bool_int,P),Q),R) = hAPP_real_bool(P,hAPP_int_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__HOL__Obool_000tc__Int__Oint_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5020 (all P all Q all R hAPP_nat_bool(hAPP_f737665877t_bool(hAPP_f605995867t_bool(cOMBB_real_bool_nat,P),Q),R) = hAPP_real_bool(P,hAPP_nat_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5021 (all P all Q all R hAPP_int_bool(hAPP_r481142414t_bool(hAPP_f1845081853t_bool(cOMBC_int_real_bool,P),Q),R) = hAPP_real_bool(hAPP_i688218208l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__RealDef__Oreal_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5022 (all P all Q all R hAPP_real_bool(hAPP_f1861673493l_bool(hAPP_f1010710745l_bool(cOMBS_real_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_r1938957037l_bool(P,R),hAPP_real_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5023 (all P all Q all R hAPP_int_real(hAPP_f269654879t_real(hAPP_f766218899t_real(cOMBB_real_real_int,P),Q),R) = hAPP_real_real(P,hAPP_int_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__Int__Oin) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5024 (all P all Q all R hAPP_nat_real(hAPP_f1888375463t_real(hAPP_f1690286043t_real(cOMBB_real_real_nat,P),Q),R) = hAPP_real_real(P,hAPP_nat_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__Nat__Ona) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5025 (all P all Q all R hAPP_nat_real(hAPP_r474017924t_real(hAPP_f42270917t_real(cOMBC_nat_real_real,P),Q),R) = hAPP_real_real(hAPP_n546711566l_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__RealDef__Oreal_000tc__RealDef__Orea) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5026 (all P all Q all R hAPP_real_real(hAPP_n546711566l_real(hAPP_f248847589l_real(cOMBC_real_nat_real,P),Q),R) = hAPP_nat_real(hAPP_r474017924t_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__Nat__Onat_000tc__RealDef__Orea) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5027 (all P all Q hAPP_f957591787ol_nat(cOMBK_1643584600t_bool(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5028 (all P all Q all R hAPP_nat_real(hAPP_f1888375463t_real(hAPP_f197615720t_real(cOMBS_nat_real_real,P),Q),R) = hAPP_real_real(hAPP_n546711566l_real(P,R),hAPP_nat_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__RealDef__Oreal_000tc__RealDef__Orea) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5029 (all P all Q all R hAPP_real_bool(hAPP_f1402056515l_bool(hAPP_f824790735l_bool(cOMBB_real_bool_real,P),Q),R) = hAPP_real_bool(P,hAPP_real_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__HOL__Obool_000tc__RealDef__Ore) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5030 (all P all Q all R hAPP_real_bool(hAPP_r1134773055l_bool(hAPP_f695504873l_bool(cOMBC_real_real_bool,P),Q),R) = hAPP_real_bool(hAPP_r1134773055l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5031 (all P all Q all R hAPP_nat_real(hAPP_f1290670424t_real(hAPP_f327026105t_real(cOMBB_722610049al_nat,P),Q),R) = hAPP_complex_real(P,hAPP_nat_complex(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Complex__Ocomplex_000tc__RealDef__Oreal_000tc__Nat__) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5032 (all P all Q all R hAPP_nat_complex(hAPP_f219720582omplex(hAPP_f1052840010omplex(cOMBS_696648398omplex,P),Q),R) = hAPP_real_complex(hAPP_n1983812447omplex(P,R),hAPP_nat_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__RealDef__Oreal_000tc__Complex__Ocom) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5033 (all P all Q all R hAPP_real_real(hAPP_f1950183573l_real(hAPP_f1992866895l_real(cOMBB_real_real_real,P),Q),R) = hAPP_real_real(P,hAPP_real_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__RealDef_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5034 (all P all Q all R hAPP_real_real(hAPP_r1250527377l_real(hAPP_f203520653l_real(cOMBC_real_real_real,P),Q),R) = hAPP_real_real(hAPP_r1250527377l_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__RealDef_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5035 (all P all Q all R hAPP_real_real(hAPP_f1950183573l_real(hAPP_f2069516469l_real(cOMBS_real_real_real,P),Q),R) = hAPP_real_real(hAPP_r1250527377l_real(P,R),hAPP_real_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__RealDef_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5036 (all P all Q all R hAPP_nat_complex(hAPP_f1646117269omplex(hAPP_f1457396693omplex(cOMBB_117013006ex_nat,P),Q),R) = hAPP_complex_complex(P,hAPP_nat_complex(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Complex__Ocomplex_000tc__Complex__Ocomplex_000tc__Na) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5037 (all P all Q all R hAPP_int_fun_int_int(hAPP_f1760145644nt_int(hAPP_f1629352853nt_int(cOMBB_1496585939nt_int,P),Q),R) = hAPP_int_fun_int_int(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5038 (all P all Q all R hAPP_nat_fun_int_int(hAPP_f1935805932nt_int(hAPP_f125788821nt_int(cOMBB_859312247nt_nat,P),Q),R) = hAPP_int_fun_int_int(P,hAPP_nat_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_001) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5039 (all P all Q all R hAPP_nat_fun_nat_nat(hAPP_f1639111240at_nat(hAPP_f1731313045at_nat(cOMBB_963856155at_nat,P),Q),R) = hAPP_nat_fun_nat_nat(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5040 (all P all Q all R hAPP_nat_fun_rat_rat(hAPP_f1830834240at_rat(hAPP_f1073644437at_rat(cOMBB_1926947at_nat,P),Q),R) = hAPP_rat_fun_rat_rat(P,hAPP_nat_rat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Rat__Orat_000tc__fun_Itc__Rat__Orat_Mtc__Rat__Orat_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5041 (all P all Q all R hAPP_P1175774780nt_int(hAPP_f521271395nt_int(hAPP_f11151005nt_int(cOMBB_47643171nt_int,P),Q),R) = hAPP_int_int(P,hAPP_P1175774780nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Int__Oint_000tc__prod_Itc__Int__Oin) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5042 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f1791153283t_bool(hAPP_f1399575567t_bool(cOMBB_118231410ol_int,P),Q),R) = hAPP_i1948725293t_bool(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5043 (all P all Q all R hAPP_i1524277240nt_int(hAPP_f883232462nt_int(hAPP_f2002277285nt_int(cOMBB_1846624359nt_int,P),Q),R) = hAPP_i1524277240nt_int(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5044 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f618557131t_bool(hAPP_f1505651103t_bool(cOMBB_800536526ol_nat,P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5045 (all P all Q all R hAPP_i16292313t_bool(hAPP_f601898971t_bool(hAPP_f857296063t_bool(cOMBB_214503962ol_int,P),Q),R) = hAPP_r2115560837t_bool(P,hAPP_int_rat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Rat__Orat_000tc__fun_Itc__Rat__Orat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5046 (all P all Q all R hAPP_i1948725293t_bool(hAPP_i345030060t_bool(hAPP_f791698359t_bool(cOMBC_241247961t_bool,P),Q),R) = hAPP_i1948725293t_bool(hAPP_i345030060t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__fun_Itc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5047 (all P all Q all R hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(hAPP_f465821005nt_int(cOMBC_1964283556nt_int,P),Q),R) = hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__prod_Itc__Int__Oin) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5048 (all P all Q all R hAPP_P1175774780nt_int(hAPP_i61245889nt_int(hAPP_f578362681nt_int(cOMBC_1417754532nt_int,P),Q),R) = hAPP_int_int(hAPP_P2110489235nt_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oin) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5049 (all P all Q all R hAPP_P1175774780nt_int(hAPP_f521271395nt_int(hAPP_f1914742907nt_int(cOMBS_2019229620nt_int,P),Q),R) = hAPP_int_int(hAPP_P2110489235nt_int(P,R),hAPP_P1175774780nt_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oin) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5050 (all P all Q all R hAPP_P1853363688nt_rat(hAPP_f1065357839nt_rat(hAPP_f1120137083nt_rat(cOMBS_549334880nt_rat,P),Q),R) = hAPP_int_rat(hAPP_P507092031nt_rat(P,R),hAPP_P1175774780nt_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oin_002) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5051 (all P all Q all R hAPP_P603027463t_bool(hAPP_f892584630t_bool(hAPP_f492612297t_bool(cOMBB_798864284nt_int,P),Q),R) = hAPP_int_bool(P,hAPP_P1175774780nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__prod_Itc__Int__Oi) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5052 (all P all Q all R hAPP_P603027463t_bool(hAPP_f1084724746t_bool(hAPP_f374502857t_bool(cOMBB_569260360nt_int,P),Q),R) = hAPP_rat_bool(P,hAPP_P1853363688nt_rat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Rat__Orat_000tc__HOL__Obool_000tc__prod_Itc__Int__Oi) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5053 (all P all Q all R hAPP_int_bool(hAPP_f2119767738t_bool(hAPP_f423804115t_bool(cOMBB_1418110531ol_int,P),Q),R) = hAPP_f448129468l_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5054 (all P all Q all R hAPP_int_bool(hAPP_f41603166t_bool(hAPP_f389116883t_bool(cOMBB_1593174431ol_int,P),Q),R) = hAPP_f54304608l_bool(P,hAPP_i418383825t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5055 (all P all Q all R hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_f202917053t_bool(cOMBC_94739984l_bool,P),Q),R) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5056 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5057 (all P all Q all R hAPP_P603027463t_bool(hAPP_i119638232t_bool(hAPP_f2018027565t_bool(cOMBC_33652895t_bool,P),Q),R) = hAPP_int_bool(hAPP_P252494982t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oin_003) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5058 (all P all Q all R hAPP_P603027463t_bool(hAPP_f892584630t_bool(hAPP_f1325804733t_bool(cOMBS_480885903t_bool,P),Q),R) = hAPP_int_bool(hAPP_P252494982t_bool(P,R),hAPP_P1175774780nt_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oin_004) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5059 (all P all Q all R hAPP_P603027463t_bool(hAPP_f237669397t_bool(hAPP_f513299955t_bool(cOMBB_1344650379nt_int,P),Q),R) = hAPP_bool_bool(P,hAPP_P603027463t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Int__O) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5060 (all P all Q all R hAPP_i68813070l_bool(hAPP_f2144054103l_bool(hAPP_f1734373249l_bool(cOMBB_1652995168ol_int,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5061 (all P all Q all R hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_005) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5062 (all P all Q all R hAPP_P603027463t_bool(hAPP_f237669397t_bool(hAPP_f461489489t_bool(cOMBS_400904860l_bool,P),Q),R) = hAPP_bool_bool(hAPP_P921862901l_bool(P,R),hAPP_P603027463t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5063 (all P all Q all R hAPP_nat_real(hAPP_f292751352t_real(hAPP_f1607377819t_real(cOMBB_1533963633al_nat,P),Q),R) = hAPP_f1406902706l_real(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__RealDef_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5064 (all P all Q all R hAPP_real_bool(hAPP_f101635158l_bool(hAPP_f1925507189l_bool(cOMBB_1121934354l_real,P),Q),R) = hAPP_f448129468l_bool(P,hAPP_r481142414t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo_006) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5065 (all P all Q all R hAPP_r1938957037l_bool(hAPP_f60716669l_bool(hAPP_f1485493409l_bool(cOMBB_624415285l_real,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_real_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5066 (all P all Q all R hAPP_n546711566l_real(hAPP_f1904307534l_real(hAPP_f224989205l_real(cOMBB_1419615765al_nat,P),Q),R) = hAPP_n546711566l_real(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__RealDef__Oreal_Mtc__RealDe) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5067 (all P all Q all R hAPP_i688218208l_bool(hAPP_f801032407l_bool(hAPP_f499530369l_bool(cOMBB_1317819104ol_int,P),Q),R) = hAPP_r1134773055l_bool(P,hAPP_int_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5068 (all P all Q all R hAPP_real_real(hAPP_f2119584768l_real(hAPP_f59594445l_real(cOMBC_2010481033l_real,P),Q),R) = hAPP_f1406902706l_real(hAPP_r1409264866l_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5069 (all P all Q all R hAPP_r474017924t_real(hAPP_f1407095736t_real(hAPP_f1796904975t_real(cOMBB_599996122l_real,P),Q),R) = hAPP_r474017924t_real(P,hAPP_real_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__Nat__Onat_Mtc__RealDe) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5070 (all P all Q all R hAPP_i371647666l_real(hAPP_f1352333353l_real(hAPP_f318350629l_real(cOMBB_1946221070al_int,P),Q),R) = hAPP_r1250527377l_real(P,hAPP_int_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__R) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5071 (all P all Q all R hAPP_n546711566l_real(hAPP_f451358433l_real(hAPP_f1092742621l_real(cOMBB_1308947378al_nat,P),Q),R) = hAPP_r1250527377l_real(P,hAPP_nat_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__R_008) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5072 (all P all Q all R hAPP_real_real(hAPP_f1122023986l_real(hAPP_f1786887945l_real(cOMBB_1896127834l_real,P),Q),R) = hAPP_f352196356l_real(P,hAPP_r474017924t_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__RealDef__Oreal_J_000tc__Real) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5073 (all P all Q all R hAPP_n546711566l_real(hAPP_r195310020l_real(hAPP_f2126667875l_real(cOMBC_746811033l_real,P),Q),R) = hAPP_r1250527377l_real(hAPP_n682674106l_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__RealDef__Oreal_000tc__fun_Itc__Real) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5074 (all P all Q all R hAPP_n546711566l_real(hAPP_f451358433l_real(hAPP_f335634176l_real(cOMBS_337378985l_real,P),Q),R) = hAPP_r1250527377l_real(hAPP_n682674106l_real(P,R),hAPP_nat_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__RealDef__Oreal_000tc__fun_Itc__Real) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5075 (all P all Q all R hAPP_r1134773055l_bool(hAPP_f1393328161l_bool(hAPP_f1900646853l_bool(cOMBB_430461877l_real,P),Q),R) = hAPP_r1134773055l_bool(P,hAPP_real_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__H_009) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5076 (all P all Q all R hAPP_nat_real(hAPP_f73570213t_real(hAPP_f918606171t_real(cOMBB_64450052al_nat,P),Q),R) = hAPP_P731461727l_real(P,hAPP_n332733730l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5077 (all P all Q all R hAPP_real_bool(hAPP_f330985925l_bool(hAPP_f940061907l_bool(cOMBB_1795223523l_real,P),Q),R) = hAPP_P1333854989l_bool(P,hAPP_r1195171167l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_000tc_010) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5078 (all P all Q all R hAPP_n1983812447omplex(hAPP_f23851874omplex(hAPP_f406530075omplex(cOMBB_1714920583ex_nat,P),Q),R) = hAPP_r265291036omplex(P,hAPP_nat_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__C) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5079 (all P all Q all R hAPP_r1250527377l_real(hAPP_f556082547l_real(hAPP_f1960414057l_real(cOMBB_882763271l_real,P),Q),R) = hAPP_r1250527377l_real(P,hAPP_real_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__R_011) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5080 (all P all Q all R hAPP_r1250527377l_real(hAPP_r337325687l_real(hAPP_f1644353557l_real(cOMBC_1508019322l_real,P),Q),R) = hAPP_r1250527377l_real(hAPP_r337325687l_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5081 (all P all Q all R hAPP_r1195171167l_real(hAPP_f617735571l_real(hAPP_f800361423l_real(cOMBB_2107848501l_real,P),Q),R) = hAPP_r1195171167l_real(P,hAPP_real_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__prod_Itc__RealDef__Oreal_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5082 (all P all Q all R hAPP_r1195171167l_real(hAPP_f617735571l_real(hAPP_f1730463541l_real(cOMBS_511527878l_real,P),Q),R) = hAPP_r1195171167l_real(hAPP_r2019696015l_real(P,R),hAPP_real_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__RealDef__Oreal_000tc__prod_Itc) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5083 (all P all Q all R hAPP_int_fun_int_int(hAPP_f1760145644nt_int(hAPP_f808647893nt_int(cOMBC_736024425nt_int,P),Q),R) = hAPP_f1356864277nt_int(hAPP_i744251628nt_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5084 (all P all Q all R hAPP_P2110489235nt_int(hAPP_f1855025978nt_int(hAPP_f1038672605nt_int(cOMBB_1506897658nt_int,P),Q),R) = hAPP_int_fun_int_int(P,hAPP_P1175774780nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_012) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5085 (all P all Q all R hAPP_P507092031nt_rat(hAPP_f1547007718nt_rat(hAPP_f382317021nt_rat(cOMBB_170828966nt_int,P),Q),R) = hAPP_int_fun_int_rat(P,hAPP_P1175774780nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Rat__Orat_J) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5086 (all P all Q all R hAPP_i1584592887nt_int(hAPP_f1574055885nt_int(hAPP_f2054677283nt_int(cOMBB_782625832nt_int,P),Q),R) = hAPP_i1584592887nt_int(P,hAPP_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__prod_Itc__I) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5087 (all P all Q all R hAPP_n1865633855at_nat(hAPP_f837737749at_nat(hAPP_f999082675at_nat(cOMBB_348438404at_nat,P),Q),R) = hAPP_n1865633855at_nat(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__prod_Itc__N) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5088 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f720654810t_bool(hAPP_f908327869t_bool(cOMBB_1290694363ol_int,P),Q),R) = hAPP_f429935748t_bool(P,hAPP_int_fun_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc__) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5089 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f1791153283t_bool(hAPP_f735247205t_bool(cOMBC_983868720t_bool,P),Q),R) = hAPP_f429935748t_bool(hAPP_i872162435t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_013) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5090 (all P all Q all R hAPP_i1584592887nt_int(hAPP_f1574055885nt_int(hAPP_f434654626nt_int(cOMBS_2011279539nt_int,P),Q),R) = hAPP_i1584592887nt_int(hAPP_i1778081398nt_int(P,R),hAPP_int_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__Int__Oint_000tc__fun_Itc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5091 (all P all Q all R hAPP_P252494982t_bool(hAPP_f291087797t_bool(hAPP_f214467655t_bool(cOMBB_182850971nt_int,P),Q),R) = hAPP_i1948725293t_bool(P,hAPP_P1175774780nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__014) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5092 (all P all Q all R hAPP_n215258509l_bool(hAPP_f66927821l_bool(hAPP_f2037783381l_bool(cOMBB_1146692694ol_nat,P),Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5093 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f428220345t_bool(hAPP_f654702867t_bool(cOMBB_591320580ol_int,P),Q),R) = hAPP_f1805168059t_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5094 (all P all Q all R hAPP_i1524277240nt_int(hAPP_f1735705551nt_int(hAPP_f151095827nt_int(cOMBB_1389251822nt_int,P),Q),R) = hAPP_P1975530577nt_int(P,hAPP_i1524277240nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__prod_Itc) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.86 