0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n003.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 15:12:02 EDT 2019
0.12/0.33	% CPUTime    : 
2.06/2.48	============================== Prover9 ===============================
2.06/2.48	Prover9 (32) version 2009-11A, November 2009.
2.06/2.48	Process 11658 was started by sandbox on n003.cluster.edu,
2.06/2.48	Thu Aug 29 15:12:04 2019
2.06/2.48	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_11505_n003.cluster.edu".
2.06/2.48	============================== end of head ===========================
2.06/2.48	
2.06/2.48	============================== INPUT =================================
2.06/2.48	
2.06/2.48	% Reading from file /tmp/Prover9_11505_n003.cluster.edu
2.06/2.48	
2.06/2.48	set(prolog_style_variables).
2.06/2.48	set(auto2).
2.06/2.48	    % set(auto2) -> set(auto).
2.06/2.48	    % set(auto) -> set(auto_inference).
2.06/2.48	    % set(auto) -> set(auto_setup).
2.06/2.48	    % set(auto_setup) -> set(predicate_elim).
2.06/2.48	    % set(auto_setup) -> assign(eq_defs, unfold).
2.06/2.48	    % set(auto) -> set(auto_limits).
2.06/2.48	    % set(auto_limits) -> assign(max_weight, "100.000").
2.06/2.48	    % set(auto_limits) -> assign(sos_limit, 20000).
2.06/2.48	    % set(auto) -> set(auto_denials).
2.06/2.48	    % set(auto) -> set(auto_process).
2.06/2.48	    % set(auto2) -> assign(new_constants, 1).
2.06/2.48	    % set(auto2) -> assign(fold_denial_max, 3).
2.06/2.48	    % set(auto2) -> assign(max_weight, "200.000").
2.06/2.48	    % set(auto2) -> assign(max_hours, 1).
2.06/2.48	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
2.06/2.48	    % set(auto2) -> assign(max_seconds, 0).
2.06/2.48	    % set(auto2) -> assign(max_minutes, 5).
2.06/2.48	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
2.06/2.48	    % set(auto2) -> set(sort_initial_sos).
2.06/2.48	    % set(auto2) -> assign(sos_limit, -1).
2.06/2.48	    % set(auto2) -> assign(lrs_ticks, 3000).
2.06/2.48	    % set(auto2) -> assign(max_megs, 400).
2.06/2.48	    % set(auto2) -> assign(stats, some).
2.06/2.48	    % set(auto2) -> clear(echo_input).
2.06/2.48	    % set(auto2) -> set(quiet).
2.06/2.48	    % set(auto2) -> clear(print_initial_clauses).
2.06/2.48	    % set(auto2) -> clear(print_given).
2.06/2.48	assign(lrs_ticks,-1).
2.06/2.48	assign(sos_limit,10000).
2.06/2.48	assign(order,kbo).
2.06/2.48	set(lex_order_vars).
2.06/2.48	clear(print_given).
2.06/2.48	
2.06/2.48	% formulas(sos).  % not echoed (1194 formulas)
2.06/2.48	
2.06/2.48	============================== end of input ==========================
2.06/2.48	
2.06/2.48	% From the command line: assign(max_seconds, 180).
2.06/2.48	
2.06/2.48	============================== PROCESS NON-CLAUSAL FORMULAS ==========
2.06/2.48	
2.06/2.48	% Formulas that are not ordinary clauses:
2.06/2.48	1 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_129_finite__Diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	2 (all X_b all Q_3 all Ga all Ca all Pa ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> (exists P_3 exists Q_4 ((all S_4 ((all Z_5 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_3,Z_5),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_4,Z_5),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_4)))) & hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_3),Ca),Q_4)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_51_conseq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	3 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_2 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z)))))) # label(fact_583_min__max_Odistrib__imp2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	4 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_726_add__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	5 (all X_a (linordered_semidom(X_a) -> (all M all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))))) # label(fact_884_power__less__imp__less__exp) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	6 (all X_b all A_2 all Ba all Ca all D (ti(X_b,Ba) = ti(X_b,Ca) & ti(X_b,D) = ti(X_b,A_2) | ti(X_b,Ba) = ti(X_b,D) & ti(X_b,A_2) = ti(X_b,Ca) <-> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D),bot_bot(fun(X_b,bool)))))) # label(fact_37_doubleton__eq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	7 (all X all Y (X = Y | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)))) # label(fact_891_zless__linear) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	8 (all X_b all Pa all Ga all P_4 all Ca all Q_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_4),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_4,Z_4),S_3)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	9 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_2) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_576_Max_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	10 (all I all J -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),I))) # label(fact_723_not__add__less1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	11 (all X_a (bot(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),bot_bot(X_a))) -> bot_bot(X_a) = ti(X_a,A_1))))) # label(fact_301_le__bot) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	12 (all X_b (group_add(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,uminus_uminus(X_b),Ba) = ti(X_b,A_2) <-> hAPP(X_b,X_b,uminus_uminus(X_b),A_2) = ti(X_b,Ba))))) # label(fact_487_equation__minus__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	13 (all X_b all Pa all A_3 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),F_2),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all A_5 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))))))) # label(fact_330_finite__subset__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	14 (all X_b (group_add(X_b) -> (all A_2 all Ba (ti(X_b,A_2) = hAPP(X_b,X_b,uminus_uminus(X_b),Ba) <-> hAPP(X_b,X_b,uminus_uminus(X_b),A_2) = ti(X_b,Ba))))) # label(fact_488_minus__equation__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	15 (all X_b all X_c (ord(X_c) -> (all F all G ((all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))) -> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)))))) # label(fact_335_le__funI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	16 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least) = ti(X_a,Least))))) # label(fact_399_min__leastR) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	17 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N) = 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_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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),N)))) # label(fact_450_nat__eq__add__iff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	18 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	19 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3)))) # label(fact_260_equalityI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	20 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),C)))) # label(fact_349_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	21 (all X all Y all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z))) # label(fact_701_zadd__left__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	22 (all X_b all F all A_2 all X_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),X_3)),X_1)) -> -(all A_5 all A_4 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),X_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_5),A_4),X_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4))))))) # label(fact_108_insert__fold1SetE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	23 (all X_c all X_b (ord(X_c) & order(X_b) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_610_xt2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	24 (all X_c all X_b all F all Z_2 all A1 all A2 (ti(fun(X_b,bool),A1) = bot_bot(fun(X_b,bool)) & ti(X_c,A2) = ti(X_c,Z_2) | (exists X_2 exists A_4 exists Y_1 (hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Y_1) = ti(X_c,A2) & hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_4),Y_1)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) & hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_4) = ti(fun(X_b,bool),A1))) <-> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A1),A2)))) # label(fact_118_fold__graph_Osimps) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	25 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_728_add__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	26 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_566_Max_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	27 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_984_mult__pos__pos) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	28 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_615_card__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	29 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_763_xt1_I7_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	30 (all X_a (dense_linorder(X_a) -> (all Z all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)))))) # label(fact_917_dense__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	31 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_507_minus__mult__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	32 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (M != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_740_le__neq__implies__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	33 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (ti(X_b,X_1) = ti(X_b,Y_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))))))) # label(fact_753_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	34 (all U_1 all M all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)))) # label(fact_451_nat__diff__add__eq2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	35 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))) # label(fact_650_card_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	36 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),X_1))))))) # label(fact_382_Min__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	37 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,Y) != ti(X_a,X))))) # label(fact_782_order__less__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	38 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3))))))) # label(fact_376_Min_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	39 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))) & (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = ti(X_b,X_1)))))) # label(fact_519_Max_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	40 (all X_1 all A_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_896_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	41 (all X_b all Ba all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) -> ti(X_b,Ba) = ti(X_b,A_2))) # label(fact_36_singletonE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	42 (all X_b all A_3 ((exists N_2 exists F_1 hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_1),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))) = ti(fun(X_b,bool),A_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_888_finite__conv__nat__seg__image) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	43 (all X_b all F all X_1 -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),bot_bot(fun(X_b,bool))),X_1))) # label(fact_85_empty__fold1SetE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	44 (all X_b (linord2061991079up_add(X_b) -> (all K_1 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),N_3)))))))))) # label(fact_601_add__Min__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	45 (all X_b all Ts all Ga all Ts_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts_1)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_318_weaken) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	46 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)))) # label(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	47 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_734_min__max_Oless__infI2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	48 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)) = hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),N_3)))))))) # label(fact_478_min__max_OInf__fin_Ohom__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	49 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite908156982e_idem(X_b,X_c)) = finite908156982e_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	50 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_4)))))))) # label(fact_883_power__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	51 (all X_b all F all A_2 ti(X_b,A_2) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_61_fold1__singleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	52 (all X_a (bot(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_1))))) # label(fact_303_bot__least) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	53 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3)))))) # label(fact_176_setprod_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	54 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)))))) # label(fact_213_setsum__diff1_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	55 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),A_2),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))))) # label(fact_477_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	56 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	57 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	58 (all X_a (monoid_mult(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),A_1)))) # label(fact_873_power__commutes) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	59 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = one_one(X_c))))) # label(fact_643_setprod_Oinfinite) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	60 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3))))))) # label(fact_198_setprod_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	61 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_144_Diff__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	62 (all X_c all X_b all Ca all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool))) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3))) # label(fact_86_image__constant) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	63 (all P (fTrue = ti(bool,P) | fFalse = ti(bool,P))) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	64 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_801_less__not__refl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	65 (all X_b all X_c (uminus(X_c) -> (all A_3 all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),uminus_uminus(fun(X_b,X_c)),A_3),X_2) = hAPP(X_c,X_c,uminus_uminus(X_c),hAPP(X_b,X_c,A_3,X_2))))) # label(fact_482_fun__Compl__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	66 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)))))))) # label(fact_940_mult__right__le__one__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	67 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))) # label(fact_649_card_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	68 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b)) = finite_fold1(X_b)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	69 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)))) # label(fact_132_Diff__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	70 (all X_b all X_1 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))) # label(fact_30_insert__absorb2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	71 (all X_c all X_b (comm_monoid_mult(X_b) -> (all F all G all A_3 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F)),G)),A_3)))) # label(fact_186_setprod__timesf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	72 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),A_2)))))) # label(fact_495_minus__le__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.48	73 (all X_b all D all R_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Q_3),D),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,Ca),D)),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_46_Comp) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	74 (all X_b all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_283_set__mp) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	75 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (exists B_3 (ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_3)))))) # label(fact_49_mk__disjoint__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	76 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)))))) # label(fact_871_card__psubset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	77 (all X_c all X_b all Ba all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(X_b,X_c,F,X_1) = ti(X_c,Ba) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Ba),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))))) # label(fact_67_rev__image__eqI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	78 (all Z1 all Z2 all 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)) = 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)) # label(fact_700_zadd__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	79 (all X_b all X_c (order(X_b) & order(X_c) -> (all F all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Ba)),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),Ca)))))))) # label(fact_925_order__less__le__subst2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	80 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_124_folding__one_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	81 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)))) # label(fact_423_le__add2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	82 (all J all I -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),I))) # label(fact_722_not__add__less2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	83 (all X all Y all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z))) # label(fact_460_nat__add__left__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	84 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)),A_3)))))))) # label(fact_580_Max_Oclosed) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	85 (all X_c all X_b all F all Z_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (exists X1 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),X1))))) # label(fact_113_finite__imp__fold__graph) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	86 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	87 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))) # label(fact_593_min__max_OSup__fin_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	88 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L_1))))) # label(fact_438_diff__le__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	89 (all Z Z = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z)) # label(fact_708_zmult__1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	90 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))))) # label(fact_629_mult__1__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	91 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_955_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	92 (all X_c all X_b (ord(X_c) & order(X_b) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_926_xt6) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	93 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),B_2) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)))))) # label(fact_255_setsum__cong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	94 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))))) # label(fact_350_min__max_Oinf__left__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	95 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_368_min__max_Oinf__le2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	96 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),Y_2),Z_2))))))) # label(fact_366_min__max_Ole__inf__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	97 (all M all K 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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) # label(fact_432_diff__cancel2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	98 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K))))) # label(fact_405_mult__le__mono1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	99 (all X_b all A_2 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) # label(fact_33_insertI1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	100 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_363_min__max_Oinf__absorb1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	101 (all X_a (preorder(X_a) -> (all X -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))) # label(fact_791_order__less__irrefl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	102 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_221_diff__add__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	103 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hAPP(X_b,X_b,uminus_uminus(X_b),Y_2) = hAPP(X_b,X_b,uminus_uminus(X_b),X_1) <-> ti(X_b,Y_2) = ti(X_b,X_1))))) # label(fact_485_compl__eq__compl__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	104 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),A_2),A_3))))) # label(fact_578_Max_Oeq__fold__idem_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	105 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S_1 all T_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),S_1),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),T_4),S_1))) -> one_one(X_c) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),T_4) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),S_1))))))) # label(fact_653_setprod__mono__one__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	106 (all X_a (comm_semiring_1(X_a) -> (all X all P_2 all Q_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_2)),Q_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_2),Q_1))))) # label(fact_724_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	107 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_878_one__le__power) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	108 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_821_add__le__less__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	109 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_779_order__less__asym_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	110 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),N_1) = M)) # label(fact_443_le__add__diff__inverse2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	111 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),D))))))) # label(fact_304_diff__eq__diff__less__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	112 (all X_c all X_b all F all A_2 all B_2 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))) # label(fact_83_image__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	113 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)))) # label(fact_409_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	114 (all X_b (linordered_semidom(X_b) -> (all X_1 all Y_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),X_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2))))))) # label(fact_846_power__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	115 (all X_b (linorder(X_b) -> ord_min(X_b) = hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),max(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),ord_less_eq(X_b))))) # label(fact_397_dual__max) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	116 (all I_1 all Pa all K_1 (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_931_int__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	117 (all X_b (order(X_b) -> ti(fun(X_b,fun(X_b,fun(X_b,bool))),ord_atLeastAtMost(X_b)) = ord_atLeastAtMost(X_b))) # label(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	118 (all X_b (ordered_ab_group_add(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_494_neg__le__iff__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	119 (all N_1 N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),one_one(nat))) # label(fact_624_nat__mult__1__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	120 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)))))))) # label(fact_881_power__less__power__Suc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	121 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)))) # label(fact_288_set__eq__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	122 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) & (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_604_min__max_OSup__fin_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	123 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) -> ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3))))) # label(fact_614_card__seteq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	124 (all X_b (cancel_semigroup_add(X_b) -> (all Ba all A_2 all Ca (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2) <-> ti(X_b,Ba) = ti(X_b,Ca))))) # label(fact_230_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	125 (all X_b (ordere236663937imp_le(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),Ba))))))) # label(fact_730_add__less__cancel__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	126 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)),A_3)))))))) # label(fact_607_min__max_OSup__fin_Oclosed) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	127 (all X_b all X_c (comm_monoid_mult(X_c) -> (all H all G all A_3 all B_2 (ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,H,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),B_2) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3)))))) # label(fact_253_setprod_OF__cong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	128 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_508_minus__mult__minus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	129 (all X_b all X_c (order(X_b) & order(X_c) -> (all F all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Ba)),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),Ca)))))))) # label(fact_928_order__le__less__subst2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	130 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B)))) # label(fact_222_add__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	131 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_279_linorder__linear) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	132 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(X_b,X_c,Ba,A_2) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Ba)),one_one(X_c))),S_1)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Ba)),one_one(X_c))),S_1) = one_one(X_c)))))) # label(fact_644_setprod__delta_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	133 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),X_1)))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),X_1)))))))) # label(fact_839_fold1__strict__below__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	134 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all Y_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = ti(X_b,X_1))))))) # label(fact_395_Min__eqI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	135 (all X_b all A_2 all A_3 (bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_17_equals0D) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	136 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	137 (all X_b (minus(X_b) -> minus_minus(X_b) = ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	138 (all X_b (linorder(X_b) -> (all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all B_1 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),B_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),A_4))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)))))))) # label(fact_932_finite__linorder__max__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	139 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all A_2 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),F_2)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),F_2)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),F_2))))))) # label(fact_217_setsum__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	140 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_757_order__less__imp__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	141 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_294_add__le__imp__le__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	142 (all X_b all F all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),F_2) = one_one(nat) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> one_one(nat) = hAPP(X_b,nat,F,X_2)))))) # label(fact_633_setprod__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	143 (all A_3 all B_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_2)))) # label(fact_900_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	144 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))))) # label(fact_281_equalityE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	145 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))))) # label(fact_660_of__nat__add) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	146 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_988_zero__less__mult__pos2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	147 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_993_mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	148 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)))) # label(fact_512_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	149 (all X_1 all Y_2 all Pa ((-hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)) = hAPP(nat,int,semiring_1_of_nat(int),Y_2)) & (hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))))) # label(fact_898_int__if__cong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	150 (all X_b (comm_monoid_add(X_b) -> (all Pa all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(nat,X_b,Pa,M_1)),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),M_1),N))))))) # label(fact_935_setsum__head) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	151 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))))) # label(fact_218_setsum_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	152 (all Z hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z)))) # label(fact_953_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	153 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)))) # label(fact_537_min__max_Osup__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	154 (all K_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))))) # label(fact_721_nat__add__left__cancel__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	155 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) # label(fact_456_nat__mult__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	156 (all X_b all X_c (comm_monoid_add(X_c) -> (all H all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,H,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),B_2)))))) # label(fact_256_setsum_OF__cong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	157 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),G_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_2_cut) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	158 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	159 (all X_b (comm_monoid_add(X_b) -> (all F all M_1 all K_1 all N hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1))) = hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))))) # label(fact_835_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	160 (all X_b all A_2 all Pa ((exists X_2 ((all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,Y_1) = ti(X_b,X_2))) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) -> (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_116_the1__equality) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	161 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K))) # label(fact_446_add__diff__assoc2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	162 (all X_b (ab_sem1668676832m_mult(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_2),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))))) # label(fact_206_fold1__eq__fold__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	163 (all X_b all X_2 (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))))) # label(fact_59_bot__empty__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	164 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))),B_2),A_3))) # label(fact_177_minus__fold__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	165 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all G all A_3 all B_2 (ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),B_2) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3)))))) # label(fact_252_setprod__cong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	166 (all X_b all Q_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_3)))))) # label(fact_97_finite__Collect__conjI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	167 (all X_b all A_2 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),A_2),A_3) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))))) # label(fact_204_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	168 (all X_c all X_b (ab_group_add(X_b) -> (all F all A_3 hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),combb(X_b,X_b,X_c),uminus_uminus(X_b)),F)),A_3)))) # label(fact_510_setsum__negf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	169 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M)))))) # label(fact_743_diff__less__mono2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	170 (all K_1 all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1) <-> K_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)))) # label(fact_444_le__imp__diff__is__add) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	171 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),X_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),Y_2)))))) # label(fact_735_min__less__iff__conj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	172 (all N_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1))))) # label(fact_950_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	173 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M)))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	174 (all N all Q_3 all Pa ((all X_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_3,X_2)),hAPP(nat,nat,Pa,X_2)))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Pa),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Q_3),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),Pa)),Q_3)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N)))) # label(fact_337_sum__diff__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	175 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),J))))) # label(fact_706_zadd__left__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	176 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all F_2 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> one_one(X_c) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),F_2) = one_one(X_c))))) # label(fact_655_setprod__1_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	177 (all X_c all X_b hoare_1759541758le_rec(X_c,X_b) = ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_1759541758le_rec(X_c,X_b))) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	178 (all X_c all X_b (comm_monoid_mult(X_b) -> (all F hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),F),bot_bot(fun(X_c,bool))) = one_one(X_b)))) # label(fact_641_setprod__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	179 (all X_b (ring(X_b) -> (all A_2 all E all Ca all Ba all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca) <-> ti(X_b,D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca))))) # label(fact_220_eq__add__iff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	180 (all X_b all Q_3 all Pa all X_1 (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Q_3)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_291_rev__predicate1D) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	181 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_490_Compl__anti__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	182 (all X_b all X_c all F all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_2))))) # label(fact_322_image__diff__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	183 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	184 (all N_1 all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N_1)),K)))) # label(fact_742_less__imp__diff__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	185 (all X_b all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)))) # label(fact_311_insert__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	186 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)) = ti(X_a,B)))) # label(fact_503_add__minus__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	187 (all Z1 all Z2 all W_2 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_2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_2))) # label(fact_705_zadd__zmult__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	188 (all X_b all Ba all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B_2))))) # label(fact_25_insertI2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	189 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_416_add__le__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	190 (all X_b all A_3 hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),A_3)) # label(fact_646_card__eq__setsum) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	191 (all X_b all Ba all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B_2))))) # label(fact_309_subset__insertI2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	192 (all Pa all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_893_int__less__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	193 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),W_1),Z_2)))) # label(fact_867_add1__zle__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	194 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_2)) # label(fact_702_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	195 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ba all Ca (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2))))))) # label(fact_989_mult__less__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	196 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))) # label(fact_343_finite__lessThan) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	197 (all P (fFalse = ti(bool,P) | ti(bool,P) = fTrue)) # label(help_If_3_1_T) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	198 (all L all U hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U)))) # label(fact_681_finite__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	199 (all X_b (ord(X_b) -> ord_lessThan(X_b) = ti(fun(X_b,fun(X_b,bool)),ord_lessThan(X_b)))) # label(tsy_c_SetInterval_Oord__class_OlessThan_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	200 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))))) # label(fact_627_mult_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	201 (all X_b all X_c (minus(X_c) -> (all A_3 all B_2 all X_2 hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_2,X_2)) = hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_2),X_2)))) # label(fact_160_fun__diff__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	202 (all X_b all Ga hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	203 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))))) # label(fact_375_Min_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	204 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_406_le__cube) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	205 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),big_Inf_fin(X_b)) = big_Inf_fin(X_b))) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	206 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))))) # label(fact_374_Min__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	207 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	208 (all M all N_1 all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_965_nat__power__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.49	209 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),A_3))))))) # label(fact_384_Min__in) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	210 (all X_b (ord(X_b) -> ord_max(X_b) = hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),max(X_b),ord_less_eq(X_b)))) # label(fact_568_max__ord__max) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	211 (all X_a (linorder(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X))))))) # label(fact_556_min__max_Osup__least) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	212 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z),X))))) # label(fact_529_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	213 (all X_b (ab_semigroup_mult(X_b) -> (all A_2 all Ba all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_3),X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))),X_1)))))))) # label(fact_143_fold__graph__permute__diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	214 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (ti(fun(X_b,bool),F_2) != bot_bot(fun(X_b,bool)) -> ((all X_2 hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),F_3) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))))))) # label(fact_120_finite__ne__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	215 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_798_less__irrefl__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	216 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K)) # label(fact_459_nat__add__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	217 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X)))) # label(fact_528_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	218 (all X_b (order(X_b) -> (all A_2 all Ba (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = bot_bot(fun(X_b,bool)))))) # label(fact_829_atLeastatMost__empty__iff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	219 (all X_b ti(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)))),power_1(X_b)) = power_1(X_b)) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	220 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N))) -> hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),M_1),N)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N)))) # label(fact_864_atLeastAtMostPlus1__int__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	221 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (exists B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3)))))) # label(fact_913_psubset__imp__ex__mem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	222 (all X_b the(X_b) = ti(fun(fun(X_b,bool),X_b),the(X_b))) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	223 (all X_b all X_c finite1357897459simple(X_b,X_c) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c))) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	224 (all X_b partial_flat_lub(X_b) = ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b))) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	225 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all Y_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_396_Max__eqI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	226 (all X_b all Ca all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_520_ComplI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	227 (all X_b ti(fun(fun(X_b,bool),nat),finite_card(X_b)) = finite_card(X_b)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	228 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K_1))))) # label(fact_344_finite__Collect__le__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	229 (all X_a (linorder(X_a) -> (all X all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B))))))) # label(fact_358_min__max_Ole__infE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	230 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_418_trans__le__add2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	231 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),Ba)),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),A_3)))))))) # label(fact_567_min__max_Osup__le__fold__sup) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	232 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_937_le0) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	233 (all X_c all X_b all F all Z_2 all X_1 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),X_1)) -> ti(X_c,X_1) = ti(X_c,Z_2))) # label(fact_106_empty__fold__graphE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	234 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_545_min__max_Osup_Oidem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	235 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)))))) # label(fact_111_finite__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	236 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_251_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	237 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) <-> hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) # label(fact_525_Compl__eq__Compl__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	238 (all X_b all Q_3 all Pa all Ga all P_4 all Ca all Q_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_4),Ca),Q_5)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> (all S_4 ((all Z_5 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_4,Z_5),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_5,Z_5),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_4)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_8_conseq12) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	239 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)))) # label(fact_543_min__max_Osup__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	240 (all X_c all X_d all X_b (semiring_0(X_b) -> (all F all A_3 all G all B_2 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_d,bool),fun(X_c,X_b),hAPP(fun(X_c,fun(fun(X_d,bool),X_b)),fun(fun(X_d,bool),fun(X_c,X_b)),combc(X_c,fun(X_d,bool),X_b),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b)),hAPP(fun(fun(X_d,X_b),fun(fun(X_d,bool),X_b)),fun(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b))),combb(fun(X_d,X_b),fun(fun(X_d,bool),X_b),X_c),big_co1399186613setsum(X_d,X_b)),hAPP(fun(X_d,X_b),fun(X_c,fun(X_d,X_b)),hAPP(fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b))),fun(fun(X_d,X_b),fun(X_c,fun(X_d,X_b))),combc(X_c,fun(X_d,X_b),fun(X_d,X_b)),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b))),hAPP(fun(fun(X_b,X_b),fun(fun(X_d,X_b),fun(X_d,X_b))),fun(fun(X_c,fun(X_b,X_b)),fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b)))),combb(fun(X_b,X_b),fun(fun(X_d,X_b),fun(X_d,X_b)),X_c),combb(X_b,X_b,X_d)),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F))),G))),B_2)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_d,bool),X_b,hAPP(fun(X_d,X_b),fun(fun(X_d,bool),X_b),big_co1399186613setsum(X_d,X_b),G),B_2))))) # label(fact_187_setsum__product) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	241 (all P all Q (hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	242 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca)),D)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))))))) # label(fact_836_less__add__iff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	243 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b)))) # label(fact_163_comp__fun__idem__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	244 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))))))))) # label(fact_588_min__max_Osup__Inf1__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	245 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(Q))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	246 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1))))) # label(fact_413_add__leE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	247 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_855_psubset__imp__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	248 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int)))))) # label(fact_869_zle__diff1__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	249 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),Y_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),X_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2))))))) # label(fact_559_le__max__iff__disj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	250 (all X_b (linordered_semidom(X_b) -> (all M_1 all N all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),A_2)) -> (N = M_1 <-> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),A_2),M_1) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),A_2),N)))))) # label(fact_879_power__inject__exp) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	251 (all X_b (linorder(X_b) -> (all Y_2 all X_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> ti(X_b,Y_2) = ti(X_b,X_1)))))) # label(fact_787_linorder__antisym__conv3) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	252 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M))))) # label(fact_437_diff__le__mono2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	253 (all X_b all Ca -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),bot_bot(fun(X_b,bool))))) # label(fact_19_empty__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	254 (all X_b (order(X_b) -> (all A_2 all Ba all Ca all D ((-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),A_2)) & (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),A_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),D))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),D))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),D)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),Ca),D))))))) # label(fact_794_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	255 (all X_b finite2073411215e_idem(X_b) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b))) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	256 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K))) # label(fact_441_add__diff__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	257 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	258 (all P all Q (-hBOOL(P) | hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	259 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),A_3)))))))) # label(fact_393_Min_Oclosed) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	260 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_233_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	261 (all X_b all X_c (comm_monoid_mult(X_c) -> ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),big_co302546470etprod(X_b,X_c)) = big_co302546470etprod(X_b,X_c))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	262 (all X_b (ab_sem1668676832m_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))))) # label(fact_164_comp__fun__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	263 (all X_b (linorder(X_b) -> big_Sup_fin(X_b) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),big_Sup_fin(X_b)))) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	264 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_513_ab__diff__minus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	265 (all X_a (preorder(X_a) -> (all X all Y (X = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_277_order__eq__refl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	266 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_754_order__neq__le__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	267 (all X_b (linord2061991079up_add(X_b) -> (all K_1 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),N_3))))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3))))))) # label(fact_600_add__Max__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	268 (all I all U_1 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),U_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K))) # label(fact_464_left__add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	269 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_134_DiffD1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	270 (all X_b all A_3 all X_1 all B_2 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2))))) # label(fact_870_psubset__insert__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	271 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))) & (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = ti(X_b,X_1)))))) # label(fact_605_min__max_OSup__fin_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	272 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_471_min__max_OInf__fin_Osingleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	273 (all X_b all A_3 ((all Y_1 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3))) -> bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3))) # label(fact_50_equals0I) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	274 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	275 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))) # label(fact_196_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	276 (all X_1 all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)))) # label(fact_903_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	277 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),Ba)))))))) # label(fact_387_min__max_Ofold__inf__le__inf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	278 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),Pa))) # label(fact_521_Collect__neg__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	279 (all X_b (ord(X_b) -> ord_max(X_b) = ti(fun(X_b,fun(X_b,X_b)),ord_max(X_b)))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	280 (all X_b all F all A_2 all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)),hAPP(X_b,nat,F,A_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))))) # label(fact_199_setsum__diff1__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	281 (all X_b (linorder(X_b) -> (all Ca all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Ba)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ca),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),Ba),Ca)))))))) # label(fact_581_min__max_Ofold__sup__le__sup) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	282 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_527_ComplE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	283 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_712_min__max_Oless__supI2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	284 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),A_2),A_3) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))))) # label(fact_378_Min_Oeq__fold__idem_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	285 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) # label(fact_131_set__diff__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	286 (all U all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))))) # label(fact_398_finite__less__ub) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	287 (all X_b hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) = bot_bot(fun(X_b,bool))) # label(fact_23_empty__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	288 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | M_1 = N <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_738_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	289 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))))) # label(fact_531_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	290 (all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))))) # label(fact_806_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	291 (all X_b all X_c all Z_2 all X_1 all A_3 all V all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),V)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> -(all Y_1 (hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_1) = ti(X_c,V) -> -hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_1)))))))) # label(fact_207_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	292 (all X_b all X_c all F all G ((all X_2 hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_75_ext) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	293 (all X_b all X_a all P all Q ti(X_a,P) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	294 (all N_3 ((exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)))) # label(fact_345_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	295 (all X_b (linord581940658strict(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))))))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	296 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) & N != M_1)) # label(fact_737_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	297 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	298 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_747_linorder__le__less__linear) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	299 (all K_1 all M_1 all N (M_1 = N <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) # label(fact_458_nat__add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	300 (all X_b (linorder(X_b) -> (all M_3 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),M_3),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),M_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),M_3))))))))) # label(fact_341_Min__antimono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	301 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> 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),N_1)) = M)) # label(fact_440_le__add__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	302 (all Z Z = hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z))) # label(fact_860_zminus__zminus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	303 (all W_2 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2))) # label(fact_704_zadd__zmult__distrib2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	304 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1) = hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_1759541758le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1_1),Com_1),Fun2_1))) # label(fact_16_triple_Orecs) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	305 (all X_b all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) # label(fact_32_insert__compr) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	306 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_227_add__imp__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	307 (all Vname_1 all Fun_1 all Com1 all Com2 hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_72_com_Osimps_I24_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	308 (all X_b all A_3 all B_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),A_3))) # label(fact_317_Diff__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	309 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_3)))))) # label(fact_923_pinf_I6_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	310 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))))) # label(fact_402_le__diff__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	311 (all X_b all F all A_2 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_2),A_3),X_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)),X_1))))) # label(fact_92_fold1Set_Ointros) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	312 (all X_b all Q_3 all Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Q_3,X_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Q_3)))) # label(fact_339_predicate1I) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	313 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),D))))))) # label(fact_768_diff__eq__diff__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	314 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> one_one(X_c) = hAPP(X_b,X_c,G,X_2))) -> one_one(X_c) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3)))))) # label(fact_654_setprod_Oneutral) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	315 (all X_b all X_1 all Y_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))) # label(fact_29_insert__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	316 (all X_b all X_c (order(X_b) & order(X_c) -> (all Ca all A_2 all F all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_c,X_b,F,Ba))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ba),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ca))))))))) # label(fact_930_order__le__less__subst1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	317 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) <-> (all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))))))) # label(fact_280_le__fun__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	318 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_760_order__le__neq__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	319 (all X_b (linordered_semidom(X_b) -> (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))))))) # label(fact_973_of__nat__0__less__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.50	320 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I))) # label(fact_447_diff__add__assoc2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	321 (all X_a (linordered_semidom(X_a) -> (all N_1 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_1)))))))) # label(fact_823_less__1__mult) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	322 (all X_c all X_b all F all A_3 (bot_bot(fun(X_c,bool)) = ti(fun(X_c,bool),A_3) <-> hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_79_image__is__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	323 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ba all Ca (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba))))))) # label(fact_983_mult__less__cancel__left__pos) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	324 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),Z_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2)),Z_2)))))) # label(fact_736_min__less__iff__disj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	325 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))))))) # label(fact_197_setprod__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	326 (all Vname all Fun skip != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun)) # label(fact_74_com_Osimps_I8_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	327 (all M_1 all K_1 all F ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)))))) # label(fact_911_mono__nat__linear__lb) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	328 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_1))))) # label(fact_282_subset__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	329 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	330 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_936_less__zeroE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	331 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_762_order__less__le__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	332 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)))) # label(fact_544_min__max_Osup_Ocommute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	333 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	334 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	335 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (ti(X_a,Y) != ti(X_a,X) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_770_linorder__cases) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	336 (all X_b all A_3 bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)) # label(fact_137_empty__Diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	337 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_214_setsum_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	338 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3))))) # label(fact_195_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	339 (all X_c all X_b (order(X_b) & order(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_927_xt4) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	340 (all N_1 all M -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),M))))) # label(fact_848_not__int__zless__negative) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	341 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z)))) # label(fact_370_min__add__distrib__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	342 (all X_b all A_3 all Ba ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))) -> ti(X_b,Ba) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_3)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_3)))) # label(fact_336_flat__lub__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	343 (all X_c all X_b all X_d (comm_monoid_add(X_d) -> (all F all R_1 all T_4 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_4)) -> hAPP(fun(X_c,bool),X_d,hAPP(fun(X_c,X_d),fun(fun(X_c,bool),X_d),big_co1399186613setsum(X_c,X_d),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,X_d),hAPP(fun(X_c,fun(fun(X_b,bool),X_d)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,X_d)),combs(X_c,fun(X_b,bool),X_d),hAPP(fun(X_c,fun(X_b,X_d)),fun(X_c,fun(fun(X_b,bool),X_d)),hAPP(fun(fun(X_b,X_d),fun(fun(X_b,bool),X_d)),fun(fun(X_c,fun(X_b,X_d)),fun(X_c,fun(fun(X_b,bool),X_d))),combb(fun(X_b,X_d),fun(fun(X_b,bool),X_d),X_c),big_co1399186613setsum(X_b,X_d)),hAPP(fun(X_b,fun(X_c,X_d)),fun(X_c,fun(X_b,X_d)),combc(X_b,X_c,X_d),F))),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),collect(X_b)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1)))),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),R_1))))),T_4) = hAPP(fun(X_b,bool),X_d,hAPP(fun(X_b,X_d),fun(fun(X_b,bool),X_d),big_co1399186613setsum(X_b,X_d),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,X_d),hAPP(fun(X_b,fun(fun(X_c,bool),X_d)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,X_d)),combs(X_b,fun(X_c,bool),X_d),hAPP(fun(X_b,fun(X_c,X_d)),fun(X_b,fun(fun(X_c,bool),X_d)),hAPP(fun(fun(X_c,X_d),fun(fun(X_c,bool),X_d)),fun(fun(X_b,fun(X_c,X_d)),fun(X_b,fun(fun(X_c,bool),X_d))),combb(fun(X_c,X_d),fun(fun(X_c,bool),X_d),X_b),big_co1399186613setsum(X_c,X_d)),F)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_4)))),R_1)))),S_1)))))) # label(fact_211_setsum__setsum__restrict) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	344 (all U U = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U))) # label(fact_612_card__lessThan) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	345 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))))) # label(fact_325_le__add__iff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	346 (all X_b (order(X_b) -> (all A_2 hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),A_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))) # label(fact_833_atLeastAtMost__singleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	347 (all X_b all B_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_284_set__rev__mp) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	348 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_613_card__insert__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	349 (all X_c all X_b (comm_monoid_mult(X_b) -> (all H all G all S_1 all R_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,one_one(X_b)),one_one(X_b))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2))))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),H),S_1)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),S_1)))))))))) # label(fact_657_setprod_Orelated) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	350 (all X_a all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) != ti(X_a,Y))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	351 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) <-> ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_853_psubset__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	352 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_598_min__max_OSup__fin_Oinsert__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	353 (all X_b (order(X_b) -> (all K_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),K_1),bot_bot(fun(X_b,bool)))),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),K_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),K_1),bot_bot(fun(X_b,bool)))))) # label(fact_257_single__Diff__lessThan) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	354 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_751_leI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	355 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))) & (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = ti(X_b,X_1)))))) # label(fact_123_folding__one_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	356 (all X_c all X_b all F all Z_2 all Y_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),Y_2)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),A_3),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_2)))))) # label(fact_172_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	357 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),A_3)))))))) # label(fact_479_min__max_OInf__fin_Oclosed) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	358 (all Vname_1 all Fun_1 all Vname all Fun (ti(vname,Vname) = ti(vname,Vname_1) & Fun_1 = Fun <-> hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun) = hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1))) # label(fact_66_com_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	359 (all X_b all X_c all X_1 all Z_2 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3)))) # label(fact_178_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	360 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))) # label(fact_661_of__nat__mult) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	361 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M_1) = N))) # label(fact_453_nat__eq__add__iff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	362 (all X_b all X_c (order(X_c) & order(X_b) -> (all Ca all A_2 all F all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ba))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ba),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ca))))))))) # label(fact_929_order__less__le__subst1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	363 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z)))) # label(fact_348_min__max_Oinf__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	364 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> -(all B_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_3) = ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_3)))))) # label(fact_48_Set_Oset__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	365 (all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X1)))))) # label(fact_109_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	366 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,A_2) = ti(X_b,X_2))) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_93_the__equality) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	367 (all X_b all Ga all Pa all X_3 all A_2 hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,state),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(X_b,fun(state,bool))),combc(X_b,fun(state,state),fun(state,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),X_b),combb(state,bool,state)),Pa)),hAPP(fun(state,nat),fun(state,state),hAPP(fun(state,fun(nat,state)),fun(fun(state,nat),fun(state,state)),combs(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),X_3)),A_2))),hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_2)),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_60_Ass) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	368 (all X_a (linord20386208strict(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_987_zero__less__mult__pos) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	369 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ca))))))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	370 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_498_compl__le__swap1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	371 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_166_times_Oidem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	372 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2) = ti(X_b,X_1))))) # label(fact_367_min__max_Ole__iff__inf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	373 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,Y_2) = ti(X_b,X_1) <-> hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1) = hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),Y_2))))) # label(fact_293_lessThan__eq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	374 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_739_less__imp__le__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	375 (all U_1 all M all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_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)),U_1)),M)),N_1))) # label(fact_454_nat__diff__add__eq1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	376 (all W_2 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),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_2),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z2))) # label(fact_699_zdiff__zmult__distrib2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	377 (all T_2 all T_1 (uminus(T_1) -> uminus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ouminus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	378 (all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),B_2)) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_258_setsum__diff__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	379 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_617_card__Diff__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	380 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_184_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	381 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3))))) # label(fact_372_Min_OF__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	382 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_max(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))) # label(fact_596_min__max_OSup__fin_OF__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	383 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,Y) = ti(X_a,X))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	384 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1)) = hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1))))) # label(fact_517_image__uminus__greaterThan) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	385 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_2) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_599_min__max_OSup__fin_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	386 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_276_le__funD) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	387 (all X_c all X_b hoare_225284258e_case(X_c,X_b) = ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_225284258e_case(X_c,X_b))) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__case_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	388 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Q_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),Q_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),Q_1)))) # label(fact_732_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	389 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	390 (all Z all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),Z)) -> Z = W_2))) # label(fact_694_zle__antisym) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	391 (all X_b (comm_monoid_add(X_b) -> (all F all P_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)))) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),P_1))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),P_1)))))))) # label(fact_843_setsum__ub__add__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	392 (all X_b big_semilattice_big(X_b) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),big_semilattice_big(X_b))) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	393 (all X_d all X_b all X_c (comm_monoid_add(X_c) -> (all G all F all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),S_1) = hAPP(fun(X_d,bool),X_c,hAPP(fun(X_d,X_c),fun(fun(X_d,bool),X_c),big_co1399186613setsum(X_d,X_c),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,X_c),hAPP(fun(fun(X_b,bool),X_c),fun(fun(X_d,fun(X_b,bool)),fun(X_d,X_c)),combb(fun(X_b,bool),X_c,X_d),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G)),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_d),collect(X_b)),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_d),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1)))),hAPP(fun(X_b,fun(X_d,bool)),fun(X_d,fun(X_b,bool)),combc(X_b,X_d,bool),hAPP(fun(X_b,X_d),fun(X_b,fun(X_d,bool)),hAPP(fun(X_d,fun(X_d,bool)),fun(fun(X_b,X_d),fun(X_b,fun(X_d,bool))),combb(X_d,fun(X_d,bool),X_b),fequal(X_d)),F)))))),hAPP(fun(X_b,bool),fun(X_d,bool),hAPP(fun(X_b,X_d),fun(fun(X_b,bool),fun(X_d,bool)),image(X_b,X_d),F),S_1)))))) # label(fact_208_setsum__image__gen) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	394 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N_1)) # label(fact_684_int__power) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	395 (all X_a all X all Y ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	396 (all W_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),W_2))) # label(fact_691_zle__refl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	397 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))))) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	398 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W_2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W_2)) # label(fact_688_diff__int__def__symmetric) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	399 (all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	400 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1) = hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_225284258e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1_1),Com_1),Fun2_1))) # label(fact_42_triple_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	401 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_945_add__nonneg__pos) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	402 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))))) # label(fact_826_less__diff__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	403 (all X_c all X_b all F bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool)))) # label(fact_80_image__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	404 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_356_min__max_Oinf_Oidem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	405 (all X_c all X_b (uminus(X_b) -> (all A_3 all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),uminus_uminus(fun(X_c,X_b)),A_3),X_1) = hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_c,X_b,A_3,X_1))))) # label(fact_484_uminus__apply) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	406 (all X_b (order(X_b) -> (all X_1 all Y_2 (ti(X_b,Y_2) = ti(X_b,X_1) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)))))) # label(fact_750_order__le__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	407 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_243_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	408 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)))) # label(fact_415_add__leD2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	409 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)) = hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R)) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	410 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y))) # label(fact_906_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	411 (all X_c all X_b (minus(X_b) -> (all A_3 all B_2 all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_2),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_2,X_1))))) # label(fact_159_minus__apply) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	412 (all X_c all X_b all F all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),B_2)))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_2)))) # label(fact_334_image__subsetI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	413 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_506_minus__mult__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	414 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_745_linorder__not__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	415 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))))) # label(fact_837_less__add__iff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	416 (all X_b all A_3 all X_1 all B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2)))) # label(fact_141_insert__Diff__if) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	417 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_765_xt1_I8_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	418 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K))))) # label(fact_411_le__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	419 (all Z all W_2 hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z)),W_2)) # label(fact_687_zmult__zminus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	420 (all X_b all Ba all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) <-> ti(X_b,Ba) = ti(X_b,A_2))) # label(fact_38_singleton__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	421 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) # label(fact_82_insert__image) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	422 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3)))))) # label(fact_152_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	423 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_944_add__pos__nonneg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	424 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_606_min__max_OSup__fin_Ohom__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	425 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),Z_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Z_2)))))) # label(fact_710_max__less__iff__conj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	426 (all X_b all Ba all A_2 all B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> ti(X_b,A_2) = ti(X_b,Ba)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B_2))))) # label(fact_10_insertCI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	427 (all X all Y all Z hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z))) # label(fact_703_zpower__zadd__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	428 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,Y) != ti(X_a,X))))) # label(fact_781_order__less__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	429 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))))) # label(fact_161_comp__fun__idem__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	430 (all X_b (cancel_semigroup_add(X_b) -> (all A_2 all Ba all Ca (ti(X_b,Ca) = ti(X_b,Ba) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ba))))) # label(fact_231_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	431 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))) # label(fact_511_diff__minus__eq__add) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	432 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)))))))) # label(fact_475_min__max_OInf__fin_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	433 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (N = M_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))))) # label(fact_448_eq__diff__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	434 (all X_b all A_3 (bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3) <-> (all X_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))))) # label(fact_22_all__not__in__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	435 (all X_c all X_b all F all Z_2 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),Z_2))) # label(fact_105_fold__graph_OemptyI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.51	436 (all Vname all Fun hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun) != skip) # label(fact_78_com_Osimps_I9_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	437 (all X_b all X_c all A_3 all Ba all F all X_1 (ti(X_b,Ba) = hAPP(X_c,X_b,F,X_1) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))))) # label(fact_64_image__eqI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	438 (all X_b all A_3 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))) # label(fact_852_not__psubset__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	439 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_778_xt1_I9_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	440 (all X_b (ab_sem1668676832m_mult(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_153_hom__fold1__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	441 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K_1))))) # label(fact_682_finite__Collect__less__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	442 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))))) # label(fact_597_min__max_OSup__fin_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	443 (all X_c all X_b (order(X_c) & order(X_b) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,Ba))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_924_xt7) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	444 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),A_2))))))) # label(fact_389_min__max_Ofold1__belowI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	445 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G)) <-> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) & -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),G),F)))))) # label(fact_851_less__fun__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	446 (all M all N_1 M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),N_1)) # label(fact_426_diff__add__inverse2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	447 (all X_b all X_c all F all A_3 (ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)) <-> bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) # label(fact_81_empty__is__image) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	448 (all X_b all B_2 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_2) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_2,B_2)),hAPP(fun(X_b,bool),X_b,F_2,A_3))))))) # label(fact_328_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	449 (all X_a all P ti(X_a,P) = hAPP(X_a,X_a,combi(X_a),P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	450 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Y_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Y_2)),A_3) = hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Y_2),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_838_setprod__constant) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	451 (all X_b finite_finite_1(X_b) = ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b))) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	452 (all N_1 all M M = 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)),N_1)) # label(fact_427_diff__add__inverse) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	453 (all X_b (linordered_semidom(X_b) -> (all X_1 all Y_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),X_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))))))) # label(fact_885_power__strict__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	454 (all X_c all X_b all F all Z_2 ti(X_b,Z_2) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_2),bot_bot(fun(X_c,bool)))) # label(fact_182_fold__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	455 (all X_a (comm_semiring_1(X_a) -> (all X all P_2 all Q_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),P_2),Q_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_2)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_1))))) # label(fact_816_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	456 (all Y all X all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_467_termination__basic__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	457 (all Pa ((exists X_2 (hBOOL(hAPP(int,bool,Pa,X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_952_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	458 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_985_mult__pos__neg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	459 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_717_add__less__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	460 (all W_2 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),one_one(int))),Z)))) # label(fact_866_zless__imp__add1__zle) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	461 (all X_b (ord(X_b) -> max(X_b) = ti(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b))),max(X_b)))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	462 (all Y all X all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_803_termination__basic__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	463 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))))) # label(fact_562_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	464 (all M_1 all N (M_1 = N <-> hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(nat,int,semiring_1_of_nat(int),M_1))) # label(fact_686_int__int__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	465 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_774_xt1_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	466 (all X_b all X_c all X_a ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	467 (all X_c all X_d all X_b (comm_monoid_add(X_b) -> (all F all B_2 all A_3 hAPP(fun(X_d,bool),X_b,hAPP(fun(X_d,X_b),fun(fun(X_d,bool),X_b),big_co1399186613setsum(X_d,X_b),hAPP(fun(X_c,bool),fun(X_d,X_b),hAPP(fun(X_d,fun(fun(X_c,bool),X_b)),fun(fun(X_c,bool),fun(X_d,X_b)),combc(X_d,fun(X_c,bool),X_b),hAPP(fun(X_d,fun(X_c,X_b)),fun(X_d,fun(fun(X_c,bool),X_b)),hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),fun(fun(X_d,fun(X_c,X_b)),fun(X_d,fun(fun(X_c,bool),X_b))),combb(fun(X_c,X_b),fun(fun(X_c,bool),X_b),X_d),big_co1399186613setsum(X_c,X_b)),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_d,fun(X_c,X_b)),combc(X_c,X_d,X_b),F))),A_3)),B_2) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_d,bool),fun(X_c,X_b),hAPP(fun(X_c,fun(fun(X_d,bool),X_b)),fun(fun(X_d,bool),fun(X_c,X_b)),combc(X_c,fun(X_d,bool),X_b),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b)),hAPP(fun(fun(X_d,X_b),fun(fun(X_d,bool),X_b)),fun(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b))),combb(fun(X_d,X_b),fun(fun(X_d,bool),X_b),X_c),big_co1399186613setsum(X_d,X_b)),F)),B_2)),A_3)))) # label(fact_180_setsum__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	468 (all X_b (ab_sem1668676832m_mult(X_b) -> (all X_1 all A_3 (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))))) # label(fact_126_fold1__insert__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	469 (all X_b all Q_3 all Ga all Pa all Ca all Q_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_5)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_5,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_3)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	470 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),A_2),A_3))))) # label(fact_602_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	471 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N_1)))) # label(fact_875_of__nat__power) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	472 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)),A_3))))))) # label(fact_383_Max__in) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	473 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,C) = ti(X_a,B))))) # label(fact_228_add__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	474 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	475 (all X_a (comm_monoid_mult(X_a) -> (all A_1 all B