5095 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(hAPP_f472159229t_bool(cOMBC_1683390479t_bool,P),Q),R) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__015) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5096 (all P all Q all R hAPP_i418383825t_bool(hAPP_f289318786t_bool(hAPP_f729588221t_bool(cOMBC_678732631t_bool,P),Q),R) = hAPP_f800510211t_bool(hAPP_i1796122964t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5097 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f428220345t_bool(hAPP_f1878066172t_bool(cOMBS_1720984575t_bool,P),Q),R) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(P,R),hAPP_i1948725293t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5098 (all P all Q all R hAPP_i1524277240nt_int(hAPP_f1735705551nt_int(hAPP_f713949180nt_int(cOMBS_1891347093nt_int,P),Q),R) = hAPP_P1975530577nt_int(hAPP_i1216375074nt_int(P,R),hAPP_i1524277240nt_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5099 (all P all Q all R hAPP_P921862901l_bool(hAPP_f365317245l_bool(hAPP_f1961001761l_bool(cOMBB_1550063917nt_int,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P603027463t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5100 (all P all Q all R hAPP_i1948725293t_bool(hAPP_f351634443t_bool(hAPP_f1576199059t_bool(cOMBB_95956018ol_int,P),Q),R) = hAPP_f429384717t_bool(P,hAPP_i627165055t_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__RealDef__Oreal_J_000tc__fun_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5101 (all P all Q all R hAPP_i418383825t_bool(hAPP_f1222178131t_bool(hAPP_f743790483t_bool(cOMBB_1647910634ol_int,P),Q),R) = hAPP_f737665877t_bool(P,hAPP_i157317923t_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__RealDef__Oreal_J_000tc__fun_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5102 (all P all Q all R hAPP_i627165055t_real(hAPP_f1323932638t_real(hAPP_f352226557t_real(cOMBC_824100275t_real,P),Q),R) = hAPP_f269654879t_real(hAPP_i1671359920t_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__RealDef__Or) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5103 (all P all Q all R hAPP_i157317923t_real(hAPP_f1613846310t_real(hAPP_f1720068861t_real(cOMBC_295337211t_real,P),Q),R) = hAPP_f1888375463t_real(hAPP_i447943416t_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__RealDef__Or) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5104 (all P all Q all R hAPP_r474017924t_real(hAPP_f1501741374t_real(hAPP_f1135648319t_real(cOMBC_1329014627t_real,P),Q),R) = hAPP_f1676298106t_real(hAPP_r50993370t_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__fun_Itc__Nat__Onat_Mtc__Nat__O) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5105 (all P all Q all R hAPP_r474017924t_real(hAPP_f1993765077t_real(hAPP_f895854793t_real(cOMBB_1948233853l_real,P),Q),R) = hAPP_f1888375463t_real(P,hAPP_r474017924t_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__RealDef__Oreal_J_000tc__fun__017) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5106 (all P all Q all R hAPP_n682674106l_real(hAPP_f1129044203l_real(hAPP_f264196187l_real(cOMBB_1480366270al_nat,P),Q),R) = hAPP_b646336293l_real(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__RealDef__Oreal_Mtc__fun_I) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5107 (all P all Q all R hAPP_r2019696015l_real(hAPP_f1591894897l_real(hAPP_f2114902373l_real(cOMBB_237479429l_real,P),Q),R) = hAPP_r2019696015l_real(P,hAPP_real_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__p) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5108 (all P all Q all R hAPP_i345030060t_bool(hAPP_f725770969t_bool(hAPP_f983569339t_bool(cOMBB_550562460ol_int,P),Q),R) = hAPP_f1791153283t_bool(P,hAPP_int_fun_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___018) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5109 (all P all Q all R hAPP_i1584592887nt_int(hAPP_f1574055885nt_int(hAPP_f960630521nt_int(cOMBC_1805044090nt_int,P),Q),R) = hAPP_f883232462nt_int(hAPP_i998473677nt_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_019) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5110 (all P all Q all R hAPP_r1195171167l_real(hAPP_f1736103445l_real(hAPP_f1908301369l_real(cOMBS_902912708l_real,P),Q),R) = hAPP_P1860904029l_real(hAPP_r938550413l_real(P,R),hAPP_r1195171167l_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__prod_Itc__RealDef__Oreal_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5111 (all P all Q all R hAPP_P1668131738nt_int(hAPP_f167782601nt_int(hAPP_f400538607nt_int(cOMBB_866192175nt_int,P),Q),R) = hAPP_i61245889nt_int(P,hAPP_P1175774780nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__I) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5112 (all P all Q all R hAPP_i1823918693l_bool(hAPP_f1344929775l_bool(hAPP_f1830214065l_bool(cOMBB_793166024ol_int,P),Q),R) = hAPP_f2144054103l_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__020) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5113 (all P all Q all R hAPP_i614188481l_bool(hAPP_f252743847l_bool(hAPP_f643658017l_bool(cOMBB_2046938128ol_int,P),Q),R) = hAPP_f1146629647l_bool(P,hAPP_i418383825t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5114 (all P all Q all R hAPP_r481142414t_bool(hAPP_f1625314454t_bool(hAPP_f340152631t_bool(cOMBB_1453147152l_real,P),Q),R) = hAPP_f2119767738t_bool(P,hAPP_r632163725t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Int__Oint_Mtc__HOL_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5115 (all P all Q all R hAPP_r481142414t_bool(hAPP_f1341793266t_bool(hAPP_f571820015t_bool(cOMBB_1159313332l_real,P),Q),R) = hAPP_f41603166t_bool(P,hAPP_r373117745t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Nat__Onat_Mtc__HOL_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5116 (all P all Q all R hAPP_r632163725t_bool(hAPP_f1832844496t_bool(hAPP_f1990636069t_bool(cOMBC_412863505t_bool,P),Q),R) = hAPP_f1048215610t_bool(hAPP_r1623423338t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__fun_Itc__Int__Oint_Mtc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5117 (all P all Q all R hAPP_r373117745t_bool(hAPP_f1115375056t_bool(hAPP_f271976045t_bool(cOMBC_1801450329t_bool,P),Q),R) = hAPP_f289318786t_bool(hAPP_r653725362t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__O_021) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5118 (all P all Q all R hAPP_r1409264866l_real(hAPP_f1523861863l_real(hAPP_f1067681227l_real(cOMBB_1934313333l_real,P),Q),R) = hAPP_f1509287679l_real(P,hAPP_r474017924t_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__RealDef__Oreal_J_000tc__fun__022) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5119 (all P all Q all R hAPP_i744251628nt_int(hAPP_f836602773nt_int(hAPP_f888249301nt_int(cOMBB_1875755114nt_int,P),Q),R) = hAPP_f747162069nt_int(P,hAPP_int_fun_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___023) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5120 (all P all Q all R hAPP_i1778081398nt_int(hAPP_f2004554147nt_int(hAPP_f1228585167nt_int(cOMBB_1102189010nt_int,P),Q),R) = hAPP_f1574055885nt_int(P,hAPP_int_fun_int_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___024) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5121 (all P all Q all R hAPP_r1134773055l_bool(hAPP_f1884005689l_bool(hAPP_f172451459l_bool(cOMBB_421479067l_real,P),Q),R) = hAPP_f330985925l_bool(P,hAPP_r2019696015l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__prod_Itc__RealDef__Orea) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5122 (all P all Q all R hAPP_i872162435t_bool(hAPP_f1251097615t_bool(hAPP_f1475822739t_bool(cOMBB_2027861294ol_int,P),Q),R) = hAPP_f1512942609t_bool(P,hAPP_i1948725293t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__025) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5123 (all P all Q all R hAPP_i345030060t_bool(hAPP_f791698359t_bool(hAPP_f847817363t_bool(cOMBB_562416518ol_int,P),Q),R) = hAPP_f428220345t_bool(P,hAPP_i345030060t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Int__Oint_Mtc__HOL__026) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5124 (all P all Q all R hAPP_i1584592887nt_int(hAPP_f465821005nt_int(hAPP_f1081447804nt_int(cOMBS_1470252563nt_int,P),Q),R) = hAPP_f1735705551nt_int(hAPP_i1836591008nt_int(P,R),hAPP_i1584592887nt_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__prod_Itc__I) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5125 (all P all Q all R hAPP_i1216375074nt_int(hAPP_P621635040nt_int(hAPP_f1582586579nt_int(cOMBC_707974837nt_int,P),Q),R) = hAPP_P1145851913nt_int(hAPP_i2104874254nt_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5126 (all P all Q all R hAPP_i1216375074nt_int(hAPP_f1375227553nt_int(hAPP_f1311564564nt_int(cOMBS_1640193733nt_int,P),Q),R) = hAPP_P1145851913nt_int(hAPP_i2104874254nt_int(P,R),hAPP_i1524277240nt_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint__027) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5127 (all P all Q all R hAPP_i1529485324t_bool(hAPP_f1315737299t_bool(hAPP_f538565589t_bool(cOMBB_1211207212ol_int,P),Q),R) = hAPP_f627970963t_bool(P,hAPP_i68813070l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5128 (all P all Q all R hAPP_r337325687l_real(hAPP_f1732848529l_real(hAPP_f1310479593l_real(cOMBB_2092576745l_real,P),Q),R) = hAPP_f556082547l_real(P,hAPP_r1250527377l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_000tc_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5129 (all P all Q all R