all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))))) # label(fact_872_power__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	476 (all X_b (linorder(X_b) -> big_linorder_Min(X_b) = ti(fun(fun(X_b,bool),X_b),big_linorder_Min(X_b)))) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	477 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))))) # label(fact_493_le__imp__neg__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	478 (all X_b all X_c (ordere223160158up_add(X_c) & comm_monoid_add(X_c) -> (all F all G all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3))))))))) # label(fact_847_setsum__strict__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	479 (all T_2 all T_1 (boolean_algebra(T_1) -> boolean_algebra(fun(T_2,T_1)))) # label(arity_fun___Lattices_Oboolean__algebra) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	480 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_764_order__le__less__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	481 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_502_minus__add) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	482 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool))) # label(fact_39_insert__not__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	483 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	484 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),A_1)))) # label(fact_355_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	485 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)))) # label(fact_286_equalityD2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	486 (all X_b all Pa ((all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))) <-> bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) # label(fact_20_empty__Collect__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	487 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)))))))) # label(fact_882_power__gt1__lemma) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	488 (all X_a (ordere216010020id_add(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	489 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),Y_2))))))) # label(fact_292_lessThan__subset__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	490 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3))))))) # label(fact_470_min__max_OInf__fin_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	491 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z)),hAPP(int,int,uminus_uminus(int),W_2)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_2))) # label(fact_690_zminus__zadd__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	492 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))))) # label(fact_379_Min_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	493 (all Z all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),Z)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_2)))) # label(fact_692_zle__linear) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	494 (all M 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),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),N_1)),I)) # label(fact_424_min__diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	495 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b)) = finite_fold1Set(X_b)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	496 (all X_b (order(X_b) -> (all A_2 all Ba (ti(X_b,Ba) = ti(X_b,A_2) -> hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))))) # label(fact_831_atLeastAtMost__singleton_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	497 (all X_b all X_1 all Pa all Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),Pa),Q_3)) -> (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_290_predicate1D) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	498 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold(X_b,X_c)) = finite_fold(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	499 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))) # label(fact_535_max__diff__distrib__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	500 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_777_ord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	501 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_385_Min_Osingleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	502 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_822_less__add__one) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	503 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_858_psubset__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	504 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)))) # label(fact_534_max__add__distrib__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	505 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)))))) # label(fact_346_Min_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	506 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_3))) # label(fact_148_insert__Diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	507 (all X_b all B_2 all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))))) # label(fact_127_DiffI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	508 (all X_b (order(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) -> hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = bot_bot(fun(X_b,bool)))))) # label(fact_792_atLeastatMost__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	509 (all X_b all A_3 ((exists X_2 exists B_3 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_3) = ti(fun(X_b,bool),A_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_3)))) <-> bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3))) # label(fact_52_nonempty__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	510 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool))))) # label(fact_98_finite_OemptyI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	511 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) <-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_524_Compl__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	512 (all X_a (ab_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	513 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & ti(X_b,X_1) != ti(X_b,Y_2))))) # label(fact_748_order__less__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	514 (all X_b (linorder(X_b) -> (all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all B_1 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),X_2)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),A_4))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)))))))) # label(fact_933_finite__linorder__min__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	515 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_591_min__max_Oinf__Sup1__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	516 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1)),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_500_compl__le__compl__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	517 (all X_a (linorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)))))))) # label(fact_360_min__max_Oinf__greatest) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	518 (all X_b all Y_2 -(all Fun1 all Com all Fun2 hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com),Fun2) != Y_2)) # label(fact_47_triple_Oexhaust) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	519 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))))) # label(fact_819_of__nat__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	520 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_725_add__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	521 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)))))) # label(fact_151_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	522 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_759_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	523 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) | N_1 = M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_741_less__or__eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	524 (all X_a (linorder(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C),D_1)))))))) # label(fact_359_min__max_Oinf__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	525 (all X_b all Ts all Ga all T_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_5),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_5),Ts)))))) # label(fact_3_hoare__derivs_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	526 (all X_c all X_b all Ca all A_3 ((bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool))) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3)) & (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3) = bot_bot(fun(X_c,bool))))) # label(fact_63_image__constant__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	527 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	528 (all X_b (ab_semigroup_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite100568337ommute(X_b,X_b),times_times(X_b))))) # label(fact_192_comp__fun__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	529 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = ti(X_b,A_2)))))) # label(fact_595_min__max_Oinf__Sup__absorb) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	530 (all X_b all A_2 all Ba all A_3 (ti(X_b,Ba) = ti(X_b,A_2) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_3))))) # label(fact_28_insert__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	531 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_733_min__max_Oless__infI1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	532 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_820_add__less__le__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	533 (all X all Y (Y != X -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_799_linorder__neqE__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	534 (all X_b all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_331_subsetI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	535 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_466_termination__basic__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	536 (all X_b all A_2 ti(X_b,A_2) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))) # label(fact_89_the__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	537 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),X_1),A_3)))))) # label(fact_377_Min_Oeq__fold_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	538 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_571_greaterThan__subset__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	539 (all X_b all X_c all Z_2 all A_3 all Y_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3) = ti(X_c,Y_2)))) # label(fact_181_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	540 (all X_c all X_b (comm_monoid_add(X_b) -> (all F all G all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),plus_plus(X_b)),F)),G)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),G),A_3))))) # label(fact_215_setsum__addf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	541 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_168_mult__left__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	542 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_783_order__less__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	543 (all X_c all X_b all Q_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> ((all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(X_b,fun(X_c,bool),hAPP(fun(X_c,fun(X_b,bool)),fun(X_b,fun(X_c,bool)),combc(X_c,X_b,bool),Q_3),Y_1)))))) <-> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_c,fun(X_b,bool)),fun(X_c,bool)),combb(fun(X_b,bool),bool,X_c),fEx(X_b)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa))),Q_3)))))))) # label(fact_589_finite__Collect__bounded__ex) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	544 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_298_add__right__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	545 (all K_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_420_nat__add__left__cancel__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	546 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_419_trans__le__add1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	547 (all X_b all X_c all B_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists AA (ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA) & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_3)))))) # label(fact_314_subset__image__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	548 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_297_add__left__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	549 (all X_b the_elem(X_b) = ti(fun(fun(X_b,bool),X_b),the_elem(X_b))) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	550 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))))) # label(fact_68_imageI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	551 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3)))))) # label(fact_212_setsum_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	552 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_959_zero__less__int__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	553 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),plus_plus(X_c)),G)),H)),A_3))))) # label(fact_216_setsum_Odistrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	554 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 all Y_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),X_1),Y_2)) = hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2)),hAPP(X_b,X_b,uminus_uminus(X_b),X_1))))) # label(fact_834_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	555 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)))) # label(fact_715_add__lessD1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	556 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_647_card_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	557 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))))) # label(fact_575_Max_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	558 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_3),X_2)))))) # label(fact_918_minf_I8_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	559 (all X_b (ord(X_b) -> min(X_b) = ti(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b))),min(X_b)))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	560 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_554_min__max_Osup__absorb1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	561 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_865_psubset__card__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	562 (all X_b all Ga all Pa hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_45_hoare__derivs_OSkip) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	563 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> ti(X_b,Y_2) != ti(X_b,X_1))))) # label(fact_790_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	564 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))))) # label(fact_157_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	565 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_158_folding__image__simple_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	566 (all X_b all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) <-> (exists A_4 exists A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) & hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) = ti(fun(X_b,bool),A_2))) | ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)))) # label(fact_110_finite_Osimps) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	567 (all X_b (one(X_b) -> (all X_1 (one_one(X_b) = ti(X_b,X_1) <-> one_one(X_b) = ti(X_b,X_1))))) # label(fact_634_one__reorient) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	568 (all X_b all A_3 all X_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))))) # label(fact_326_diff__single__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	569 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))))))) # label(fact_267_xt1_I6_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	570 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) -> (ti(X_b,Y_2) = ti(X_b,X_1) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))))))) # label(fact_758_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	571 (all X_b (linorder(X_b) -> (all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))) # label(fact_594_min__max_OSup__fin_Osingleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	572 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_386_Max_Osingleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	573 (all X_b (comm_semiring_1(X_b) -> (all N hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),one_one(X_b))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),one_one(X_b))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),semiring_1_of_nat(X_b)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N)))))) # label(fact_677_gauss__sum) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	574 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.52	575 (all M_1 all N ((exists K_3 N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_3)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_421_le__iff__add) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	576 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))))) # label(fact_175_setprod_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	577 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,Y) = ti(X_a,X)))))) # label(fact_270_order__antisym) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	578 (all X_b all X_1 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> ti(X_b,X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1))) # label(fact_130_folding__one__idem_Oidem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	579 (all X_b all A_3 all F all N (hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N))) = ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_714_nat__seg__image__imp__finite) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	580 (all X_b all A_3 all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_149_finite__Diff__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	581 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_956_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	582 (all X_b (semiring_char_0(X_b) -> (all M_1 all N (hAPP(nat,X_b,semiring_1_of_nat(X_b),N) = hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1) <-> M_1 = N)))) # label(fact_658_of__nat__eq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	583 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W_2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W_2)) # label(fact_689_diff__int__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	584 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2)))))) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	585 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all Ca all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),Ca)),S_1) = hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Ca),hAPP(fun(X_b,bool),nat,finite_card(X_b),S_1))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),Ca)),S_1) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,Ba,A_2)),hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Ca),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),S_1)),one_one(nat))))))))) # label(fact_678_setprod__gen__delta) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	586 (all X_c all X_b all X_d all F all G all A_3 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3)) # label(fact_70_image__image) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	587 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))))) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	588 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_1) = N_1) # label(fact_626_nat__mult__1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	589 (all X_b all D_2 all B_2 all A_3 all C_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),D_2),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_1),D_2)))))) # label(fact_316_Diff__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	590 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> T_3 != S)) # label(fact_796_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	591 (all X_c all X_b all F all Z_2 all Y_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_2)))))) # label(fact_107_fold__graph_OinsertI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	592 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) <-> hBOOL(hAPP(X_b,bool,A_3,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	593 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))) # label(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	594 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	595 (all X_a (ring_1(X_a) -> (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))))) # label(fact_663_of__nat__diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	596 (all X_b (ord(X_b) -> ord_less(X_b) = ti(fun(X_b,fun(X_b,bool)),ord_less(X_b)))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	597 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))) # label(fact_472_min__max_OInf__fin_OF__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	598 (all M all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1))) # label(fact_685_zpower__int) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	599 (all X_a (linord893533164strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_994_comm__mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	600 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)))) # label(fact_354_min__max_Oinf__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	601 (all X_c all X_b all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> ti(X_b,Z_2) = hAPP(X_c,X_b,G,X_2))) -> ti(X_b,Z_2) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_170_folding__image__simple_Oneutral) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	602 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_365_min__max_Ole__infI1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	603 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)))) # label(fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	604 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_13_singleton__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	605 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)) # label(fact_461_nat__add__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	606 (all X_b (one(X_b) -> one_one(X_b) = ti(X_b,one_one(X_b)))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	607 (all K_1 all I_1 all J_1 hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I_1),J_1)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_1))) # label(fact_805_image__add__atLeastAtMost) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	608 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_720_trans__less__add1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	609 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) <-> M_1 != N)) # label(fact_800_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	610 (all X_b all A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3))) # label(fact_262_empty__subsetI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	611 (all X_b all A_2 all Ba (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))) -> ti(X_b,Ba) = ti(X_b,A_2))) # label(fact_35_singleton__inject) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	612 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3)) = ti(fun(X_b,bool),A_3)) # label(fact_523_double__complement) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	613 (all X_b (linorder(X_b) -> (all M_3 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),M_3),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),M_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),M_3)),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3))))))))) # label(fact_342_Max__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	614 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,bool),X_b),big_linorder_Max(X_b)) = big_linorder_Max(X_b))) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	615 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3)) # label(fact_138_Diff__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	616 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),X_1),A_3) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_203_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	617 (all X_b (linorder(X_b) -> hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),min(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),ord_less_eq(X_b))) = ord_max(X_b))) # label(fact_573_dual__min) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	618 (all X_b all N_3 all H all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> ((all X_2 all Y_1 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1)) = hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)) = hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_2,N_3))))))) # label(fact_155_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	619 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	620 (all X_c all X_b all F all Z_2 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),Z_2))) # label(fact_191_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	621 (all K_1 all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),L)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L)))) # label(fact_960_less__bin__lemma) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	622 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3)) # label(fact_522_Compl__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	623 (all N_1 (zero_zero(nat) != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_968_gr0I) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	624 (all X_b (ab_group_add(X_b) -> (all F all M_1 all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(nat,X_b,F,M_1)),hAPP(nat,X_b,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)))) = hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,X_b)),combs(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),minus_minus(X_b)),F)),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,X_b)),combs(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),minus_minus(X_b)),F)),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N)) = zero_zero(X_b)))))) # label(fact_934_setsum__natinterval__difff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	625 (all X_b all X_c all Ba all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> -(all X_2 (hAPP(X_c,X_b,F,X_2) = ti(X_b,Ba) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)))))) # label(fact_87_imageE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	626 (all X_a (linorder(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X)))) # label(fact_347_Min_Oidem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	627 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Least))))) # label(fact_585_max__leastR) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	628 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))) # label(fact_504_minus__add__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	629 (all X_b (group_add(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,uminus_uminus(X_b),Ba) = hAPP(X_b,X_b,uminus_uminus(X_b),A_2) <-> ti(X_b,Ba) = ti(X_b,A_2))))) # label(fact_489_neg__equal__iff__equal) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	630 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))))) # label(fact_586_min__max_OInf__le__Sup) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	631 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))))) # label(fact_353_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	632 (all Pa all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_909_int__gr__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	633 (all X_c all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))))) # label(fact_321_finite__surj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	634 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = ti(X_b,X_1)) & (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3))))))) # label(fact_380_Min_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	635 (all X_b (ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) -> (ti(X_b,D) = ti(X_b,Ca) <-> ti(X_b,A_2) = ti(X_b,Ba)))))) # label(fact_247_diff__eq__diff__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	636 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_274_ord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	637 (all X_b (linorder(X_b) -> (all M_1 all N (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),M_1)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),N))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),M_1),N)))))) # label(fact_793_lessThan__strict__subset__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	638 (all Pa all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_910_int__ge__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	639 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all G all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3))))) # label(fact_254_setsum__cong2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	640 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	641 (all X_b all B_2 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))),one_one(nat)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))))))) # label(fact_648_card__Diff__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	642 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (-hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3)) = hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)))))) # label(fact_169_folding__image__simple_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	643 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))) # label(fact_539_min__max_Osup__left__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	644 (all X_b (linorder(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),ord_max(X_b))))) # label(fact_560_min__max_Ocomp__fun__idem__sup) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	645 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_905_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	646 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_425_diff__mult__distrib2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	647 (all Com1 all Com2 all Vname_1 all Fun_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1)) # label(fact_73_com_Osimps_I25_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	648 (all X_b all Q_3 all Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Q_3,X_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))))) # label(fact_340_Collect__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	649 (all X_b (linordered_semidom(X_b) -> (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))))))) # label(fact_817_of__nat__less__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	650 (all X_b (ab_semigroup_mult(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),A_3)))))))) # label(fact_154_fold1__in) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	651 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3))))))) # label(fact_468_min__max_OInf__fin_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	652 (all X_b all X_c all X_1 all Y_2 all Z_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_2),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_2),Z_2)))) # label(fact_179_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	653 (all X_b (ab_semigroup_mult(X_b) -> (all Z_2 all Ba all A_3 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_3),Y_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Z_2),Y_2)))))))) # label(fact_150_fold__graph__insert__swap) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	654 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = ti(X_a,A_1)))) # label(fact_486_minus__minus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	655 (all X_b (linord219039673up_add(X_b) -> (all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),S_1) -> hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),S_1)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),S_1))))))) # label(fact_481_minus__Min__eq__Max) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	656 (all X_c all X_b all F all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_c,fun(X_b,bool)),fun(X_c,bool)),combb(fun(X_b,bool),bool,X_c),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_c,fun(X_b,bool)),hAPP(fun(X_c,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_c,fun(X_b,bool))),combc(X_c,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_c,fun(X_b,fun(bool,bool))),fun(X_c,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_c,fun(X_b,fun(bool,bool))),fun(X_c,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_c),combs(X_b,bool,bool)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_c),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj)),hAPP(fun(X_b,X_c),fun(X_c,fun(X_b,bool)),hAPP(fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool))),fun(fun(X_b,X_c),fun(X_c,fun(X_b,bool))),combc(X_c,fun(X_b,X_c),fun(X_b,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool))),hAPP(fun(fun(X_c,bool),fun(fun(X_b,X_c),fun(X_b,bool))),fun(fun(X_c,fun(X_c,bool)),fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool)))),combb(fun(X_c,bool),fun(fun(X_b,X_c),fun(X_b,bool)),X_c),combb(X_c,bool,X_b)),fequal(X_c))),F)))),Pa))))))) # label(fact_590_finite__image__set) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	657 (all X_b hoare_1301688828derivs(X_b) = ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_1301688828derivs(X_b))) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Ohoare__derivs_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	658 (all K all M all 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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))) # label(fact_462_add__mult__distrib2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	659 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_672_int__mult) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	660 (all X_b (ord(X_b) -> (all I_1 all K_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_1),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),K_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),I_1),K_1)))))) # label(fact_744_lessThan__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	661 (all X_a (monoid_mult(X_a) -> (all N_1 one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),N_1)))) # label(fact_874_power__one) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	662 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_119_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	663 (all X_b all Pa all A_2 ((-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool))) & (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))) # label(fact_15_Collect__conv__if) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	664 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_392_Min_Ohom__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	665 (all A_3 all B_2 (hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2) <-> B_2 = A_3)) # label(fact_897_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	666 (all X_b all A_2 all G all F (G = hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F) -> hAPP(fun(X_b,bool),X_b,G,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) = ti(X_b,A_2))) # label(fact_62_fold1__singleton__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	667 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_graph(X_b,X_c)) = finite_fold_graph(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold__graph_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	668 (all M all N_1 (N_1 = M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_410_eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	669 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_538_min__max_Osup_Oassoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	670 (all X_c all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) -> (exists C_2 (hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_2) = ti(fun(X_b,bool),B_2) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),C_2)) & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_3))))))) # label(fact_332_finite__subset__image) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	671 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_964_zero__less__power) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	672 (all X_b all F all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X_1)) -> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_84_fold1Set__nonempty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	673 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))) # label(fact_621_card__Diff__singleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	674 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_773_order__less__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	675 (all X_b all A_3 (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))))) # label(fact_305_subset__empty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	676 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))))) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	677 (all X_b (ab_group_add(X_b) -> zero_zero(X_b) = ti(X_b,zero_zero(X_b)))) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	678 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_977_pos__add__strict) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	679 (all X_b (bot(X_b) -> bot_bot(X_b) = ti(X_b,bot_bot(X_b)))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	680 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_272_ord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	681 (all Z1 all Z2 all W_2 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_2) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_2))) # label(fact_698_zdiff__zmult__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	682 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_2,A_3)),A_3))))))) # label(fact_96_folding__one_Oclosed) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	683 (all M all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M))) # label(fact_433_diff__le__self) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	684 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_505_minus__mult__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	685 (all X_b (power(X_b) -> ti(fun(X_b,fun(X_b,X_b)),times_times(X_b)) = times_times(X_b))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	686 (all X_a fEx(X_a) = ti(fun(fun(X_a,bool),bool),fEx(X_a))) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	687 (all X_b all A_3 bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3)) # label(fact_139_Diff__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	688 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_364_min__max_Ole__infI2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	689 (all X_b all X_c (ab_group_add(X_c) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),B_2))))))) # label(fact_329_setsum__diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.53	690 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1)) = hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1))))) # label(fact_516_image__uminus__lessThan) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	691 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))) # label(fact_183_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	692 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_812_compl__less__swap1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	693 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite100568337ommute(X_b,X_c)) = finite100568337ommute(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__commute_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	694 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_776_xt1_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	695 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_497_compl__le__swap2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	696 (all M all N_1 all K all L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_716_less__add__eq__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	697 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)))) # label(fact_491_Compl__subset__Compl__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	698 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_265_linorder__le__cases) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	699 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),Z_2)))))) # label(fact_357_min__le__iff__disj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	700 (all M_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = one_one(nat) <-> one_one(nat) = M_1 & one_one(nat) = N)) # label(fact_625_nat__1__eq__mult__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	701 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_771_order__less__asym) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	702 (all X_b ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hoare_759811442triple(X_b)) = hoare_759811442triple(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	703 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_362_min__max_Oinf__absorb2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	704 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))) # label(fact_542_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	705 (all W_1 all Z_2 ((exists N_2 Z_2 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)))) # label(fact_683_zle__iff__zadd) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	706 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_3)))))) # label(fact_922_minf_I6_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	707 (all X_b (ord(X_b) -> ord_greaterThan(X_b) = ti(fun(X_b,fun(X_b,bool)),ord_greaterThan(X_b)))) # label(tsy_c_SetInterval_Oord__class_OgreaterThan_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	708 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_414_add__leD1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	709 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))))) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	710 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_b,X_b,uminus_uminus(X_b),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))))))) # label(fact_496_le__minus__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	711 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z)) # label(fact_697_zmult__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	712 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	713 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_455_nat__mult__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	714 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_408_le__refl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	715 (all J_1 all I_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),I_1)) -> hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),I_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_1),one_one(int))),J_1)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),I_1),J_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),I_1)) -> bot_bot(fun(int,bool)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),I_1),J_1)))) # label(fact_892_simp__from__to) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	716 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),J)))))) # label(fact_961_zmult__zless__mono2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	717 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = ti(X_b,X_1)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))))) # label(fact_469_min__max_OInf__fin_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	718 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),A_3)))))) # label(fact_569_min__max_Ofold__sup__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	719 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)))))) # label(fact_746_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	720 (all A_3 all B_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))))) # label(fact_895_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	721 (all X_b (linorder(X_b) -> (all Ca all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),X_2)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),Ba),Ca)),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ca),A_3)))))))) # label(fact_394_min__max_Oinf__le__fold__inf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	722 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_417_add__le__mono1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	723 (all X_c all X_b (order(X_b) & order(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),hAPP(X_b,X_c,F,Ba))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_921_xt5) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	724 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> ti(X_a,Least) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X))))) # label(fact_400_min__leastL) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	725 (all X_b (linorder(X_b) -> (all B_2 all A_3 (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))))))) # label(fact_338_fold1__antimono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	726 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_268_xt1_I5_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	727 (all X_c all X_b (semiring_1(X_b) -> (all Y_2 all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),Y_2)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,finite_card(X_c),A_3))),Y_2)))) # label(fact_664_setsum__constant) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	728 (all X_c all X_b all F all G all M_3 all N_3 (ti(fun(X_b,bool),M_3) = ti(fun(X_b,bool),N_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N_3)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_3) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3)))) # label(fact_91_image__cong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	729 (all X_c all X_b (bot(X_b) -> (all X_1 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)))) # label(fact_43_bot__apply) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	730 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_718_add__less__mono1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	731 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_2) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),B_2)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool)),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,bool),X_b),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b))),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))))),combb(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),X_b),combs(X_b,fun(X_b,bool),fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))))),combb(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),X_b),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool))))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),X_b),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj))),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))))),combb(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),X_b),combb(fun(X_b,X_b),fun(X_b,bool),X_b)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b)))),ord_min(X_b)))))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combb(bool,bool,X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))))))))))))) # label(fact_592_min__max_Oinf__Sup2__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	732 (all X_b all A_2 all C_1 all D_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_1),D_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),D_2))))) # label(fact_308_insert__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	733 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_986_mult__pos__neg2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	734 (all X_b (ordered_ab_group_add(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)))))) # label(fact_808_neg__less__iff__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	735 (all X_b all A_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),A_3))) # label(fact_289_subset__refl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	736 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_1),I_1)),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N)))))) # label(fact_842_nat__less__add__iff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	737 (all M all N_1 all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))),Z)) # label(fact_668_zadd__int__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	738 (all X_b all X_3 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3)) # label(fact_55_the__elem__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	739 (all M_1 all N (one_one(nat) = N & M_1 = one_one(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = one_one(nat))) # label(fact_623_nat__mult__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	740 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K)) # label(fact_428_diff__diff__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	741 (all P (hBOOL(hAPP(bool,bool,fNot,P)) | hBOOL(P))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	742 (all X_b all Ga all Pa all Ca all Q_3 all C_1 ((hBOOL(C_1) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C_1)),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_4_constant) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	743 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = ti(X_a,X)))) # label(fact_533_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	744 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_295_add__le__imp__le__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	745 (all X_b all B_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> (ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) <-> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))) # label(fact_26_insert__ident) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	746 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_976_add__pos__pos) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	747 (all X_a (linorder(X_a) -> (all Y all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_752_not__leE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	748 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	749 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))))) # label(fact_473_min__max_OInf__fin_Oinsert__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	750 (all X_c all X_b all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> ti(X_b,Z_2) = hAPP(fun(X_c,bool),X_b,F_2,bot_bot(fun(X_c,bool))))) # label(fact_165_folding__image__simple_Oempty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	751 (all I_1 all J_1 all F ((all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1)))))) # label(fact_915_less__mono__imp__le__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	752 (all X_c all X_b (ab_group_add(X_b) -> (all F all G all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),minus_minus(X_b)),F)),G)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),G),A_3))))) # label(fact_190_setsum__subtractf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	753 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(Q))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	754 (all X_b all A_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_11_emptyE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	755 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_548_le__maxI2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	756 (all X_b all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) # label(fact_41_the__elem__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	757 (all X_b all Pa all Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_3)))))) # label(fact_103_finite__Collect__disjI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	758 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))))) # label(fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	759 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) | W_1 = Z_2 <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))))) # label(fact_863_zless__add1__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	760 (all X_b all Y_2 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,A_3,X_1)) | ti(X_b,Y_2) = ti(X_b,X_1) <-> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_3),X_1)))) # label(fact_27_insert__code) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	761 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	762 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_802_termination__basic__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	763 (all X_b all Pa ((exists X1 hBOOL(hAPP(X_b,bool,Pa,X1))) <-> (all Q_2 ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(Q_2))) -> hBOOL(Q_2))))) # label(fact_608_Ex__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	764 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_3),X_2)))))) # label(fact_919_pinf_I8_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	765 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_518_Max_Oremove) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	766 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_880_power__add) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	767 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K)) # label(fact_463_add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	768 (all L all U hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U)))) # label(fact_890_finite__atLeastAtMost__int) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	769 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) = ti(X_b,Y_2) <-> hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),Y_2) = hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1))))) # label(fact_546_greaterThan__eq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	770 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))) # label(fact_371_min__diff__distrib__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	771 (all X_b all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_285_in__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	772 (all X_b (bot(X_b) -> (all A_2 (bot_bot(X_b) != ti(X_b,A_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)))))) # label(fact_767_bot__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	773 (all X_b all X_c (bot(X_c) -> (all X_2 hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c)))) # label(fact_44_bot__fun__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	774 (all X_b all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_3))) # label(fact_147_Diff__insert__absorb) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	775 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_669_zadd__int) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	776 (all X_b all X_1 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1))) # label(fact_58_folding__one_Osingleton) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	777 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),X_1),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))))) # label(fact_603_min__max_OSup__fin_Oeq__fold_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	778 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_261_subsetD) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	779 (all K -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int)))) # label(fact_958_int__less__0__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	780 (all X_b all A_3 (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_515_subset__Compl__self__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	781 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_407_le__square) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	782 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_541_min__max_Osup__left__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	783 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))))) # label(fact_868_zle__add1__eq__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	784 (all X_b all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com_2),Fun2_2) <-> Fun1_1 = Fun1_2 & Fun2_1 = Fun2_2 & Com_1 = Com_2)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	785 (all X_b all X_c all Y_2 all Z_2 all A_3 all X_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),X_1)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> ti(X_c,Y_2) = ti(X_c,X_1))))) # label(fact_193_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	786 (all X_c all X_b (semiring_1(X_b) & comm_monoid_mult(X_b) -> (all F all A_3 hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co302546470etprod(X_c,nat),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(fun(X_c,nat),fun(X_c,X_b),hAPP(fun(nat,X_b),fun(fun(X_c,nat),fun(X_c,X_b)),combb(nat,X_b,X_c),semiring_1_of_nat(X_b)),F)),A_3)))) # label(fact_666_of__nat__setprod) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	787 (all Pa all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_889_int__le__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	788 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),X_2)))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))))))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	789 (all X_b (linordered_idom(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_979_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	790 (all X_c all X_b (comm_monoid_mult(X_b) -> (all A_3 one_one(X_b) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),one_one(X_b))),A_3)))) # label(fact_622_setprod__1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	791 (all X_a (linorder(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X)))) # label(fact_536_Max_Oidem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	792 (all X_a all X_b all X_c combc(X_a,X_b,X_c) = ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c))) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	793 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_632_mult__1__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	794 (all X_a (boolean_algebra(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_483_double__compl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	795 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3)))))) # label(fact_210_setsum_Ocong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	796 (all X_b (order(X_b) -> (all A_2 all Ba (hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = bot_bot(fun(X_b,bool)) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_828_atLeastatMost__empty__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	797 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_761_xt1_I11_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	798 (all X_b all X_2 all Xa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))) # label(fact_34_insert__compr__raw) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	799 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_273_xt1_I3_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	800 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))))) # label(fact_876_power__mult) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	801 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_121_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	802 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K)) # label(fact_430_diff__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	803 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_775_ord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	804 (all X_b all F all A_3 hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co1399186613setsum(X_b,int),hAPP(fun(X_b,nat),fun(X_b,int),hAPP(fun(nat,int),fun(fun(X_b,nat),fun(X_b,int)),combb(nat,int,X_b),semiring_1_of_nat(int)),F)),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3))) # label(fact_674_int__setsum) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	805 (all X_1 all N (zero_zero(nat) = N | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N))))) # label(fact_963_nat__zero__less__power__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.54	806 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),X_2)))))))))) # label(fact_840_strict__below__fold1__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	807 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_769_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	808 (all X_b (linordered_semidom(X_b) -> (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))))))) # label(fact_659_of__nat__le__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	809 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_978_add__neg__neg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	810 (all Q all P (hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	811 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_526_ComplD) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	812 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3))))))) # label(fact_94_folding__one_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	813 (all X_b finite_folding_one(X_b) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b))) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	814 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_361_min__max_Ole__infI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	815 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),B_2)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool)),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,bool),X_b),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b))),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))))),combb(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),X_b),combs(X_b,fun(X_b,bool),fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))))),combb(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),X_b),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool))))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),X_b),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj))),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))))),combb(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),X_b),combb(fun(X_b,X_b),fun(X_b,bool),X_b)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b)))),ord_max(X_b)))))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combb(bool,bool,X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))))))))))))) # label(fact_587_min__max_Osup__Inf2__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	816 (all Com1_2 all Com2_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != skip) # label(fact_54_com_Osimps_I12_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	817 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> N_1 = M))) # label(fact_412_le__antisym) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	818 (all Pa all M_1 all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> ((N = M_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1)))))) # label(fact_795_nat__less__cases) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	819 (all X_b (order(X_b) -> (all A_2 all Ba all Ca (hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),bot_bot(fun(X_b,bool))) <-> ti(X_b,Ba) = ti(X_b,Ca) & ti(X_b,Ba) = ti(X_b,A_2))))) # label(fact_832_atLeastAtMost__singleton__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	820 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)))) # label(fact_167_mult__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	821 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))))) # label(fact_99_finite_OinsertI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	822 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_719_trans__less__add2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	823 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),A_3))))) # label(fact_194_setprod_Odistrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	824 (all N_1 all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_680_negative__zle) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	825 (all X_c all X_b (semiring_0(X_b) -> (all F all A_3 all R_2 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(X_b,fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(X_c,X_b)),combc(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F)),R_2)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),R_2)))) # label(fact_188_setsum__left__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	826 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_4)))))))) # label(fact_886_power__increasing) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	827 (all X_b all Y_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))))) # label(fact_679_card__Diff2__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	828 (all Com1_2 all Com2_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != skip) # label(fact_53_com_Osimps_I13_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	829 (all X_a (semiring(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	830 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_563_minus__min__eq__max) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	831 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa))))) # label(fact_14_Collect__conv__if2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	832 (all X_a (ordere779506340up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_296_add__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	833 (all I_1 all K_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_1))))) # label(fact_442_le__diff__conv2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	834 (all X_b all A_3 all X_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))) # label(fact_142_insert__Diff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	835 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_756_leD) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	836 (all A_3 hAPP(fun(nat,bool),nat,finite_card(nat),A_3) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) # label(fact_901_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	837 (all X_c all X_a all B_1_1 all B_2_1 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	838 (all X_b (ring_11004092258visors(X_b) -> (all X_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1) = one_one(X_b) <-> one_one(X_b) = ti(X_b,X_1) | hAPP(X_b,X_b,uminus_uminus(X_b),one_one(X_b)) = ti(X_b,X_1))))) # label(fact_638_square__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	839 (all X_c all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_2))))) # label(fact_313_image__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	840 (all X_b (linorder(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),ord_min(X_b))))) # label(fact_373_min__max_Ocomp__fun__idem__inf) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	841 (all N hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N))) = N) # label(fact_815_card__Collect__less__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	842 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))) # label(fact_530_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	843 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(X_b,X_c,Ba,A_2) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),one_one(X_c))),S_1)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Ba)),one_one(X_c))),S_1) = one_one(X_c)))))) # label(fact_645_setprod__delta) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	844 (all X_b all F all A1 all A2 ((exists A_5 exists A_4 exists X_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) = ti(fun(X_b,bool),A1) & hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_5),A_4),X_2)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4)) & ti(X_b,X_2) = ti(X_b,A2))) <-> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A1),A2)))) # label(fact_114_fold1Set_Osimps) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	845 (all X_b all A_3 all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3) | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_320_subset__singletonD) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	846 (all X_b (semiri456707255roduct(X_b) -> (all W_1 all Y_2 all X_1 all Z_2 (ti(X_b,Z_2) = ti(X_b,Y_2) | ti(X_b,X_1) = ti(X_b,W_1) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2)))))) # label(fact_223_crossproduct__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	847 (all X_c (uminus(X_c) -> uminus_uminus(X_c) = ti(fun(X_c,X_c),uminus_uminus(X_c)))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	848 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_552_min__max_Ole__supI2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	849 (all X_b (ord(X_b) -> (all I_1 all K_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_1),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),K_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),K_1),I_1)))))) # label(fact_807_greaterThan__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	850 (all X_c all X_b (comm_monoid_add(X_b) -> ti(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),big_co1399186613setsum(X_c,X_b)) = big_co1399186613setsum(X_c,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	851 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_547_le__maxI1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	852 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_713_min__max_Oless__supI1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	853 (all X_b all One all Times all A_2 hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),hAPP(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b))),power_1(X_b),One),Times),A_2),zero_zero(nat)) = ti(X_b,One)) # label(fact_943_power_Opower_Opower__0) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	854 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_947_add__strict__increasing2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	855 (all J_1 all K_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1)),I_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))))) # label(fact_435_le__diff__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	856 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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_1),I_1)),U)),N)))))) # label(fact_452_nat__le__add__iff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	857 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)) = one_one(X_a))) # label(fact_662_of__nat__1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	858 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J)) # label(fact_429_diff__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	859 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> N_1 != zero_zero(nat))) # label(fact_969_gr__implies__not0) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	860 (all X_a (linord581940658strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_991_mult__neg__neg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	861 (all X_a combi(X_a) = ti(fun(X_a,X_a),combi(X_a))) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	862 (all Z_2 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) & W_1 != Z_2)) # label(fact_849_zless__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	863 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_266_le__funE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	864 (all X_b all X_c fold_graph(X_b,X_c) = ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),fold_graph(X_b,X_c))) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	865 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),Z_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)))))) # label(fact_550_min__max_Ole__sup__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	866 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = ti(X_b,A_2)))))) # label(fact_570_min__max_Osup__Inf__absorb) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	867 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),big_semilattice_big(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_122_semilattice__big_OF__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	868 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),K)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K))))) # label(fact_850_zadd__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	869 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_729_add__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	870 (all N_1 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),M)) # label(fact_565_nat__minus__add__max) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	871 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_784_order__less__not__sym) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	872 (all X_b ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	873 (all Pa ((all X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))) <-> (all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,Pa,X_2)))))) # label(fact_951_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	874 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M_1)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N)))))) # label(fact_465_nat__le__add__iff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	875 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,A_2) = ti(X_b,X_2))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))))) # label(fact_115_theI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	876 (all X_b (bot(X_b) -> (all A_2 (ti(X_b,A_2) = bot_bot(X_b) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b))))))) # label(fact_302_bot__unique) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	877 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_b,X_b,uminus_uminus(X_b),Ba))))))) # label(fact_810_less__minus__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	878 (all X_b (idom(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),A_2) <-> ti(X_b,A_2) = ti(X_b,Ba) | hAPP(X_b,X_b,uminus_uminus(X_b),Ba) = ti(X_b,A_2))))) # label(fact_509_square__eq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	879 (all X_b (preorder(X_b) -> (all Pa all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> hBOOL(Pa)))))) # label(fact_780_order__less__imp__triv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	880 (all X_a (linordered_ring(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))) # label(fact_980_not__square__less__zero) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	881 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	882 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) | ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_854_subset__iff__psubset__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	883 (all X_b all Ga all Ca all Q_3 all Pa ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),S_3))),Ca),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Q_3,Z_4)))),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_5_escape) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	884 (all X_b all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) <-> (exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))))) # label(fact_21_ex__in__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	885 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_max(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))) # label(fact_572_Max_OF__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	886 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))) # label(fact_445_diff__add__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	887 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_101_finite) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	888 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_755_xt1_I12_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	889 (all M_1 all K_1 all N (N = M_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1))) # label(fact_457_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	890 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool))) # label(fact_40_empty__not__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	891 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) | ti(X_a,Y) = ti(X_a,X) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_788_linorder__less__linear) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	892 (all X_a (ord(X_a) -> ord_min(X_a) = ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	893 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_990_mult__neg__pos) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	894 (all X_b all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1))) # label(fact_88_the__sym__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	895 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)))))))) # label(fact_941_mult__left__le__one__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	896 (all X_c all X_b all X_1 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> ti(X_b,X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1))) # label(fact_136_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	897 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),X_1)) <-> (exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),X_1)))))))))) # label(fact_390_fold1__below__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	898 (all X_b (ordere236663937imp_le(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),Ba))))))) # label(fact_299_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	899 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3)))) # label(fact_201_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	900 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z))))) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	901 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,H,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3)))))) # label(fact_209_setprod_Ocong) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	902 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,Y_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)))))) # label(fact_549_min__max_Ole__iff__sup) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	903 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_727_add__strict__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	904 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_948_add__neg__nonpos) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	905 (all X_a (semiring_1(X_a) -> ti(fun(nat,X_a),semiring_1_of_nat(X_a)) = semiring_1_of_nat(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	906 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	907 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_772_xt1_I10_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	908 (all N_1 all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))))) # label(fact_449_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	909 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_352_min__max_Oinf__left__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	910 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_140_finite__Diff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	911 (all X_b all X_c (ordere779506340up_add(X_c) & semiring_1(X_c) -> (all F all K_2 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_2),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,I_2)),K_2)))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(nat,X_c,semiring_1_of_nat(X_c),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))),K_2))))))) # label(fact_665_setsum__bounded) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	912 (all X_b all Ts all Ga (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ga)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))) # label(fact_319_asm) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	913 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_786_linorder__neqE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	914 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_996_mult__strict__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	915 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite_1(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_3)))))) # label(fact_263_finite__Collect__subsets) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	916 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_306_finite__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	917 (all X_b ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	918 (all X_b all B_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))))) # label(fact_310_subset__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	919 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))))))))) # label(fact_967_power__strict__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	920 (all X_b all X_c all A_2 all Z_2 all A_3 all Y_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (exists Y_3 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),Y_3)) & ti(X_c,Y_2) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,A_2),Y_3))))))) # label(fact_171_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	921 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))) # label(fact_492_minus__diff__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	922 (all X_b (ab_semigroup_mult(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_2),A_3)))))) # label(fact_205_fold1__eq__fold) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	923 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),A_2)))))) # label(fact_809_minus__less__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	924 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_785_less__imp__neq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	925 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_862_zless__int) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	926 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_307_rev__finite__subset) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	927 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	928 (all X_c all X_b all R_1 all K_1 all T_5 all S_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_5)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),T_5)) -> hAPP(X_c,nat,K_1,X_2) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_2))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),R_1),X_2)))))) -> hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co1399186613setsum(X_c,nat),K_1),T_5) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,nat),hAPP(fun(fun(X_c,bool),nat),fun(fun(X_b,fun(X_c,bool)),fun(X_b,nat)),combb(fun(X_c,bool),nat,X_b),finite_card(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_5)))),R_1)))),S_2))))) # label(fact_620_setsum__multicount__gen) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	929 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X))))))) # label(fact_558_min__max_Ole__supE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	930 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	931 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_676_zdiff__int) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	932 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_3)))) # label(fact_894_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	933 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_351_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	934 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_946_add__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	935 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)))) # label(fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	936 (all X_b (preorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_749_less__le__not__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	937 (all X_b all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co302546470etprod(X_b,int),hAPP(fun(X_b,nat),fun(X_b,int),hAPP(fun(nat,int),fun(fun(X_b,nat),fun(X_b,int)),combb(nat,int,X_b),semiring_1_of_nat(int)),F)),A_3)) # label(fact_675_int__setprod) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	938 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_553_min__max_Osup__absorb2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.55	939 (all X_b all X_c (comm_monoid_add(X_c) & ordere779506340up_add(X_c) -> (all F all G all K_2 ((all I_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_2),K_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,I_2)),hAPP(X_b,X_c,G,I_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),K_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),K_2))))))) # label(fact_333_setsum__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	940 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) <-> ti(X_b,X_1) = ti(X_b,Y_2))))) # label(fact_278_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	941 (all X_a all X_b all X_c combs(X_a,X_b,X_c) = ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c))) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	942 (all K all M 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),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) # label(fact_431_diff__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	943 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))))) # label(fact_618_diff__card__le__card__Diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	944 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_804_termination__basic__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	945 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X))))))) # label(fact_555_min__max_Ole__supI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	946 (all X_c all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_616_card__image__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	947 (all X_b (power(X_b) -> hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),hAPP(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b))),power_1(X_b),one_one(X_b)),times_times(X_b)) = power_power(X_b))) # label(fact_916_power__power__power) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	948 (all Z_3 all Z all W_3 all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_3),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z)))))) # label(fact_861_zadd__zless__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	949 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_859_psubsetD) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	950 (all X_b (comm_semiring_1(X_b) -> (all A_2 all D all N hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),one_one(X_b))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(X_b,X_b),fun(fun(nat,X_b),fun(nat,X_b)),combb(X_b,X_b,nat),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2)),hAPP(X_b,fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),combc(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),times_times(X_b)),semiring_1_of_nat(X_b))),D))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),D))))))) # label(fact_656_arith__series__general) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	951 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_818_less__imp__of__nat__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	952 (all Z -(all M_2 all N_2 Z != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_914_int__diff__cases) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	953 (all I_1 all J_1 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1))))) # label(fact_825_less__diff__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	954 (all X_b all X_c image(X_b,X_c) = ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c))) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	955 (all X_c (ord(X_c) -> ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)) = ord_less_eq(X_c))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	956 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))))) # label(fact_561_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	957 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),Ca))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)))))) # label(fact_731_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	958 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> ti(X_a,A_1) = ti(X_a,B)))))))) # label(fact_966_power__eq__imp__eq__base) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	959 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = ti(fun(X_b,bool),A_3))) # label(fact_24_insert__absorb) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	960 (all X_b all A_3 all X_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2))) <-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))))) # label(fact_327_subset__insert__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	961 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)))) # label(fact_422_le__add1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	962 (all X_1 all Y_2 (Y_2 = X_1 <-> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_2))) # label(fact_899_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	963 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),Y_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),X_1)))))) # label(fact_711_less__max__iff__disj) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	964 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)))) # label(fact_135_DiffD2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	965 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),B_2)) # label(fact_133_Diff__idemp) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	966 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),X_1),A_3)))))) # label(fact_577_Max_Oeq__fold_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	967 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_540_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	968 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca)),D)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))))))) # label(fact_324_le__add__iff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	969 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),X_1),A_3)))))) # label(fact_476_min__max_OInf__fin_Oeq__fold_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	970 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_857_subset__psubset__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	971 (all X_b all A_2 all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) # label(fact_31_insert__Collect) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	972 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,Y_2) = ti(X_b,X_1) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)))))) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	973 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)))))))) # label(fact_474_min__max_OInf__fin_Oinsert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	974 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_995_mult__strict__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	975 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_95_folding__one_Oeq__fold) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	976 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_259_order__refl) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	977 (all Pa all I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))))) # label(fact_814_finite__M__bounded__by__nat) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	978 (all X_b all A_2 all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_3))) -> (ti(X_b,Ba) != ti(X_b,A_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))))) # label(fact_9_insertE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	979 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))))) # label(fact_388_min__max_Ofold__inf__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	980 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3))))) # label(fact_202_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	981 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M_1)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N)))))) # label(fact_841_nat__less__add__iff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	982 (all X_a (dense_linorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))))))) # label(fact_920_dense__le__bounded) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	