hAPP_r2019696015l_real(hAPP_f1591894897l_real(hAPP_f644105375l_real(cOMBC_467724138l_real,P),Q),R) = hAPP_f617735571l_real(hAPP_r712953929l_real(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__R) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5130 (all P all Q all R hAPP_r2019696015l_real(hAPP_f320596107l_real(hAPP_f850851693l_real(cOMBS_193881978l_real,P),Q),R) = hAPP_f617735571l_real(hAPP_r712953929l_real(P,R),hAPP_r1250527377l_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__R) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5131 (all P all Q all R hAPP_r632163725t_bool(hAPP_f956464319t_bool(hAPP_f422375781t_bool(cOMBC_243356514t_bool,P),Q),R) = hAPP_f351634443t_bool(hAPP_r1392521531t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__fun_Itc__Int__Oint_Mtc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5132 (all P all Q all R hAPP_r373117745t_bool(hAPP_f1459420095t_bool(hAPP_f693283245t_bool(cOMBC_1113900202t_bool,P),Q),R) = hAPP_f1222178131t_bool(hAPP_r2052264067t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__fun_Itc__Int__Oint_Mtc__fun_It_028) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5133 (all P all Q all R hAPP_r50993370t_real(hAPP_f1163894827t_real(hAPP_f1998755145t_real(cOMBB_421464275l_real,P),Q),R) = hAPP_f1566856189t_real(P,hAPP_r474017924t_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__RealDef__Oreal_J_000tc__fun__029) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5134 (all P all Q all R hAPP_r847664445t_bool(hAPP_f1920544743t_bool(hAPP_f866672739t_bool(cOMBB_1247074793l_real,P),Q),R) = hAPP_f1173902867t_bool(P,hAPP_r1134773055l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__HOL__Obool_J_000tc__fun) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5135 (all P all Q all R hAPP_r279757445t_bool(hAPP_f1840085295t_bool(hAPP_f1083049571t_bool(cOMBB_2050079537l_real,P),Q),R) = hAPP_f605995867t_bool(P,hAPP_r1134773055l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__HOL__Obool_J_000tc__fun_030) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5136 (all P all Q all R hAPP_i1671359920t_real(hAPP_f74147283t_real(hAPP_f1169087445t_real(cOMBB_2129825580al_int,P),Q),R) = hAPP_f766218899t_real(P,hAPP_i371647666l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_000tc__031) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5137 (all P all Q all R hAPP_i447943416t_real(hAPP_f1295083291t_real(hAPP_f212164053t_real(cOMBB_929094628al_int,P),Q),R) = hAPP_f1690286043t_real(P,hAPP_i371647666l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_000tc__032) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5138 (all P all Q all R hAPP_i1153444985nt_int(hAPP_f1148171384nt_int(hAPP_f334321603nt_int(cOMBB_1484610687nt_int,P),Q),R) = hAPP_P621635040nt_int(P,hAPP_i1524277240nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5139 (all P all Q all R hAPP_P1668131738nt_int(hAPP_f167782601nt_int(hAPP_f1769710159nt_int(cOMBC_2037038898nt_int,P),Q),R) = hAPP_f521271395nt_int(hAPP_P752050971nt_int(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5140 (all P all Q all R hAPP_i2104874254nt_int(hAPP_f251264923nt_int(hAPP_f279307923nt_int(cOMBB_662120866nt_int,P),Q),R) = hAPP_b40753821nt_int(P,hAPP_int_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5141 (all P all Q all R hAPP_i1529485324t_bool(hAPP_f1545556668t_bool(hAPP_f85237525t_bool(cOMBB_389152643ol_int,P),Q),R) = hAPP_f727283836t_bool(P,hAPP_i1823918693l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__HOL__Obool_Mtc__HOL) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5142 (all P all Q all R hAPP_i1796122964t_bool(hAPP_f1902329768t_bool(hAPP_f1182713365t_bool(cOMBB_2087181719ol_int,P),Q),R) = hAPP_f561022312t_bool(P,hAPP_i614188481l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__fun_Itc__HOL__Obool_Mtc__HOL) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5143 (all P all Q all R hAPP_P989584703t_bool(hAPP_f1187443546t_bool(hAPP_f11709033t_bool(cOMBS_1676841879t_bool,P),Q),R) = hAPP_f892584630t_bool(hAPP_P1400155668t_bool(P,R),hAPP_P1668131738nt_int(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5144 (all P all Q all R hAPP_P989584703t_bool(hAPP_f1781059817t_bool(hAPP_f326728547t_bool(cOMBB_2086486755nt_int,P),Q),R) = hAPP_f237669397t_bool(P,hAPP_P989584703t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5145 (all P all Q all R hAPP_P989584703t_bool(hAPP_f1781059817t_bool(hAPP_f125837377t_bool(cOMBS_1610675060t_bool,P),Q),R) = hAPP_f237669397t_bool(hAPP_P877703507t_bool(P,R),hAPP_P989584703t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc__033) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5146 (all P all Q all R hAPP_r1150855451l_bool(hAPP_f381769257l_bool(hAPP_f512004221l_bool(cOMBB_188663909l_real,P),Q),R) = hAPP_f1344929775l_bool(P,hAPP_r632163725t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Int__Oint_Mtc__HOL__034) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5147 (all P all Q all R hAPP_r285062775l_bool(hAPP_f834119977l_bool(hAPP_f848516149l_bool(cOMBB_270132509l_real,P),Q),R) = hAPP_f252743847l_bool(P,hAPP_r373117745t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Nat__Onat_Mtc__HOL__035) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5148 (all P all Q all R hAPP_r337325687l_real(hAPP_f1644353557l_real(hAPP_f1874145443l_real(cOMBB_1768400739l_real,P),Q),R) = hAPP_f203520653l_real(P,hAPP_r337325687l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__fun_Itc__RealDef__Oreal) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5149 (all P all Q all R hAPP_r579619957l_real(hAPP_f823702159l_real(hAPP_f1040184293l_real(cOMBB_557258983l_real,P),Q),R) = hAPP_f1591894897l_real(P,hAPP_r1250527377l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__RealDef__Oreal_J_000tc__036) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5150 (all P all Q all R hAPP_r2019696015l_real(hAPP_f2072293513l_real(hAPP_f1763467369l_real(cOMBS_163651580l_real,P),Q),R) = hAPP_f1736103445l_real(hAPP_r224952523l_real(P,R),hAPP_r2019696015l_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__p) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5151 (all P all Q all R hAPP_r938550413l_real(hAPP_f1293550189l_real(hAPP_f183342685l_real(cOMBS_794971624l_real,P),Q),R) = hAPP_P1982799375l_real(hAPP_r931665397l_real(P,R),hAPP_r1195171167l_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__prod_Itc__RealDef__Oreal_Mtc___037) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5152 (all P all Q all R hAPP_i1778081398nt_int(hAPP_f2094497995nt_int(hAPP_f534361363nt_int(cOMBB_1657320178nt_int,P),Q),R) = hAPP_f465821005nt_int(P,hAPP_i1778081398nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Int__Oint_Mtc__prod) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5153 (all P all Q all R hAPP_i998473677nt_int(hAPP_f142232355nt_int(hAPP_f1377453843nt_int(cOMBB_320287386nt_int,P),Q),R) = hAPP_f2002277285nt_int(P,hAPP_i1584592887nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__prod_Itc__Int__Oint_Mtc__Int) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5154 (all P all Q all R hAPP_i1153444985nt_int(hAPP_f55007289nt_int(hAPP_f747475781nt_int(cOMBB_222539774nt_int,P),Q),R) = hAPP_f1375227553nt_int(P,hAPP_i1584592887nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__prod_Itc__Int__Oint_Mtc__Int_038) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5155 (all P all Q all R hAPP_P2053772734t_bool(hAPP_f1198736473t_bool(hAPP_f2042071795t_bool(cOMBB_773384995nt_int,P),Q),R) = hAPP_f291087797t_bool(P,hAPP_P1668131738nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_Mtc__I) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5156 (all P all Q all R hAPP_r931665397l_real(hAPP_f1607917947l_real(hAPP_f1076489843l_real(cOMBB_415306361l_real,P),Q),R) = hAPP_b1482221219l_real(P,hAPP_real_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__RealDef__Oreal_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5157 (all P all Q all R hAPP_P752050971nt_int(hAPP_f301246617nt_int(hAPP_f1151807883nt_int(cOMBB_563965291nt_int,P),Q),R) = hAPP_f11151005nt_int(P,hAPP_P2110489235nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___039) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5158 (all P all Q all R hAPP_P877703507t_bool(hAPP_f1965248563t_bool(hAPP_f1273270095t_bool(cOMBB_595786433nt_int,P),Q),R) = hAPP_f513299955t_bool(P,hAPP_P921862901l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_040) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5159 (all P all Q all R hAPP_r1962736578t_bool(hAPP_f1063001928t_bool(hAPP_f2050994651t_bool(cOMBB_2138578194l_real,P),Q),R) = hAPP_f1545556668t_bool(P,hAPP_r1150855451l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Int__Oint_Mtc__fun_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5160 (all P all Q all R hAPP_r1562208522t_bool(hAPP_f2084827628t_bool(hAPP_f1121609875t_bool(cOMBB_2125215742l_real,P),Q),R) = hAPP_f1902329768t_bool(P,hAPP_r285062775l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Nat__Onat_Mtc__fun_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5161 (all P all Q all R hAPP_r712953929l_real(hAPP_f1119546819l_real(hAPP_f555557763l_real(cOMBB_422423973l_real,P),Q),R) = hAPP_f800361423l_real(P,hAPP_r2019696015l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__prod_Itc__RealDef__Orea_041) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5162 (all P all Q all R hAPP_r1230691443l_real(hAPP_f324002831l_real(hAPP_f677014621l_real(cOMBS_107495110l_real,P),Q),R) = hAPP_f1293550189l_real(hAPP_r1043989325l_real(P,R),hAPP_r2019696015l_real(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__RealDef__Oreal_000tc__fun_Itc__RealDef__Oreal_Mtc__p_042) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5163 (all P all Q all R hAPP_i1836591008nt_int(hAPP_f400200275nt_int(hAPP_f1731308757nt_int(cOMBB_735549356nt_int,P),Q),R) = hAPP_f151095827nt_int(P,hAPP_i1216375074nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_Mtc__p) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5164 (all P all Q all R hAPP_r1623423338t_bool(hAPP_f704188951t_bool(hAPP_f1456711209t_bool(cOMBB_690122963l_real,P),Q),R) = hAPP_f472159229t_bool(P,hAPP_r1962736578t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__fun_Itc__Int__Oint_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5165 (all P all Q all R hAPP_r653725362t_bool(hAPP_f1927674023t_bool(hAPP_f1261108921t_bool(cOMBB_172850899l_real,P),Q),R) = hAPP_f729588221t_bool(P,hAPP_r1562208522t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__fun_Itc__Nat__Onat_) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5166 (all P all Q all R hAPP_r1392521531t_bool(hAPP_f332806115t_bool(hAPP_f1177545951t_bool(cOMBB_1459832681l_real,P),Q),R) = hAPP_f1576199059t_bool(P,hAPP_r847664445t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__RealDef__Oreal_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5167 (all P all Q all R hAPP_r2052264067t_bool(hAPP_f77155443t_bool(hAPP_f403082607t_bool(cOMBB_984071017l_real,P),Q),R) = hAPP_f743790483t_bool(P,hAPP_r279757445t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__RealDef__Oreal_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 4.84/4.87 5168 (all P all Q all R hAPP_r794344869l_real(hAPP_f517738447l_real(hAPP_f1879982819l_real(cOMBB_731595089l_real,P),Q),R) = hAPP_f1607917947l_real(P,hAPP_r1134773055l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__HOL__Obool_J_000tc__fun_043) # label(axiom) # label(non_clause). [assumption].
% 32.88/32.92 5169 (all P all Q all R hAPP_r712953929l_real(hAPP_f1108539711l_real(hAPP_f1109256153l_real(cOMBB_44084907l_real,P),Q),R) = hAPP_f1730463541l_real(P,hAPP_r579619957l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__fun_Itc__RealDef__Oreal_044) # label(axiom) # label(non_clause). [assumption].
% 32.88/32.92 5170 (all P all Q all R hAPP_i1836591008nt_int(hAPP_f617310012nt_int(hAPP_f197974549nt_int(cOMBB_638531587nt_int,P),Q),R) = hAPP_f713949180nt_int(P,hAPP_i1153444985nt_int(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__prod_Itc__Int__Oint) # label(axiom) # label(non_clause). [assumption].
% 32.88/32.92 5171 (all P all Q all R hAPP_P1400155668t_bool(hAPP_f223623489t_bool(hAPP_f1815301987t_bool(cOMBB_650041899nt_int,P),Q),R) = hAPP_f1325804733t_bool(P,hAPP_P2053772734t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_Mtc__f) # label(axiom) # label(non_clause). [assumption].
% 32.88/32.92 5172 (all P all Q all R hAPP_r224952523l_real(hAPP_f1663701695l_real(hAPP_f774948957l_real(cOMBB_3698607l_real,P),Q),R) = hAPP_f1908301369l_real(P,hAPP_r1230691443l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__fun_Itc__prod_Itc__Real) # label(axiom) # label(non_clause). [assumption].
% 32.88/32.92 5173 (all P all Q all R hAPP_r1043989325l_real(hAPP_f1161935955l_real(hAPP_f328572565l_real(cOMBB_520243667l_real,P),Q),R) = hAPP_f183342685l_real(P,hAPP_r794344869l_real(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__RealDef__Oreal_Mtc__fun_Itc__prod_Itc__Real_045) # label(axiom) # label(non_clause). [assumption].
% 32.88/32.92
% 32.88/32.92 ============================== end of process non-clausal formulas ===
% 32.88/32.92
% 32.88/32.92 ============================== PROCESS INITIAL CLAUSES ===============
% 32.88/32.92
% 32.88/32.92 ============================== PREDICATE ELIMINATION =================
% 32.88/32.92
% 32.88/32.92 ============================== end predicate elimination =============
% 32.88/32.92
% 32.88/32.92 Auto_denials: (non-Horn, no changes).
% 32.88/32.92
% 32.88/32.92 Term ordering decisions:
% 32.88/32.92 Function symbol KB weights: zero_zero_int=1. ord_less_int=1. zero_zero_real=1. ord_less_eq_real=1. ord_less_real=1. times_times_int=1. zero_zero_nat=1. ord_less_eq_int=1. one_one_int=1. bit1=1. plus_plus_int=1. times_times_real=1. ord_less_nat=1. pls=1. bit0=1. member_int=1. minus_minus_int=1. times_times_nat=1. suc=1. number_number_of_int=1. plus_plus_nat=1. plus_plus_real=1. ord_less_eq_nat=1. number_number_of_nat=1. number267125858f_real=1. zero_zero_rat=1. one_one_real=1. ord_less_eq_rat=1. ord_less_rat=1. power_power_real=1. inverse_divide_real=1. dvd_dvd_nat=1. times_times_rat=1. real_nat=1. minus_minus_real=1. one_one_nat=1. uminus_uminus_int=1. uminus_uminus_real=1. nat=1. plus_plus_rat=1. div_div_int=1. minus_minus_nat=1. semiri1621563631at_int=1. abs_abs_real=1. times_times_complex=1. dvd_dvd_int=1. min=1. abs_abs_int=1. cos=1. gcd_gcd_nat=1. product_Pair_int_int=1. times_123202395de_int=1. cOMBS_nat_real_real=1. ord_le1860547276de_int=1. plus_p1446045655de_int=1. plus_plus_complex=1. gcd_gcd_int=1. ord_le258702272de_int=1. zero_z126310315umeral=1. cOMBB_1308947378al_nat=1. pi=1. zero_z891286103de_int=1. power_power_int=1. div_div_nat=1. sin=1. fact_fact_nat=1. real_int=1. even_odd_even_nat=1. uminus_uminus_rat=1. produc865579683l_real=1. number_number_of_rat=1. sqrt=1. power_power_nat=1. root=1. times_1655362735umeral=1. cOMBB_nat_real_nat=1. abs_abs_rat=1. minus_minus_rat=1. fract=1. big_co604158596t_real=1. one_one_rat=1. zero_zero_complex=1. uminus473333897omplex=1. nat_neg=1. even_odd_even_int=1. ln=1. ord_le1304079648umeral=1. ord_le565307924umeral=1. complex=1. re=1. im=1. ord_le1568362934t_bool=1. ord_le951220754t_bool=1. minus_minus_complex=1. zprime=1. number528085621omplex=1. plus_p1627245867umeral=1. coprime=1. fconj=1. inverse_inverse_real=1. sequentially=1. powr=1. cnj=1. exp_real=1. product_Pair_nat_nat=1. cOMBC_nat_nat_nat=1. tan=1. prime=1. cOMBC_nat_real_real=1. zEven=1. ord_le1912455174t_bool=1. ord_le382113706t_bool=1. product_snd_int_int=1. member_real=1. pred=1. suminf_real=1. zOdd=1. one_one_complex=1. product_fst_int_int=1. cOMBB_882763271l_real=1. product_snd_nat_nat=1. cOMBB_1652995168ol_int=1. cOMBB_real_real_nat=1. cOMBS_int_bool_bool=1. norm_norm_complex=1. finite_finite_nat=1. nat_is_nat=1. div_di1430059507de_int=1. produc282740534nt_int=1. div_di1218280263umeral=1. member_nat=1. nat_nat_set=1. arctan=1. produc494345619at_nat=1. finite_card_int=1. produc1935615926l_real=1. produc556554744l_real=1. ii=1. invers1025623611omplex=1. one_on1645066479umeral=1. produc883642259nt_int=1. cOMBS_real_real_real=1. fact_fact_int=1. cOMBC_int_int_bool=1. one_on1684967323de_int=1. produc1318306967de_int=1. produc2136830103umeral=1. produc713279741t_bool=1. cOMBB_963856155at_nat=1. finite_finite_int=1. inverse_divide_rat=1. cOMBC_real_nat_real=1. product_fst_nat_nat=1. arccos=1. ring_1_Ints_real=1. fequal_int=1. arcsin=1. cOMBC_nat_nat_bool=1. member_rat=1. number1226105091de_int=1. ring_1_Ints_int=1. ring_1_Ints_rat=1. sRStar=1. uminus1024588959t_bool=1. uminus407446779t_bool=1. finite_card_nat=1. cOMBB_624415285l_real=1. cOMBC_real_real_real=1. cOMBS_real_bool_bool=1. member_complex=1. number1443263063umeral=1. ring_1_Ints_complex=1. cOMBB_599996122l_real=1. cOMBC_real_real_bool=1. fFalse=1. fTrue=1. member_fun_int_bool=1. quickcheck_of_int=1. fequal_real=1. ord_min_nat=1. cOMBB_real_real_real=1. cOMBC_int_int_int=1. norRRset=1. ord_lessThan_nat=1. quadRes=1. succ=1. cOMBI_int=1. if_real=1. cOMBB_64450052al_nat=1. cOMBB_722610049al_nat=1. invers1449016382omplex=1. negateSnd=1. ord_max_nat=1. sgn_sgn_int=1. sin_coeff=1. cOMBB_1480366270al_nat=1. cOMBB_782625832nt_int=1. cOMBB_nat_nat_nat=1. cos_coeff=1. ord_less_eq_bool=1. sgn_sgn_real=1. cOMBB_1419615765al_nat=1. cOMBB_1948233853l_real=1. cOMBB_430461877l_real=1. fact=1. if_Pro1731782967nt_int=1. if_nat=1. ring_1_of_int_rat=1. big_co1758102091ol_nat=1. cOMBB_1496585939nt_int=1. cOMBB_1934313333l_real=1. cOMBC_2010481033l_real=1. if_int=1. member180897546at_nat=1. norm_frac_rel=1. cOMBB_1015721476ol_nat=1. cOMBB_800536526ol_nat=1. cOMBS_nat_bool_bool=1. field_1210416355s_real=1. negDivAlg_rel=1. norm_norm_real=1. ord_atMost_nat=1. posDivAlg_rel=1. power_power_complex=1. zfact=1. big_co387207925at_nat=1. cOMBB_117013006ex_nat=1. cOMBS_337378985l_real=1. d22set=1. fEx_int=1. fNot=1. int_gcd=1. member2143287562nt_int=1. nat_gcd_rel=1. ring_1_of_int_real=1. sgn_sgn_complex=1. cOMBB_1533963633al_nat=1. cOMBB_1550063917nt_int=1. cOMBB_182850971nt_int=1. cOMBB_662120866nt_int=1. cOMBB_bool_bool_int=1. cOMBB_int_bool_int=1. cOMBC_226598744l_bool=1. cOMBC_746811033l_real=1. cOMBS_1470252563nt_int=1. finite1395289673t_bool=1. member308914164t_bool=1. ring_11397209091omplex=1. sgn_sgn_rat=1. cOMBB_1344650379nt_int=1. cOMBB_1418110531ol_int=1. cOMBB_1506897658nt_int=1. cOMBB_1768400739l_real=1. cOMBB_1846624359nt_int=1. cOMBB_1896127834l_real=1. cOMBB_1926947at_nat=1. cOMBB_2092576745l_real=1. cOMBB_320287386nt_int=1. cOMBB_421464275l_real=1. cOMBB_638531587nt_int=1. cOMBC_1329014627t_real=1. cOMBC_1508019322l_real=1. cOMBC_1805044090nt_int=1. cOMBC_1964283556nt_int=1. cOMBC_33652895t_bool=1. cOMBC_707974837nt_int=1. cOMBC_94739984l_bool=1. cOMBI_nat=1. cOMBS_1891347093nt_int=1. cOMBS_400904860l_bool=1. cOMBS_nat_rat_rat=1. fequal_nat=1. inverse_inverse_rat=1. lazy_small_lazy_rel=1. quickc1265749348ro_rel=1. semiri2020571505omplex=1. size_size_nat=1. suminf_complex=1. upto_rel=1. cOMBB_1121934354l_real=1. cOMBB_1146692694ol_nat=1. cOMBB_1484610687nt_int=1. cOMBB_1946221070al_int=1. cOMBB_2027861294ol_int=1. cOMBB_2107848501l_real=1. cOMBB_389152643ol_int=1. cOMBB_422423973l_real=1. cOMBB_591320580ol_int=1. cOMBB_