983 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),K))))) # label(fact_436_le__add__diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	984 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1)))))) # label(fact_403_mult__le__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	985 (all X_a (linorder(X_a) -> (all X all Y ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_532_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	986 (all X_b all X_c (ab_group_add(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_b,X_c,F,A_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))))))) # label(fact_173_setsum__diff1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	987 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J))) # label(fact_434_diff__diff__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	988 (all X_b (semiri456707255roduct(X_b) -> (all Ca all D all A_2 all Ba (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),D)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ca)) <-> ti(X_b,A_2) != ti(X_b,Ba) & ti(X_b,Ca) != ti(X_b,D))))) # label(fact_249_crossproduct__noteq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	989 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))))) # label(fact_651_card__Diff__singleton__if) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	990 (all X_b all Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool)) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_18_Collect__empty__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	991 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),Ca))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_300_add__le__cancel__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	992 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Least),X) = ti(X_a,X))))) # label(fact_584_max__leastL) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	993 (all X_b all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)) -> ((all A_5 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),bot_bot(fun(X_b,bool)))))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))))))) # label(fact_156_finite__empty__induct) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	994 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_939_power__less__imp__less__base) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	995 (all X_a (boolean_algebra(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),hAPP(X_a,X_a,uminus_uminus(X_a),X))))))) # label(fact_499_compl__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	996 (all X_c all X_b all F all Z_2 all A_3 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_c,bool),fun(X_b,bool)),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),fun(X_b,bool))),finite_fold_graph(X_c,X_b),F),Z_2),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_2),A_3)) # label(fact_200_fold__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	997 (all X_c all X_b all H all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_2))))) # label(fact_100_finite__imageI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	998 (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_695_zmult__assoc) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	999 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> one_one(X_c) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3))))) # label(fact_642_setprod__infinite) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1000 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_972_not__less0) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1001 (all L all U hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),L),U)))) # label(fact_938_finite__greaterThanAtMost) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1002 (all X_c all X_b (semiring_1(X_b) -> (all F all A_3 hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co1399186613setsum(X_c,nat),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,nat),fun(X_c,X_b),hAPP(fun(nat,X_b),fun(fun(X_c,nat),fun(X_c,X_b)),combb(nat,X_b,X_c),semiring_1_of_nat(X_b)),F)),A_3)))) # label(fact_667_of__nat__setsum) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1003 (all X_b (ord(X_b) -> hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),min(X_b),ord_less_eq(X_b)) = ord_min(X_b))) # label(fact_401_min__ord__min) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1004 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1005 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))))))) # label(fact_269_order__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1006 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M)) -> N_1 != M)) # label(fact_797_less__not__refl2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1007 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_271_xt1_I4_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1008 (all X_b all X_c all Z_2 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)))))) # label(fact_185_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1009 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_856_psubset__subset__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1010 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_574_Max__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1011 (all X_c all X_b all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) -> (exists X_2 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X_2)))))) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))))))) # label(fact_112_pigeonhole__infinite) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1012 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_970_less__nat__zero__code) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1013 (all X_c all X_b (comm_monoid_mult(X_b) -> (all G one_one(X_b) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),bot_bot(fun(X_c,bool)))))) # label(fact_640_setprod_Oempty) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1014 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))))) # label(fact_104_finite__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1015 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K))))) # label(fact_693_zle__trans) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1016 (all X_c all X_b all B_2 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_2,B_2)),hAPP(fun(X_c,bool),X_b,F_2,A_3)) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_323_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1017 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_287_equalityD1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1018 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_630_mult__1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1019 (all M all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),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),N_1)) = M)) # label(fact_824_add__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1020 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3)))))))) # label(fact_579_Max_Ohom__commute) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1021 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_128_DiffE) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1022 (all X_b all X_c all X_1 all Z_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)))) # label(fact_162_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1023 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_670_zle__int) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1024 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_564_minus__max__eq__min) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1025 (all X_b all X_c (ring(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_b,X_c,F,A_2)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))))))) # label(fact_174_setsum__diff1__ring) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1026 (all X_a (linordered_semidom(X_a) -> (all M all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1))))))) # label(fact_845_power__le__imp__le__exp) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1027 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1028 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1029 (all I all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N_1)) -> I = 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)))) # label(fact_439_diff__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1030 (all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int)) = Z) # label(fact_707_zmult__1__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1031 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S_1 all T_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),S_1),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),T_4),S_1))) -> one_one(X_c) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),S_1) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),T_4))))))) # label(fact_652_setprod__mono__one__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1032 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_146_insert__Diff__single) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1033 (all N all N_3 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),N)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)))) # label(fact_912_bounded__nat__set__is__finite) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1034 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_827_diff__less__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1035 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_501_minus__add__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1036 (all X_a (bot(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a)))))) # label(fact_766_not__less__bot) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1037 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J))))) # label(fact_404_mult__le__mono2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1038 (all X_a all X_b combk(X_a,X_b) = ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1039 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_102_finite__code) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1040 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_2)) # label(fact_145_Diff__insert2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1041 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_514_diff__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1042 (all X_b all Y_4 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_4) = ti(fun(X_b,bool),Y_4)) # label(fact_71_image__ident) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1043 (all X_b (order(X_b) -> (all Ca all A_2 all F all Ba (ti(X_b,A_2) = hAPP(X_b,X_b,F,Ba) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,F,Y_1)),hAPP(X_b,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,F,Ca)),A_2)))))))) # label(fact_611_xt1_I15_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1044 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_369_min__max_Oinf__le1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1045 (all X_a (linorder(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C),D_1)))))))) # label(fact_557_min__max_Osup__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1046 (all X_b (ring(X_b) -> (all A_2 all E all Ca all Ba all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D) <-> ti(X_b,Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))) # label(fact_219_eq__add__iff2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1047 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))))))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1048 (all X_a (ring_1(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N_1)))) # label(fact_887_power__minus) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1049 (all X_b all F all A_3 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3))) # label(fact_65_fold1__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1050 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_844_card__Diff1__less) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1051 (all X_b all X_1 all Y_2 all Pa ((-hBOOL(Pa) -> hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2)))) = ti(X_b,Y_2)) & (hBOOL(Pa) -> hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2)))) = ti(X_b,X_1)))) # label(fact_90_If__def) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1052 (all X_b all R_1 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),R_1),S_1)))) # label(fact_264_pred__subset__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1053 (all X_b (power(X_b) -> power_power(X_b) = ti(fun(X_b,fun(nat,X_b)),power_power(X_b)))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1054 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))))) # label(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1055 (all Com1_1 all Com2_1 all Com1 all Com2 (Com1 = Com1_1 & Com2 = Com2_1 <-> hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1))) # label(fact_56_com_Osimps_I3_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1056 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_992_mult__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1057 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1058 (all X_1 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))))) # label(fact_904_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1059 (all X_b all X_c finite_comp_fun_idem(X_b,X_c) = ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c))) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1060 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),one_one(nat)) = ti(X_a,X)))) # label(fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1061 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_551_min__max_Ole__supI1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1062 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_1)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_1),A_3)) = ti(fun(X_b,bool),A_3)))) # label(fact_315_double__diff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1063 (all X all Y all Z hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),Z)) # label(fact_696_zpower__zpower) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1064 (all X_b (ab_semigroup_mult(X_b) -> (all X_1 all A_3 (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))))))) # label(fact_125_fold1__insert) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1065 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_671_zmult__int) # label(axiom) # label(non_clause).  [assumption].
2.06/2.56	1066 (all X_a (semiring(X_a) -> (all A_1 all E_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_1)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C)))) # label(fact_224_combine__common__factor) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1067 (all X_b (linord219039673up_add(X_b) -> (all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),S_1) -> hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),S_1)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),uminus_uminus(X_b)),S_1))))))) # label(fact_480_minus__Max__eq__Min) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1068 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),one_one(nat)) = ti(X_a,A_1)))) # label(fact_877_power__one__right) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1069 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause).  [assumption].
2.06/2.57	1070 (all N (N != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_971_neq0__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1071 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) -> ti(X_a,C) = ti(X_a,B))))) # label(fact_226_add__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1072 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_811_compl__less__swap2) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1073 (all X_b all Pa ((exists X_2 ((all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,X_2) = ti(X_b,Y_1))) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))))) # label(fact_117_theI_H) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1074 (all X_b all F all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))),Ba)) <-> ti(X_b,A_2) = ti(X_b,Ba))) # label(fact_57_fold1Set__sing) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1075 (all X all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X)),N_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1))) # label(fact_908_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1076 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)))))))) # label(fact_381_Max__ge) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1077 (all X_c all X_b (semiring_0(X_b) -> (all R_2 all F all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),combb(X_b,X_b,X_c),hAPP(X_b,fun(X_b,X_b),times_times(X_b),R_2)),F)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),R_2),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3))))) # label(fact_189_setsum__right__distrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1078 (all X_a (comm_ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_639_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1079 (all X_a (comm_semiring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_250_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1080 (all X_b all X_c all Z_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists X_2 (hAPP(X_c,X_b,F,X_2) = ti(X_b,Z_2) & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)))))) # label(fact_69_image__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1081 (all X_b (order(X_b) -> (all A_2 all Ba all Ca all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),D)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),A_2)) | -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),Ca),D))))))) # label(fact_830_atLeastatMost__subset__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1082 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1)),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2))))))) # label(fact_813_compl__less__compl__iff) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1083 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_942_zero__less__two) # label(axiom) # label(non_clause).  [assumption].
2.06/2.57	1084 (all X_c all X_b all R_1 all K_1 all T_4 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),T_4)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),R_1),X_2)))) = K_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(fun(X_c,bool),nat,finite_card(X_c),T_4)) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,nat),hAPP(fun(fun(X_c,bool),nat),fun(fun(X_b,fun(X_c,bool)),fun(X_b,nat)),combb(fun(X_c,bool),nat,X_b),finite_card(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_4)))),R_1)))),S_1))))) # label(fact_619_setsum__multicount) # label(axiom) # label(non_clause).  [assumption].
2.06/2.58	1085 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_2 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y_1),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)))))) # label(fact_582_min__max_Odistrib__imp1) # label(axiom) # label(non_clause).  [assumption].
2.06/2.58	1086 (all X_b (order(X_b) -> (all Y_2 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2)))))) # label(fact_275_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
2.06/2.58	1087 (all X_b (ab_semigroup_mult(X_b) -> times_times(X_b) = ti(fun(X_b,fun(X_b,X_b)),times_times(X_b)))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause).  [assumption].
2.06/2.58	1088 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_949_add__nonpos__neg) # label(axiom) # label(non_clause).  [assumption].
2.06/2.58	1089 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_609_card__Diff1__le) # label(axiom) # label(non_clause).  [assumption].
2.06/2.58	1090 (all X_b all B_2 all A_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) # label(fact_312_subset__insertI) # label(axiom) # label(non_clause).  [assumption].
2.06/2.58	
2.06/2.58	============================== end of process non-clausal formulas ===
2.06/2.58	
2.06/2.58	============================== PROCESS INITIAL CLAUSES ===============
2.06/2.58	
2.06/2.58	============================== PREDICATE ELIMINATION =================
2.06/2.58	1091 -linord2061991079up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),plus_plus(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_601_add__Min__commute) # label(axiom).  [clausify(44)].
2.06/2.59	1092 linord2061991079up_add(nat) # label(arity_Nat_Onat___Groups_Olinordered__ab__semigroup__add) # label(axiom).  [assumption].
2.06/2.59	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),plus_plus(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)).  [resolve(1091,a,1092,a)].
2.06/2.59	1093 -linord2061991079up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),plus_plus(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_600_add__Max__commute) # label(axiom).  [clausify(267)].
2.06/2.68	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),plus_plus(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)).  [resolve(1093,a,1092,a)].
2.06/2.68	1094 linord2061991079up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__semigroup__add) # label(axiom).  [assumption].
2.06/2.68	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),plus_plus(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)).  [resolve(1094,a,1091,a)].
2.06/2.73	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),plus_plus(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)).  [resolve(1094,a,1093,a)].
2.06/2.73	1095 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom).  [assumption].
2.06/2.73	1096 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f4(A,B,C,D)),f5(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f4(A,B,C,D)),f6(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f4(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f5(A,B,C,D)),f6(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_583_min__max_Odistrib__imp2) # label(axiom).  [clausify(3)].
2.06/2.73	1097 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,big_linorder_Max(A),C)),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_576_Max_Osubset__idem) # label(axiom).  [clausify(9)].
2.06/2.73	1098 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_349_min__max_Oinf_Oassoc) # label(axiom).  [clausify(20)].
2.06/2.73	1099 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_566_Max_Oin__idem) # label(axiom).  [clausify(26)].
2.06/2.73	1100 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_753_linorder__antisym__conv1) # label(axiom).  [clausify(33)].
2.06/2.73	1101 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_753_linorder__antisym__conv1) # label(axiom).  [clausify(33)].
2.06/2.73	1102 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),C)) # label(fact_382_Min__le) # label(axiom).  [clausify(36)].
2.06/2.73	1103 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,big_linorder_Min(A),C)),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_376_Min_Osubset__idem) # label(axiom).  [clausify(38)].
2.06/2.73	1104 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_519_Max_Oinsert__remove) # label(axiom).  [clausify(39)].
2.06/2.73	1105 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_519_Max_Oinsert__remove) # label(axiom).  [clausify(39)].
2.06/2.73	1106 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_734_min__max_Oless__infI2) # label(axiom).  [clausify(47)].
2.06/2.73	1107 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,B,f23(A,C,B))),hAPP(A,A,B,f24(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f23(A,C,B)),f24(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),C)) # label(fact_478_min__max_OInf__fin_Ohom__commute) # label(axiom).  [clausify(48)].
2.06/2.73	1108 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_477_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom).  [clausify(55)].
2.06/2.73	1109 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f28(A,B)),f29(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f28(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f29(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),B)) # label(fact_580_Max_Oclosed) # label(axiom).  [clausify(84)].
2.06/2.73	1110 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_593_min__max_OSup__fin_Oin__idem) # label(axiom).  [clausify(87)].
2.06/2.73	1111 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_350_min__max_Oinf__left__commute) # label(axiom).  [clausify(94)].
2.06/2.73	1112 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),C)) # label(fact_368_min__max_Oinf__le2) # label(axiom).  [clausify(95)].
2.06/2.73	1113 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_366_min__max_Ole__inf__iff) # label(axiom).  [clausify(96)].
2.06/2.73	1114 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_366_min__max_Ole__inf__iff) # label(axiom).  [clausify(96)].
2.06/2.73	1115 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),C))) # label(fact_366_min__max_Ole__inf__iff) # label(axiom).  [clausify(96)].
2.06/2.73	1116 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_363_min__max_Oinf__absorb1) # label(axiom).  [clausify(100)].
2.06/2.73	1117 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_578_Max_Oeq__fold__idem_H) # label(axiom).  [clausify(104)].
2.06/2.73	1118 -linorder(A) | ord_min(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),max(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_397_dual__max) # label(axiom).  [clausify(115)].
2.06/2.73	1119 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) # label(fact_604_min__max_OSup__fin_Oremove) # label(axiom).  [clausify(122)].
2.06/2.73	1120 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_604_min__max_OSup__fin_Oremove) # label(axiom).  [clausify(122)].
2.06/2.73	1121 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f37(A,B)),f38(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f37(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f38(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)),B)) # label(fact_607_min__max_OSup__fin_Oclosed) # label(axiom).  [clausify(126)].
2.06/2.73	1122 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_279_linorder__linear) # label(axiom).  [clausify(131)].
2.06/2.73	1123 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),D)) # label(fact_839_fold1__strict__below__iff) # label(axiom).  [clausify(133)].
2.06/2.73	1124 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f42(A,C,B)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_839_fold1__strict__below__iff) # label(axiom).  [clausify(133)].
2.06/2.73	1125 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f42(A,C,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_839_fold1__strict__below__iff) # label(axiom).  [clausify(133)].
2.06/2.73	1126 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,C,B)),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),B) # label(fact_395_Min__eqI) # label(axiom).  [clausify(134)].
2.06/2.73	1127 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f43(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),B) # label(fact_395_Min__eqI) # label(axiom).  [clausify(134)].
2.06/2.73	1128 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f45(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom).  [clausify(138)].
2.06/2.73	1129 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),f45(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),f44(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom).  [clausify(138)].
2.06/2.74	1130 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,C,f45(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom).  [clausify(138)].
2.06/2.74	1131 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,C,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f44(A,C,B)),f45(A,C,B)))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom).  [clausify(138)].
2.06/2.74	1132 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_537_min__max_Osup__assoc) # label(axiom).  [clausify(153)].
2.06/2.74	1133 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_735_min__less__iff__conj) # label(axiom).  [clausify(171)].
2.06/2.74	1134 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_735_min__less__iff__conj) # label(axiom).  [clausify(171)].
2.06/2.74	1135 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_735_min__less__iff__conj) # label(axiom).  [clausify(171)].
2.06/2.74	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f4(int,A,B,C)),f5(int,A,B,C))),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f4(int,A,B,C)),f6(int,A,B,C))) != hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f4(int,A,B,C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f5(int,A,B,C)),f6(int,A,B,C))) | hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)).  [resolve(1095,a,1096,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,big_linorder_Max(int),B)),hAPP(fun(int,bool),int,big_linorder_Max(int),A)).  [resolve(1095,a,1097,a)].
2.06/2.74	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)).  [resolve(1095,a,1098,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)).  [resolve(1095,a,1099,a)].
2.06/2.74	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(1095,a,1100,a)].
2.06/2.74	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(1095,a,1101,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)),B)).  [resolve(1095,a,1102,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,big_linorder_Min(int),B)),hAPP(fun(int,bool),int,big_linorder_Min(int),A)).  [resolve(1095,a,1103,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1095,a,1104,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)).  [resolve(1095,a,1105,a)].
2.06/2.74	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)).  [resolve(1095,a,1106,a)].
2.06/2.74	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,A,f23(int,B,A))),hAPP(int,int,A,f24(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f23(int,B,A)),f24(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)).  [resolve(1095,a,1107,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A).  [resolve(1095,a,1108,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f28(int,A)),f29(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f28(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f29(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)),A)).  [resolve(1095,a,1109,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)).  [resolve(1095,a,1110,a)].
2.06/2.74	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)).  [resolve(1095,a,1111,a)].
2.06/2.74	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),B)).  [resolve(1095,a,1112,a)].
2.06/2.74	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))).  [resolve(1095,a,1113,a)].
2.06/2.74	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))).  [resolve(1095,a,1114,a)].
2.06/2.74	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),B))).  [resolve(1095,a,1115,a)].