793166024ol_int=1. cOMBB_real_bool_int=1. cOMBB_real_bool_real=1. cOMBC_1683390479t_bool=1. cOMBC_983868720t_bool=1. cOMBC_int_nat_int=1. cOMBS_193881978l_real=1. fequal_rat=1. if_Pro313124157l_real=1. minus_1690775515umeral=1. nat_size=1. ratrel=1. semiri132038758t_real=1. size_s945831648umeral=1. sr=1. twoSqu1907779896sum2sq=1. big_co230513141nt_int=1. cOMBB_1102189010nt_int=1. cOMBB_1159313332l_real=1. cOMBB_118231410ol_int=1. cOMBB_1211207212ol_int=1. cOMBB_1247074793l_real=1. cOMBB_1290694363ol_int=1. cOMBB_1317819104ol_int=1. cOMBB_1389251822nt_int=1. cOMBB_1453147152l_real=1. cOMBB_1459832681l_real=1. cOMBB_1593174431ol_int=1. cOMBB_1647910634ol_int=1. cOMBB_1657320178nt_int=1. cOMBB_170828966nt_int=1. cOMBB_1714920583ex_nat=1. cOMBB_172850899l_real=1. cOMBB_1795223523l_real=1. cOMBB_1875755114nt_int=1. cOMBB_188663909l_real=1. cOMBB_2046938128ol_int=1. cOMBB_2050079537l_real=1. cOMBB_2086486755nt_int=1. cOMBB_2087181719ol_int=1. cOMBB_2125215742l_real=1. cOMBB_2129825580al_int=1. cOMBB_2138578194l_real=1. cOMBB_214503962ol_int=1. cOMBB_222539774nt_int=1. cOMBB_237479429l_real=1. cOMBB_270132509l_real=1. cOMBB_348438404at_nat=1. cOMBB_3698607l_real=1. cOMBB_415306361l_real=1. cOMBB_421479067l_real=1. cOMBB_44084907l_real=1. cOMBB_47643171nt_int=1. cOMBB_520243667l_real=1. cOMBB_550562460ol_int=1. cOMBB_557258983l_real=1. cOMBB_562416518ol_int=1. cOMBB_563965291nt_int=1. cOMBB_569260360nt_int=1. cOMBB_595786433nt_int=1. cOMBB_650041899nt_int=1. cOMBB_690122963l_real=1. cOMBB_731595089l_real=1. cOMBB_735549356nt_int=1. cOMBB_773384995nt_int=1. cOMBB_798864284nt_int=1. cOMBB_859312247nt_nat=1. cOMBB_866192175nt_int=1. cOMBB_929094628al_int=1. cOMBB_95956018ol_int=1. cOMBB_984071017l_real=1. cOMBB_bool_bool_nat=1. cOMBB_int_bool_nat=1. cOMBB_int_int_int=1. cOMBB_int_int_nat=1. cOMBB_int_rat_int=1. cOMBB_int_real_int=1. cOMBB_nat_bool_int=1. cOMBB_rat_bool_int=1. cOMBB_rat_rat_nat=1. cOMBB_real_bool_nat=1. cOMBB_real_real_int=1. cOMBC_1113900202t_bool=1. cOMBC_1417754532nt_int=1. cOMBC_1801450329t_bool=1. cOMBC_2037038898nt_int=1. cOMBC_241247961t_bool=1. cOMBC_243356514t_bool=1. cOMBC_295337211t_real=1. cOMBC_412863505t_bool=1. cOMBC_467724138l_real=1. cOMBC_678732631t_bool=1. cOMBC_736024425nt_int=1. cOMBC_824100275t_real=1. cOMBC_int_rat_bool=1. cOMBC_int_real_bool=1. cOMBC_nat_int_int=1. cOMBI_real=1. cOMBS_107495110l_real=1. cOMBS_1610675060t_bool=1. cOMBS_163651580l_real=1. cOMBS_1640193733nt_int=1. cOMBS_1676841879t_bool=1. cOMBS_1720984575t_bool=1. cOMBS_2011279539nt_int=1. cOMBS_2019229620nt_int=1. cOMBS_480885903t_bool=1. cOMBS_511527878l_real=1. cOMBS_549334880nt_rat=1. cOMBS_696648398omplex=1. cOMBS_794971624l_real=1. cOMBS_902912708l_real=1. cOMBS_nat_nat_nat=1. fEx_nat=1. iszero_int=1. iszero_rat=1. member1246959636umeral=1. member1344826522l_real=1. member1747683604nt_int=1. member2092545300de_int=1. member232255508at_nat=1. member791087631nt_int=1. pair_leq=1. pair_less=1. produc1011150824nt_int=1. produc1096438694nt_int=1. produc1857364076umeral=1. produc1968959274de_int=1. produc2110120675nt_int=1. produc221809260de_int=1. produc310214954umeral=1. produc621854184at_nat=1. produc707142054at_nat=1. produc8341793nt_int=1. produc840788306t_bool=1. produc926076176t_bool=1. ring_1_of_int_int=1. semiri151668891at_rat=1. twoSqu1770640450sum2sq=1. big_co1024481617at_int=1. finite1876863882t_bool=1. frac=1. minus_534354567de_int=1. ord_lessThan_real=1. pred_nat=1. size_size_complex=1. size_size_list_int=1. a=1. b=1. p=1. q=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. hAPP_int_int=1. hAPP_int_bool=1. hAPP_i1948725293t_bool=1. hAPP_real_real=1. hAPP_int_fun_int_int=1. hAPP_nat_nat=1. hAPP_real_bool=1. hAPP_r1134773055l_bool=1. hAPP_nat_bool=1. hAPP_n1699378549t_bool=1. hAPP_r1250527377l_real=1. hAPP_nat_fun_nat_nat=1. hAPP_f448129468l_bool=1. hAPP_rat_rat=1. hAPP_i2112223885l_bool=1. hAPP_rat_bool=1. hAPP_r2115560837t_bool=1. hAPP_int_nat=1. hAPP_rat_fun_rat_rat=1. hAPP_complex_complex=1. hAPP_int_real=1. hAPP_nat_real=1. hAPP_c172932010omplex=1. hAPP_nat_int=1. hAPP_Q1762011733de_int=1. hAPP_r474017924t_real=1. hAPP_Q1729056540de_int=1. hAPP_n546711566l_real=1. hAPP_Q2096512830t_bool=1. hAPP_Q1010094925t_bool=1. hAPP_C498520661umeral=1. hAPP_int_rat=1. hAPP_C1594335432umeral=1. hAPP_f1888375463t_real=1. hAPP_f54304608l_bool=1. hAPP_complex_real=1. hAPP_i1584592887nt_int=1. hAPP_i1524277240nt_int=1. hAPP_f451358433l_real=1. hAPP_f197615720t_real=1. hAPP_C24501650l_bool=1. hAPP_C10902773l_bool=1. hAPP_f1092742621l_real=1. hAPP_int_fun_nat_int=1. hAPP_r2019696015l_real=1. hAPP_r1195171167l_real=1. deriv_real=1. hAPP_f103356543l_bool=1. hAPP_f284875647l_bool=1. hAPP_P1333854989l_bool=1. hAPP_f1566856189t_real=1. hAPP_f1676298106t_real=1. hAPP_P1175774780nt_int=1. hAPP_int_fun_int_rat=1. hAPP_P603027463t_bool=1. hAPP_f1509287679l_real=1. hAPP_f1406902706l_real=1. hAPP_r265291036omplex=1. hAPP_real_complex=1. hAPP_int_complex=1. hAPP_f1805168059t_bool=1. hAPP_P1654798560at_nat=1. hAPP_n1865633855at_nat=1. hAPP_f416620757at_nat=1. hAPP_n1289843868at_nat=1. hAPP_f42270917t_real=1. hAPP_P1555980039t_bool=1. hAPP_f1501066425l_bool=1. hAPP_r1130899993l_bool=1. hAPP_P731461727l_real=1. hAPP_f1950183573l_real=1. hAPP_f352196356l_real=1. hAPP_f1960414057l_real=1. hAPP_f1690286043t_real=1. hAPP_f1734373249l_bool=1. hAPP_P1975530577nt_int=1. hAPP_f2144054103l_bool=1. hAPP_f556082547l_real=1. hAPP_f727283836t_bool=1. hAPP_n332733730l_real=1. hAPP_P408881810nt_int=1. hAPP_f800510211t_bool=1. hAPP_i1730167831nt_int=1. hAPP_i1732201573de_int=1. hAPP_f428220345t_bool=1. hAPP_n215258509l_bool=1. divmod_nat_rel=1. hAPP_P369611207at_nat=1. hAPP_P402336767at_nat=1. posDivAlg=1. divmod_int_rel=1. hAPP_bool_bool=1. negDivAlg=1. hAPP_P230595783nt_int=1. hAPP_P941956607nt_int=1. hAPP_f2069516469l_real=1. hAPP_f957591787ol_nat=1. hAPP_C1614127039umeral=1. hAPP_C2132160860umeral=1. hAPP_Q1256397320de_int=1. hAPP_Q952608535de_int=1. hAPP_f1418982953t_bool=1. hAPP_f538843494t_bool=1. hAPP_f1639111240at_nat=1. hAPP_f1731313045at_nat=1. hAPP_f22106695ol_nat=1. image_nat_int=1. hAPP_f248847589l_real=1. image_int_nat=1. hAPP_f215623910l_bool=1. hAPP_b589554111l_bool=1. hAPP_f311463272l_bool=1. hAPP_f229349961t_bool=1. hAPP_r1889917837l_bool=1. hAPP_f1734966846l_bool=1. rcis=1. hAPP_P1463840893t_bool=1. hAPP_P62333565t_bool=1. hAPP_c769186317l_bool=1. hAPP_f1010710745l_bool=1. hAPP_f1485493409l_bool=1. hAPP_f1574055885nt_int=1. hAPP_f1861673493l_bool=1. hAPP_f60716669l_bool=1. hAPP_i769753017umeral=1. divmod_int=1. hAPP_f1407095736t_real=1. hAPP_f1796904975t_real=1. hAPP_f628503027l_bool=1. hAPP_f695504873l_bool=1. hAPP_nat_complex=1. hAPP_P178748804t_bool=1. hAPP_P880235623l_bool=1. hAPP_f203520653l_real=1. big_co1548731110nt_int=1. divmod_nat=1. hAPP_f1992866895l_real=1. hAPP_f2135977429nt_int=1. hAPP_nat_rat=1. bezw=1. hAPP_P1164677895l_bool=1. hAPP_P1709355527t_bool=1. hAPP_f1914919701at_nat=1. hAPP_f1290670424t_real=1. hAPP_f327026105t_real=1. hAPP_f73570213t_real=1. hAPP_f918606171t_real=1. hAPP_P989584703t_bool=1. hAPP_f1129044203l_real=1. hAPP_f1585078997at_nat=1. hAPP_f1760145644nt_int=1. hAPP_f2054677283nt_int=1. hAPP_f264196187l_real=1. image_int_int=1. norm_frac=1. setS=1. hAPP_b992065680at_nat=1. hAPP_f115998247l_bool=1. hAPP_f1393328161l_bool=1. hAPP_f1900646853l_bool=1. hAPP_f1904307534l_real=1. hAPP_f1993765077t_real=1. hAPP_f224989205l_real=1. hAPP_f465821005nt_int=1. hAPP_f521865025ol_nat=1. hAPP_f895854793t_real=1. hAPP_i119638232t_bool=1. rRset2norRR=1. hAPP_P1876494581l_bool=1. hAPP_b1463609396nt_int=1. hAPP_complex_bool=1. hAPP_f1067681227l_real=1. hAPP_f1523861863l_real=1. hAPP_f1629352853nt_int=1. hAPP_f1644353557l_real=1. hAPP_f2119584768l_real=1. hAPP_f237669397t_bool=1. hAPP_f59594445l_real=1. hAPP_f93439879ol_nat=1. hAPP_r337325687l_real=1. hAPP_P1145851913nt_int=1. hAPP_c1088319240omplex=1. hAPP_f1080886329l_bool=1. hAPP_f1146629647l_bool=1. hAPP_f1505651103t_bool=1. hAPP_f526364711l_bool=1. hAPP_f561022312t_bool=1. hAPP_f618557131t_bool=1. pdivmod=1. hAPP_P1062890741l_bool=1. hAPP_b40753821nt_int=1. hAPP_f1457396693omplex=1. hAPP_f1469637905l_bool=1. hAPP_f1646117269omplex=1. hAPP_f2062659861at_rat=1. hAPP_f335634176l_real=1. hAPP_f782000547ol_nat=1. hAPP_i345030060t_bool=1. fdisj=1. hAPP_P1681069257l_bool=1. hAPP_P705731903t_bool=1. hAPP_f1081447804nt_int=1. hAPP_f1607377819t_real=1. hAPP_f1722879237t_bool=1. hAPP_f1791153283t_bool=1. hAPP_f1961001761l_bool=1. hAPP_f2126667875l_real=1. hAPP_f214467655t_bool=1. hAPP_f251264923nt_int=1. hAPP_f279307923nt_int=1. hAPP_f291087797t_bool=1. hAPP_f292751352t_real=1. hAPP_f365317245l_bool=1. hAPP_f627970963t_bool=1. hAPP_nat_fun_int_int=1. hAPP_r195310020l_real=1. hAPP_r481142414t_bool=1. nat_case_nat=1. hAPP_P141737927nt_int=1. hAPP_P1477980390t_bool=1. hAPP_P1502442695at_nat=1. hAPP_P1668131738nt_int=1. hAPP_P1860904029l_real=1. hAPP_P1913525324de_int=1. hAPP_P2110489235nt_int=1. hAPP_P619277728umeral=1. hAPP_b646336293l_real=1. hAPP_f1038672605nt_int=1. hAPP_f1073644437at_rat=1. hAPP_f1122023986l_real=1. hAPP_f1131305186at_rat=1. hAPP_f1135648319t_real=1. hAPP_f1163894827t_real=1. hAPP_f1310479593l_real=1. hAPP_f1377453843nt_int=1. hAPP_f142232355nt_int=1. hAPP_f1501741374t_real=1. hAPP_f1512942609t_bool=1. hAPP_f1582586579nt_int=1. hAPP_f1591894897l_real=1. hAPP_f167782601nt_int=1. hAPP_f1732848529l_real=1. hAPP_f1781059817t_bool=1. hAPP_f1786887945l_real=1. hAPP_f1830834240at_rat=1. hAPP_f1855025978nt_int=1. hAPP_f1874145443l_real=1. hAPP_f197974549nt_int=1. hAPP_f1998755145t_real=1. hAPP_f2018027565t_bool=1. hAPP_f202917053t_bool=1. hAPP_f2119767738t_bool=1. hAPP_f213450978omplex=1. hAPP_f423804115t_bool=1. hAPP_f429935748t_bool=1. hAPP_f461489489t_bool=1. hAPP_f513299955t_bool=1. hAPP_f521271395nt_int=1. hAPP_f617310012nt_int=1. hAPP_f617735571l_real=1. hAPP_f791698359t_bool=1. hAPP_f892584630t_bool=1. hAPP_f960630521nt_int=1. hAPP_i1216375074nt_int=1. hAPP_i1529485324t_bool=1. hAPP_i1778081398nt_int=1. hAPP_i418383825t_bool=1. hAPP_r373117745t_bool=1. hAPP_r632163725t_bool=1. hAPP_r712953929l_real=1. image_nat_nat=1. xzgcd=1. hAPP_C2129356693al_nat=1. hAPP_P1982799375l_real=1. hAPP_P252494982t_bool=1. hAPP_P621635040nt_int=1. hAPP_P921862901l_bool=1. hAPP_b1482221219l_real=1. hAPP_f101635158l_bool=1. hAPP_f1048215610t_bool=1. hAPP_f1119546819l_real=1. hAPP_f1148171384nt_int=1. hAPP_f1173902867t_bool=1. hAPP_f1251097615t_bool=1. hAPP_f1344929775l_bool=1. hAPP_f1352333353l_real=1. hAPP_f1402056515l_bool=1. hAPP_f1475822739t_bool=1. hAPP_f1545556668t_bool=1. hAPP_f1735705551nt_int=1. hAPP_f1830214065l_bool=1. hAPP_f1925507189l_bool=1. hAPP_f2037783381l_bool=1. hAPP_f2105620693nt_int=1. hAPP_f222989233l_bool=1. hAPP_f251496625l_bool=1. hAPP_f318350629l_real=1. hAPP_f320596107l_real=1. hAPP_f334321603nt_int=1. hAPP_f429384717t_bool=1. hAPP_f46817975l_bool=1. hAPP_f472159229t_bool=1. hAPP_f555557763l_real=1. hAPP_f654702867t_bool=1. hAPP_f66927821l_bool=1. hAPP_f735247205t_bool=1. hAPP_f824790735l_bool=1. hAPP_f850851693l_real=1. hAPP_f851219889l_bool=1. hAPP_f85237525t_bool=1. hAPP_f879361201l_bool=1. hAPP_f928428050l_bool=1. hAPP_i1153444985nt_int=1. hAPP_i1836591008nt_int=1. hAPP_i2104874254nt_int=1. hAPP_i371647666l_real=1. hAPP_i68813070l_bool=1. hAPP_n682674106l_real=1. big_co1705425894at_nat=1. hAPP_P1251024649l_bool=1. hAPP_P1251258751nt_int=1. hAPP_P1268961545l_bool=1. hAPP_P1400155668t_bool=1. hAPP_P1853363688nt_rat=1. hAPP_P1879777545l_bool=1. hAPP_P1946311189l_bool=1. hAPP_P2045320969l_bool=1. hAPP_P2053772734t_bool=1. hAPP_P2074576781l_bool=1. hAPP_P507092031nt_rat=1. hAPP_P752050971nt_int=1. hAPP_P779853134nt_int=1. hAPP_P877703507t_bool=1. hAPP_f1040184293l_real=1. hAPP_f1052840010omplex=1. hAPP_f1063001928t_bool=1. hAPP_f1065357839nt_rat=1. hAPP_f1076489843l_real=1. hAPP_f1082758869at_rat=1. hAPP_f1083049571t_bool=1. hAPP_f1084724746t_bool=1. hAPP_f1108539711l_real=1. hAPP_f1109256153l_real=1. hAPP_f11151005nt_int=1. hAPP_f1115375056t_bool=1. hAPP_f1120137083nt_rat=1. hAPP_f1121609875t_bool=1. hAPP_f1131424617t_bool=1. hAPP_f1139079189at_int=1. hAPP_f1151807883nt_int=1. hAPP_f1154658180t_bool=1. hAPP_f1161935955l_real=1. hAPP_f1169087445t_real=1. hAPP_f11709033t_bool=1. hAPP_f1177545951t_bool=1. hAPP_f1182713365t_bool=1. hAPP_f1187443546t_bool=1. hAPP_f1198736473t_bool=1. hAPP_f1222178131t_bool=1. hAPP_f1228585167nt_int=1. hAPP_f1241350704t_bool=1. hAPP_f125788821nt_int=1. hAPP_f125837377t_bool=1. hAPP_f1261108921t_bool=1. hAPP_f1270196437nt_rat=1. hAPP_f1273270095t_bool=1. hAPP_f1293550189l_real=1. hAPP_f1295083291t_real=1. hAPP_f1311564564nt_int=1. hAPP_f1315737299t_bool=1. hAPP_f1323932638t_real=1. hAPP_f1325804733t_bool=1. hAPP_f1341793266t_bool=1. hAPP_f134192053t_real=1. hAPP_f1356864277nt_int=1. hAPP_f1361476881t_bool=1. hAPP_f1375227553nt_int=1. hAPP_f1399575567t_bool=1. hAPP_f1408247010at_nat=1. hAPP_f1431025877at_int=1. hAPP_f1448486952t_bool=1. hAPP_f1456711209t_bool=1. hAPP_f1459420095t_bool=1. hAPP_f1480506641t_bool=1. hAPP_f151095827nt_int=1. hAPP_f1547007718nt_rat=1. hAPP_f1576199059t_bool=1. hAPP_f1594865479ol_int=1. hAPP_f1607917947l_real=1. hAPP_f1613846310t_real=1. hAPP_f1625314454t_bool=1. hAPP_f1663701695l_real=1. hAPP_f1673103573at_int=1. hAPP_f1720068861t_real=1. hAPP_f172451459l_bool=1. hAPP_f1730463541l_real=1. hAPP_f1731308757nt_int=1. hAPP_f1736103445l_real=1. hAPP_f1763467369l_real=1. hAPP_f1769710159nt_int=1. hAPP_f1815301987t_bool=1. hAPP_f1832844496t_bool=1. hAPP_f183342685l_real=1. hAPP_f1840085295t_bool=1. hAPP_f1845081853t_bool=1. hAPP_f1878066172t_bool=1. hAPP_f1879982819l_real=1. hAPP_f1884005689l_bool=1. hAPP_f1900950721nt_rat=1. hAPP_f1902329768t_bool=1. hAPP_f1908301369l_real=1. hAPP_f1914742907nt_int=1. hAPP_f1920544743t_bool=1. hAPP_f1926459811ol_int=1. hAPP_f1927674023t_bool=1. hAPP_f1935805932nt_int=1. hAPP_f1965248563t_bool=1. hAPP_f1990636069t_bool=1. hAPP_f2002277285nt_int=1. hAPP_f2004554147nt_int=1. hAPP_f2042071795t_bool=1. hAPP_f2050994651t_bool=1. hAPP_f2072293513l_real=1. hAPP_f2084827628t_bool=1. hAPP_f2094497995nt_int=1. hAPP_f2114902373l_real=1. hAPP_f212164053t_real=1. hAPP_f219720582omplex=1. hAPP_f223623489t_bool=1. hAPP_f23851874omplex=1. hAPP_f252743847l_bool=1. hAPP_f269654879t_real=1. hAPP_f271976045t_bool=1. hAPP_f289318786t_bool=1. hAPP_f301246617nt_int=1. hAPP_f324002831l_real=1. hAPP_f326728547t_bool=1. hAPP_f328572565l_real=1. hAPP_f330985925l_bool=1. hAPP_f332806115t_bool=1. hAPP_f340152631t_bool=1. hAPP_f351634443t_bool=1. hAPP_f352226557t_real=1. hAPP_f374502857t_bool=1. hAPP_f381769257l_bool=1. hAPP_f382317021nt_rat=1. hAPP_f389116883t_bool=1. hAPP_f400200275nt_int=1. hAPP_f400538607nt_int=1. hAPP_f403082607t_bool=1. hAPP_f406530075omplex=1. hAPP_f41603166t_bool=1. hAPP_f422375781t_bool=1. hAPP_f434654626nt_int=1. hAPP_f492612297t_bool=1. hAPP_f499530369l_bool=1. hAPP_f512004221l_bool=1. hAPP_f517738447l_real=1. hAPP_f534361363nt_int=1. hAPP_f538565589t_bool=1. hAPP_f55007289nt_int=1. hAPP_f563293398t_real=1. hAPP_f571820015t_bool=1. hAPP_f578362681nt_int=1. hAPP_f601898971t_bool=1. hAPP_f605995867t_bool=1. hAPP_f643658017l_bool=1. hAPP_f644105375l_real=1. hAPP_f677014621l_real=1. hAPP_f693283245t_bool=1. hAPP_f696844121t_bool=1. hAPP_f704188951t_bool=1. hAPP_f713949180nt_int=1. hAPP_f720654810t_bool=1. hAPP_f725770969t_bool=1. hAPP_f729588221t_bool=1. hAPP_f737665877t_bool=1. hAPP_f74147283t_real=1. hAPP_f743790483t_bool=1. hAPP_f747162069nt_int=1. hAPP_f747475781nt_int=1. hAPP_f766218899t_real=1. hAPP_f77155443t_bool=1. hAPP_f774948957l_real=1. hAPP_f800361423l_real=1. hAPP_f801032407l_bool=1. hAPP_f808647893nt_int=1. hAPP_f823702159l_real=1. hAPP_f834119977l_bool=1. hAPP_f836602773nt_int=1. hAPP_f837737749at_nat=1. hAPP_f847817363t_bool=1. hAPP_f848516149l_bool=1. hAPP_f857296063t_bool=1. hAPP_f866672739t_bool=1. hAPP_f883232462nt_int=1. hAPP_f888249301nt_int=1. hAPP_f894608603t_bool=1. hAPP_f908327869t_bool=1. hAPP_f940061907l_bool=1. hAPP_f956464319t_bool=1. hAPP_f983569339t_bool=1. hAPP_f999082675at_nat=1. hAPP_i157317923t_real=1. hAPP_i16292313t_bool=1. hAPP_i1671359920t_real=1. hAPP_i1796122964t_bool=1. hAPP_i1823918693l_bool=1. hAPP_i447943416t_real=1. hAPP_i61245889nt_int=1. hAPP_i614188481l_bool=1. hAPP_i627165055t_real=1. hAPP_i688218208l_bool=1. hAPP_i744251628nt_int=1. hAPP_i872162435t_bool=1. hAPP_i998473677nt_int=1. hAPP_n1006566506l_bool=1. hAPP_n1983812447omplex=1. hAPP_nat_fun_rat_rat=1. hAPP_r1043989325l_real=1. hAPP_r1150855451l_bool=1. hAPP_r1230691443l_real=1. hAPP_r1392521531t_bool=1. hAPP_r1409264866l_real=1. hAPP_r1562208522t_bool=1. hAPP_r1623423338t_bool=1. hAPP_r1900510169t_bool=1. hAPP_r1938957037l_bool=1. hAPP_r1962736578t_bool=1. hAPP_r2052264067t_bool=1. hAPP_r224952523l_real=1. hAPP_r279757445t_bool=1. hAPP_r285062775l_bool=1. hAPP_r50993370t_real=1. hAPP_r579619957l_real=1. hAPP_r653725362t_bool=1. hAPP_r794344869l_real=1. hAPP_r847664445t_bool=1. hAPP_r931665397l_real=1. hAPP_r938550413l_real=1. multInvPair=1. nat_case_bool=1. code_d418564891umeral=1. hAPP_P1586233937at_nat=1. hAPP_complex_nat=1. hAPP_f1599440987ol_int=1. hAPP_f659380387ol_int=1. hAPP_list_int_nat=1. image_275383677t_bool=1. quickc495462417de_int=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f111=1. f112=1. f117=1. f118=1. f121=1. f122=1. f125=1. f128=1. f129=1. f130=1. f131=1. f164=1. f165=1. f172=1. f185=1. f186=1. f189=1. f194=1. f197=1. f198=1. f200=1. f203=1. f205=1. f206=1. f208=1. f214=1. f216=1. f218=1. f223=1. f227=1. f228=1. f229=1. f233=1. f234=1. f235=1. f236=1. f237=1. f245=1. f247=1. f285=1. f286=1. f293=1. f294=1. f299=1. f300=1. f305=1. f306=1. f307=1. f319=1. f320=1. f321=1. f322=1. f325=1. f326=1. f328=1. f334=1. f337=1. f340=1. f341=1. f345=1. f356=1. f357=1. f359=1. f360=1. f361=1. f362=1. f363=1. f364=1. f365=1. f367=1. f368=1. f373=1. f379=1. f390=1. f391=1. f392=1. f393=1. f394=1. f395=1. f412=1. f415=1. f417=1. f423=1. f425=1. f426=1. f429=1. f431=1. f434=1. f438=1. f439=1. f440=1. f443=1. f444=1. f448=1. f449=1. f450=1. f451=1. f452=1. f453=1. f454=1. f455=1. f456=1. f459=1. f460=1. f461=1. f463=1. f464=1. f500=1. f501=1. f502=1. f503=1. f508=1. f510=1. f514=1. f515=1. f518=1. f519=1. f523=1. f524=1. f530=1. f531=1. f534=1. f535=1. f536=1. f537=1. f565=1. f566=1. f567=1. f568=1. f578=1. f579=1. f580=1. f582=1. f583=1. f585=1. f587=1. f604=1. f605=1. f606=1. ord_at875362053st_int=1. div_mod_int=1. zcong=1. div_mod_nat=1. legacy_zgcd=1. ord_at4362885an_nat=1. archim1246769320r_real=1. div_mo231679042de_int=1. div_mo1740067990umeral=1. archim856651990g_real=1. isCont_real_real=1. archim1419379755ng_rat=1. archim791455193or_rat=1. natfloor=1. quickcheck_int_of=1. multInv=1. ratreal=1. summable_real=1. log=1. of_real_complex=1. accp_P2006205492nt_int=1. collect_int=1. natceiling=1. quotient_of=1. cis=1. standardRes=1. vanishes=1. ord_at238088361st_nat=1. collect_nat=1. is_RRset=1. resSet=1. wset=1. normalize=1. sums_real=1. adjust=1. comple124823625p_real=1. monoseq_real=1. bnorRset=1. ord_gr788844697n_real=1. inv=1. nat_gcd=1. ord_at641636577an_int=1. scaleR1652505878omplex=1. code_S1047413653umeral=1. summable_complex=1. the_real=1. at_real=1. cauchy_real=1. expi=1. frct=1. nat_tsub=1. accp_P490777396at_nat=1. produc1518849193nt_int=1. rsetR=1. cOMBK_1643584600t_bool=1. cauchy_complex=1. code_int_of=1. diffs_real=1. fimplies=1. phi=1. accp_int=1. arg=1. comple219730294t_bool=1. legendre=1. produc93441119t_bool=1. sums_complex=1. at_complex=1. bseq_real=1. cOMBK_rat_nat=1. code_c271388182l_size=1. code_nat_of_aux=1. collec1347809874nt_int=1. collect_real=1. hilbert_Eps_int=1. noXRRset=1. ord_at1589558736t_real=1. ord_gr1297742076an_int=1. ord_gr660468384an_nat=1. produc1319041786t_bool=1. produc1775888740l_bool=1. produc2013771390t_bool=1. produc2091540094t_bool=1. produc262399358t_bool=1. produc353512698t_bool=1. produc609372286l_bool=1. produc713050258nt_int=1. produc748992778l_bool=1. produc97574839t_bool=1. scaleR_scaleR_real=1. zcongm=1. cOMBK_bool_nat=1. collec1979865426at_nat=1. collec50511176nt_int=1. in_rel1239871883nt_int=1. in_rel1251239042umeral=1. in_rel1707483778de_int=1. in_rel293241086at_nat=1. in_rel512175208t_bool=1. in_rel682537726nt_int=1. in_rel_int_int=1. in_rel_nat_nat=1. in_rel_real_real=1. isCont_complex_real=1. nat_lcm=1. produc1298267108nt_int=1. the_int=1. z3div=1. z3mod=1. bijR_int_int=1. complex_size=1. dist_dist_complex=1. dist_dist_real=1. hilbert_Eps_real=1. int_ge_less_than=1. int_ge_less_than2=1. int_lcm=1. isCont156215680omplex=1. nat_aux=1. nat_tr160667106at_int=1. nat_tr876908586nt_nat=1. ord_at1496968948n_real=1. produc1391996073at_nat=1. produc1922581855t_bool=1. produc595218619l_real=1. produc973645403t_bool=1. quickc666637781d_zero=1. quickcheck_nat_of=1. the_Pr2103884470nt_int=1. the_Pr588456374at_nat=1. trivial_limit_nat=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f110=1. f132=1. f133=1. f134=1. f135=1. f136=1. f137=1. f138=1. f139=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f148=1. f149=1. f150=1. f151=1. f207=1. f209=1. f210=1. f211=1. f212=1. f213=1. f215=1. f219=1. f225=1. f230=1. f231=1. f232=1. f238=1. f239=1. f240=1. f241=1. f242=1. f243=1. f244=1. f246=1. f248=1. f249=1. f250=1. f251=1. f252=1. f253=1. f254=1. f255=1. f256=1. f257=1. f258=1. f259=1. f260=1. f261=1. f262=1. f263=1. f264=1. f265=1. f266=1. f289=1. f292=1. f296=1. f297=1. f301=1. f302=1. f303=1. f304=1. f308=1. f309=1. f310=1. f311=1. f312=1. f313=1. f314=1. f315=1. f316=1. f323=1. f324=1. f327=1. f332=1. f333=1. f335=1. f339=1. f342=1. f343=1. f344=1. f352=1. f353=1. f354=1. f355=1. f366=1. f396=1. f397=1. f403=1. f404=1. f405=1. f416=1. f418=1. f419=1. f422=1. f424=1. f427=1. f428=1. f436=1. f437=1. f445=1. f446=1. f447=1. f505=1. f506=1. f511=1. f512=1. f513=1. f516=1. f517=1. f525=1. f526=1. f528=1. f529=1. f532=1. f533=1. f577=1. f584=1. f586=1. f626=1. tendsto_nat_real=1. bolzano_bisect=1. tendsto_real_real=1. tendsto_nat_complex=1. tendsto_complex_real=1. tendst1507391555omplex=1. f113=1. f114=1. f115=1. f116=1. f119=1. f120=1. f123=1. f124=1. f126=1. f127=1. f152=1. f153=1. f155=1. f156=1. f157=1. f159=1. f160=1. f161=1. f162=1. f163=1. f166=1. f167=1. f168=1. f169=1. f173=1. f174=1. f175=1. f176=1. f177=1. f178=1. f179=1. f180=1. f181=1. f182=1. f183=1. f184=1. f187=1. f188=1. f190=1. f191=1. f192=1. f193=1. f195=1. f196=1. f199=1. f201=1. f202=1. f204=1. f217=1. f220=1. f222=1. f224=1. f226=1. f274=1. f275=1. f276=1. f277=1. f278=1. f279=1. f280=1. f287=1. f288=1. f290=1. f291=1. f295=1. f298=1. f317=1. f318=1. f329=1. f330=1. f331=1. f336=1. f346=1. f347=1. f348=1. f349=1. f358=1. f375=1. f376=1. f378=1. f385=1. f386=1. f398=1. f399=1. f400=1. f401=1. f402=1. f406=1. f407=1. f408=1. f409=1. f410=1. f411=1. f413=1. f414=1. f420=1. f421=1. f432=1. f433=1. f441=1. f442=1. f498=1. f504=1. f507=1. f509=1. f527=1. f538=1. f539=1. f540=1. f581=1. f607=1. f613=1. f614=1. f615=1. f616=1. f154=1. f158=1. f170=1. f171=1. f221=1. f267=1. f268=1. f269=1. f270=1. f271=1. f272=1. f273=1. f281=1. f282=1. f283=1. f284=1. f338=1. f350=1. f351=1. f369=1. f370=1. f371=1. f372=1. f374=1. f377=1. f435=1. f462=1. f465=1. f466=1. f467=1. f468=1. f469=1. f470=1. f471=1. f472=1. f473=1. f474=1. f475=1. f476=1. f477=1. f478=1. f479=1. f480=1. f481=1. f482=1. f483=1. f484=1. f485=1. f486=1. f487=1. f488=1. f489=1. f490=1. f491=1. f492=1. f493=1. f494=1. f495=1. f496=1. f497=1. f521=1. f522=1. f541=1. f542=1. f543=1. f544=1. f545=1. f546=1. f547=1. f548=1. f549=1. f550=1. f551=1. f552=1. f553=1. f554=1. f555=1. f556=1. f557=1. f558=1. f559=1. f560=1. f561=1. f562=1. f563=1. f564=1. f589=1. f590=1. f591=1. f592=1. f593=1. f594=1. f595=1. f597=1. f598=1. f599=1. f600=1. f601=1. f602=1. f603=1. f609=1. f610=1. f611=1. f612=1. f617=1. f618=1. f619=1. f620=1. f621=1. f622=1. f623=1. f624=1. f625=1. f382=1. f383=1. f384=1. f387=1. f388=1. f389=1. f430=1. f457=1. f458=1. f499=1. f520=1. f569=1. f570=1. f571=1. f572=1. f573=1. f574=1. f575=1. f576=1. f588=1. f596=1. f608=1. xzgcda=1. f380=1. f381=1.
% 32.88/32.92
% 32.88/32.92 ============================== STATISTICS ============================
% 32.88/32.92
% 32.88/32.92 Given=0. Generated=12356. Kept=8860. proofs=0.
% 32.88/32.92 Usable=0. Sos=6519. Demods=1175. Limbo=1123, Disabled=9097. Hints=0.
% 32.88/32.92 Kept_by_rule=0, Deleted_by_rule=0.
% 32.88/32.92 Forward_subsumed=3496. Back_subsumed=214.
% 32.88/32.92 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
% 32.88/32.92 New_demodulators=1456 (19 lex), Back_demodulated=988. Back_unit_deleted=15.
% 32.88/32.92 Demod_attempts=442820. Demod_rewrites=8374.
% 32.88/32.92 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 32.88/32.92 Nonunit_fsub_feature_tests=22996. Nonunit_bsub_feature_tests=20998.
% 32.88/32.92 Megabytes=419.43.
% 32.88/32.92 User_CPU=29.06, System_CPU=0.14, Wall_clock=29.
% 32.88/32.92
% 32.88/32.92 Megs malloced by palloc(): 400.
% 32.88/32.92 type (bytes each) gets frees in use bytes
% 32.88/32.92 chunk ( 104) 218406 218406 0 0.0 K
% 32.88/32.92 string_buf ( 8) 184184 184184 0 0.0 K
% 32.88/32.92 token ( 20) 480353 480353 0 0.0 K
% 32.88/32.92 pterm ( 16) 292984 292984 0 0.0 K
% 32.88/32.92 hashtab ( 8) 5173 5173 0 0.0 K
% 32.88/32.92 hashnode ( 8) 17883 17883 0 0.0 K
% 32.88/32.92 term ( 20) 2619012 2055227 563785 11011.4 K
% 32.88/32.92 term arg arrays: 2512.2 K
% 32.88/32.92 attribute ( 12) 41647 2080 39567 463.7 K
% 32.88/32.92 ilist ( 8) 188400877 188385117 15760 123.1 K
% 32.88/32.92 plist ( 8) 156382 84418 71964 562.2 K
% 32.88/32.92 i2list ( 12) 1130056 1130056 0 0.0 K
% 32.88/32.92 just ( 12) 36539 10570 25969 304.3 K
% 32.88/32.92 parajust ( 16) 0 0 0 0.0 K
% 32.88/32.92 instancejust ( 8) 0 0 0 0.0 K
% 32.88/32.92 ivyjust ( 24) 0 0 0 0.0 K
% 32.88/32.92 formula ( 28) 182732 121744 60988 1667.6 K
% 32.88/32.92 formula arg arrays: 197.8 K
% 32.88/32.92 topform ( 52) 25409 3496 21913 1112.8 K
% 32.88/32.92 clist_pos ( 20) 35028 17114 17914 349.9 K
% 32.88/32.92 clist ( 16) 8 0 8 0.1 K
% 32.88/32.92 context ( 808) 189430 189429 1 0.8 K
% 32.88/32.92 trail ( 12) 255697 255697 0 0.0 K
% 32.88/32.92 ac_match_pos (70044) 0 0 0 0.0 K
% 32.88/32.92 ac_match_free_vars_pos (20020)
% 32.88/32.92 0 0 0 0.0 K
% 32.88/32.92 btm_state ( 60) 0 0 0 0.0 K
% 32.88/32.92 btu_state ( 60) 0 0 0 0.0 K
% 32.88/32.92 ac_position (285432) 0 0 0 0.0 K
% 32.88/32.92 fpa_trie ( 20) 104069 6948 97121 1896.9 K
% 32.88/32.92 fpa_state ( 28) 78420 78420 0 0.0 K
% 32.88/32.92 fpa_index ( 12) 10 0 10 0.1 K
% 32.88/32.92 fpa_chunk ( 20) 98467 41919 56548 1104.5 K
% 32.88/32.92 fpa_list ( 16) 42218 0 42218 659.7 K
% 32.88/32.92 fpa_list chunks: 2154.8 K
% 32.88/32.92 discrim ( 12) 31860 7507 24353 285.4 K
% 32.88/32.92 discrim_pos ( 16) 24423 24423 0 0.0 K
% 32.88/32.92 flat2 ( 32) 584919 584919 0 0.0 K
% 32.88/32.92 flat ( 48) 0 0 0 0.0 K
% 32.88/32.92 flatterm ( 32) 818992 818992 0 0.0 K
% 32.88/32.92 mindex ( 28) 13 0 13 0.4 K
% 32.88/32.92 mindex_pos ( 56) 135921 135921 0 0.0 K
% 32.88/32.92 lindex ( 12) 5 0 5 0.1 K
% 32.88/32.92 clash ( 40) 0 0 0 0.0 K
% 32.88/32.92 di_tree ( 12) 37214727 4423925 32790802 384267.2 K
% 32.88/32.92 avl_node ( 20) 7736 1217 6519 127.3 K
% 32.88/32.92
% 32.88/32.92 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 32.88/32.92 List 1, length 4, 0.0 K
% 32.88/32.92 List 4, length 146, 2.3 K
% 32.88/32.92 List 5, length 7, 0.1 K
% 32.88/32.92 List 6, length 3, 0.1 K
% 32.88/32.92 List 7, length 19, 0.5 K
% 32.88/32.92 List 8, length 2038, 63.7 K
% 32.88/32.92 List 9, length 2, 0.1 K
% 32.88/32.92 List 11, length 22, 0.9 K
% 32.88/32.92 List 12, length 4, 0.2 K
% 32.88/32.92 List 14, length 1, 0.1 K
% 32.88/32.92 List 15, length 1, 0.1 K
% 32.88/32.92 List 16, length 3, 0.2 K
% 32.88/32.92 List 20, length 2, 0.2 K
% 32.88/32.92 List 25, length 2, 0.2 K
% 32.88/32.92 List 26, length 320, 32.5 K
% 32.88/32.92 List 27, length 1, 0.1 K
% 32.88/32.92 List 50, length 2, 0.4 K
% 32.88/32.92 List 53, length 2, 0.4 K
% 32.88/32.92 List 144, length 2, 1.1 K
% 32.88/32.92 List 202, length 2, 1.6 K
% 32.88/32.92
% 32.88/32.92 ============================== SELECTOR REPORT =======================
% 32.88/32.92 Sos_deleted=0, Sos_displaced=0, Sos_size=6519
% 32.88/32.92 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 32.88/32.92 I 2147483647 high age 6519 0
% 32.88/32.92 H 1 high weight 0 0
% 32.88/32.92 A 1 low age 0 0
% 32.88/32.92 F 4 low weight 0 0
% 32.88/32.92 T 4 low weight 0 0
% 32.88/32.92 ============================== end of selector report ================
% 32.88/32.92
% 32.88/32.92 ============================== end of statistics =====================
% 32.88/32.92
% 32.88/32.92 Exiting with failure.
% 32.88/32.92
% 32.88/32.92 Process 20959 exit (max_megs) Tue Jul 5 19:30:03 2022
% 32.88/32.92 Prover9 interrupted
%------------------------------------------------------------------------------