2.06/2.74	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B).  [resolve(1095,a,1116,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A).  [resolve(1095,a,1117,a)].
2.06/2.74	Derived: ord_min(int) = hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),max(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))).  [resolve(1095,a,1118,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A).  [resolve(1095,a,1119,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1095,a,1120,a)].
2.06/2.74	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f37(int,A)),f38(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f37(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f38(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)),A)).  [resolve(1095,a,1121,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),C)).  [resolve(1095,a,1123,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f42(int,B,A)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)).  [resolve(1095,a,1124,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f42(int,B,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)).  [resolve(1095,a,1125,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f43(int,B,A)),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),A).  [resolve(1095,a,1126,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f43(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),A).  [resolve(1095,a,1127,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),f45(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1095,a,1128,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),f45(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),f44(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1095,a,1129,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,B,f45(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1095,a,1130,a)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,B,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f44(int,B,A)),f45(int,B,A)))) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1095,a,1131,a)].
2.06/2.75	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)).  [resolve(1095,a,1132,a)].
2.06/2.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(1095,a,1133,a)].
2.06/2.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(1095,a,1134,a)].
2.06/2.75	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(1095,a,1135,a)].
2.06/2.75	1136 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_375_Min_Oinsert) # label(axiom).  [clausify(203)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)).  [resolve(1136,a,1095,a)].
2.06/2.75	1137 -linorder(A) | big_Inf_fin(A) = ti(fun(fun(A,fun(A,A)),fun(fun(A,bool),A)),big_Inf_fin(A)) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom).  [clausify(205)].
2.06/2.75	Derived: big_Inf_fin(int) = ti(fun(fun(int,fun(int,int)),fun(fun(int,bool),int)),big_Inf_fin(int)).  [resolve(1137,a,1095,a)].
2.06/2.75	1138 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_374_Min__insert) # label(axiom).  [clausify(206)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)).  [resolve(1138,a,1095,a)].
2.06/2.75	1139 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),B)) # label(fact_384_Min__in) # label(axiom).  [clausify(209)].
2.06/2.75	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)),A)).  [resolve(1139,a,1095,a)].
2.06/2.75	1140 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_556_min__max_Osup__least) # label(axiom).  [clausify(211)].
2.06/2.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B)).  [resolve(1140,a,1095,a)].
2.06/2.75	1141 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_529_min__max_Osup__inf__distrib2) # label(axiom).  [clausify(212)].
2.06/2.75	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B).  [resolve(1141,a,1095,a)].
2.06/2.76	1142 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_528_min__max_Oinf__sup__distrib2) # label(axiom).  [clausify(217)].
2.06/2.76	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)).  [resolve(1142,a,1095,a)].
2.06/2.76	1143 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f57(A,C,B)),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),B) # label(fact_396_Max__eqI) # label(axiom).  [clausify(225)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f57(int,B,A)),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),A).  [resolve(1143,a,1095,a)].
2.06/2.76	1144 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f57(A,C,B)),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),B) # label(fact_396_Max__eqI) # label(axiom).  [clausify(225)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f57(int,B,A)),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),A).  [resolve(1144,a,1095,a)].
2.06/2.76	1145 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_358_min__max_Ole__infE) # label(axiom).  [clausify(229)].
2.06/2.76	1146 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_358_min__max_Ole__infE) # label(axiom).  [clausify(229)].
2.06/2.76	1147 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),D),B))) # label(fact_567_min__max_Osup__le__fold__sup) # label(axiom).  [clausify(231)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),C),A))).  [resolve(1147,a,1095,a)].
2.06/2.76	1148 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_545_min__max_Osup_Oidem) # label(axiom).  [clausify(234)].
2.06/2.76	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),A).  [resolve(1148,a,1095,a)].
2.06/2.76	1149 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_543_min__max_Osup__commute) # label(axiom).  [clausify(239)].
2.06/2.76	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A).  [resolve(1149,a,1095,a)].
2.06/2.76	1150 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),ord_max(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_588_min__max_Osup__Inf1__distrib) # label(axiom).  [clausify(244)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),ord_max(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)).  [resolve(1150,a,1095,a)].
2.06/2.76	1151 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_559_le__max__iff__disj) # label(axiom).  [clausify(249)].
2.06/2.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))).  [resolve(1151,a,1095,a)].
2.06/2.76	1152 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_559_le__max__iff__disj) # label(axiom).  [clausify(249)].
2.06/2.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))).  [resolve(1152,a,1095,a)].
2.06/2.76	1153 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_559_le__max__iff__disj) # label(axiom).  [clausify(249)].
2.06/2.76	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))).  [resolve(1153,a,1095,a)].
2.06/2.76	1154 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_787_linorder__antisym__conv3) # label(axiom).  [clausify(251)].
2.06/2.76	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | ti(int,A) = ti(int,B).  [resolve(1154,a,1095,a)].
2.06/2.76	1155 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) != ti(A,C) # label(fact_787_linorder__antisym__conv3) # label(axiom).  [clausify(251)].
2.06/2.76	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | ti(int,A) != ti(int,B).  [resolve(1155,a,1095,a)].
2.06/2.76	1156 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f63(A,B)),f64(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f63(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f64(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),B)) # label(fact_393_Min_Oclosed) # label(axiom).  [clausify(259)].
2.06/2.76	1157 -linorder(A) | big_Sup_fin(A) = ti(fun(fun(A,fun(A,A)),fun(fun(A,bool),A)),big_Sup_fin(A)) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom).  [clausify(263)].
2.06/2.76	Derived: big_Sup_fin(int) = ti(fun(fun(int,fun(int,int)),fun(fun(int,bool),int)),big_Sup_fin(int)).  [resolve(1157,a,1095,a)].
2.06/2.76	1158 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_605_min__max_OSup__fin_Oinsert__remove) # label(axiom).  [clausify(271)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1158,a,1095,a)].
2.06/2.76	1159 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_605_min__max_OSup__fin_Oinsert__remove) # label(axiom).  [clausify(271)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)).  [resolve(1159,a,1095,a)].
2.06/2.76	1160 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_471_min__max_OInf__fin_Osingleton) # label(axiom).  [clausify(272)].
2.06/2.76	Derived: ti(int,A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))).  [resolve(1160,a,1095,a)].
2.06/2.76	1161 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),D),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_387_min__max_Ofold__inf__le__inf) # label(axiom).  [clausify(277)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),C),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))).  [resolve(1161,a,1095,a)].
2.06/2.76	1162 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f66(A,C,D,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_581_min__max_Ofold__sup__le__sup) # label(axiom).  [clausify(281)].
2.06/2.76	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f66(int,B,C,A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))).  [resolve(1162,a,1095,a)].
2.06/2.77	1163 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f66(A,C,D,B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_581_min__max_Ofold__sup__le__sup) # label(axiom).  [clausify(281)].
2.06/2.77	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f66(int,B,C,A)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))).  [resolve(1163,a,1095,a)].
2.06/2.77	1164 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_712_min__max_Oless__supI2) # label(axiom).  [clausify(283)].
2.06/2.77	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))).  [resolve(1164,a,1095,a)].
2.06/2.77	1165 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_378_Min_Oeq__fold__idem_H) # label(axiom).  [clausify(284)].
2.06/2.77	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A).  [resolve(1165,a,1095,a)].
2.06/2.77	1166 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_531_min__max_Osup__inf__distrib1) # label(axiom).  [clausify(289)].
2.06/2.77	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)).  [resolve(1166,a,1095,a)].
2.06/2.77	1167 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_747_linorder__le__less__linear) # label(axiom).  [clausify(298)].
2.06/2.77	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1167,a,1095,a)].
2.06/2.77	1168 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Min(A),C)),hAPP(fun(A,bool),A,big_linorder_Min(A),B))) # label(fact_341_Min__antimono) # label(axiom).  [clausify(300)].
2.06/2.77	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Min(int),B)),hAPP(fun(int,bool),int,big_linorder_Min(int),A))).  [resolve(1168,a,1095,a)].
2.06/2.77	1169 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f74(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_923_pinf_I6_J) # label(axiom).  [clausify(309)].
2.06/2.77	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f74(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1169,a,1095,a)].
2.06/2.77	1170 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_736_min__less__iff__disj) # label(axiom).  [clausify(324)].
2.06/2.77	1171 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_736_min__less__iff__disj) # label(axiom).  [clausify(324)].
2.06/2.77	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B)).  [resolve(1171,a,1095,a)].
2.06/2.77	1172 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_736_min__less__iff__disj) # label(axiom).  [clausify(324)].
2.06/2.77	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)).  [resolve(1172,a,1095,a)].
2.06/2.77	1173 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_544_min__max_Osup_Ocommute) # label(axiom).  [clausify(332)].
2.06/2.77	1174 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_770_linorder__cases) # label(axiom).  [clausify(335)].
2.06/2.77	1175 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_598_min__max_OSup__fin_Oinsert__idem) # label(axiom).  [clausify(352)].
2.06/2.77	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)).  [resolve(1175,a,1095,a)].
2.06/2.77	1176 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_751_leI) # label(axiom).  [clausify(354)].
2.06/2.77	1177 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f89(A,B)),f90(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f89(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f90(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),B)) # label(fact_479_min__max_OInf__fin_Oclosed) # label(axiom).  [clausify(357)].
2.06/2.77	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f89(int,A)),f90(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f89(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f90(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),A)).  [resolve(1177,a,1095,a)].
2.06/2.78	1178 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_348_min__max_Oinf__assoc) # label(axiom).  [clausify(363)].
2.06/2.78	1179 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_367_min__max_Ole__iff__inf) # label(axiom).  [clausify(372)].
2.06/2.78	1180 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_367_min__max_Ole__iff__inf) # label(axiom).  [clausify(372)].
2.06/2.78	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,A) != hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B).  [resolve(1180,a,1095,a)].
2.06/2.78	1181 -linorder(A) | ti(A,B) != ti(A,C) | hAPP(A,fun(A,bool),ord_lessThan(A),B) = hAPP(A,fun(A,bool),ord_lessThan(A),C) # label(fact_293_lessThan__eq__iff) # label(axiom).  [clausify(373)].
2.06/2.78	Derived: ti(int,A) != ti(int,B) | hAPP(int,fun(int,bool),ord_lessThan(int),A) = hAPP(int,fun(int,bool),ord_lessThan(int),B).  [resolve(1181,a,1095,a)].
2.06/2.78	1182 -linorder(A) | ti(A,B) = ti(A,C) | hAPP(A,fun(A,bool),ord_lessThan(A),B) != hAPP(A,fun(A,bool),ord_lessThan(A),C) # label(fact_293_lessThan__eq__iff) # label(axiom).  [clausify(373)].
2.06/2.78	Derived: ti(int,A) = ti(int,B) | hAPP(int,fun(int,bool),ord_lessThan(int),A) != hAPP(int,fun(int,bool),ord_lessThan(int),B).  [resolve(1182,a,1095,a)].
2.06/2.78	1183 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B) # label(fact_372_Min_OF__eq) # label(axiom).  [clausify(381)].
2.06/2.78	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A).  [resolve(1183,a,1095,a)].
2.06/2.78	1184 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_max(A)),B) # label(fact_596_min__max_OSup__fin_OF__eq) # label(axiom).  [clausify(382)].
2.06/2.78	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_max(int)),A).  [resolve(1184,a,1095,a)].
2.06/2.78	1185 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_599_min__max_OSup__fin_Osubset__idem) # label(axiom).  [clausify(385)].
2.06/2.78	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)).  [resolve(1185,a,1095,a)].
2.06/2.78	1186 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_356_min__max_Oinf_Oidem) # label(axiom).  [clausify(404)].
2.06/2.78	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),A).  [resolve(1186,a,1095,a)].
2.06/2.78	1187 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_745_linorder__not__less) # label(axiom).  [clausify(414)].
2.06/2.78	1188 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_745_linorder__not__less) # label(axiom).  [clausify(414)].
2.06/2.78	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1188,a,1095,a)].
2.06/2.78	1189 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,B,f97(A,C,B))),hAPP(A,A,B,f98(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f97(A,C,B)),f98(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),C)) # label(fact_606_min__max_OSup__fin_Ohom__commute) # label(axiom).  [clausify(424)].
2.06/2.78	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,A,f97(int,B,A))),hAPP(int,int,A,f98(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f97(int,B,A)),f98(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)).  [resolve(1189,a,1095,a)].
2.06/2.78	1190 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_710_max__less__iff__conj) # label(axiom).  [clausify(425)].
2.06/2.78	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).  [resolve(1190,a,1095,a)].
2.06/2.78	1191 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_710_max__less__iff__conj) # label(axiom).  [clausify(425)].
2.06/2.78	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(1191,a,1095,a)].
2.06/2.78	1192 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_710_max__less__iff__conj) # label(axiom).  [clausify(425)].
2.06/2.78	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(1192,a,1095,a)].
2.06/2.79	1193 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_475_min__max_OInf__fin_Osubset__idem) # label(axiom).  [clausify(432)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)).  [resolve(1193,a,1095,a)].
2.06/2.79	1194 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_597_min__max_OSup__fin_Oinsert) # label(axiom).  [clausify(442)].
2.06/2.79	1195 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_389_min__max_Ofold1__belowI) # label(axiom).  [clausify(444)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)).  [resolve(1195,a,1095,a)].
2.06/2.79	1196 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)))) # label(fact_562_min__max_Odistrib__sup__le) # label(axiom).  [clausify(463)].
2.06/2.79	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)))).  [resolve(1196,a,1095,a)].
2.06/2.79	1197 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_602_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom).  [clausify(470)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A).  [resolve(1197,a,1095,a)].
2.06/2.79	1198 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),B)) # label(fact_383_Max__in) # label(axiom).  [clausify(472)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)),A)).  [resolve(1198,a,1095,a)].
2.06/2.79	1199 -linorder(A) | big_linorder_Min(A) = ti(fun(fun(A,bool),A),big_linorder_Min(A)) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom).  [clausify(476)].
2.06/2.79	Derived: big_linorder_Min(int) = ti(fun(fun(int,bool),int),big_linorder_Min(int)).  [resolve(1199,a,1095,a)].
2.06/2.79	1200 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_355_min__max_Oinf_Ocommute) # label(axiom).  [clausify(484)].
2.06/2.79	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A).  [resolve(1200,a,1095,a)].
2.06/2.79	1201 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_292_lessThan__subset__iff) # label(axiom).  [clausify(489)].
2.06/2.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))).  [resolve(1201,a,1095,a)].
2.06/2.79	1202 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_292_lessThan__subset__iff) # label(axiom).  [clausify(489)].
2.06/2.79	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))).  [resolve(1202,a,1095,a)].
2.06/2.79	1203 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_470_min__max_OInf__fin_Oin__idem) # label(axiom).  [clausify(490)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)).  [resolve(1203,a,1095,a)].
2.06/2.79	1204 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_379_Min_Oinsert__remove) # label(axiom).  [clausify(492)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1204,a,1095,a)].
2.06/2.79	1205 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_379_Min_Oinsert__remove) # label(axiom).  [clausify(492)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)).  [resolve(1205,a,1095,a)].
2.06/2.79	1206 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_385_Min_Osingleton) # label(axiom).  [clausify(501)].
2.06/2.79	Derived: ti(int,A) = hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))).  [resolve(1206,a,1095,a)].
2.06/2.79	1207 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_346_Min_Oin__idem) # label(axiom).  [clausify(505)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)).  [resolve(1207,a,1095,a)].
2.06/2.79	1208 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f113(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom).  [clausify(514)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),f113(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1208,a,1095,a)].
2.06/2.79	1209 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),f113(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f112(A,C,B)),D)) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom).  [clausify(514)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),f113(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f112(int,B,A)),C)) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1209,a,1095,a)].
2.06/2.79	1210 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,C,f113(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom).  [clausify(514)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,B,f113(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1210,a,1095,a)].
2.06/2.79	1211 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,C,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f112(A,C,B)),f113(A,C,B)))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom).  [clausify(514)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,B,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f112(int,B,A)),f113(int,B,A)))) | hBOOL(hAPP(fun(int,bool),bool,B,A)).  [resolve(1211,a,1095,a)].
2.06/2.79	1212 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),ord_min(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_591_min__max_Oinf__Sup1__distrib) # label(axiom).  [clausify(515)].
2.06/2.79	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),ord_min(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)).  [resolve(1212,a,1095,a)].
2.06/2.80	1213 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_360_min__max_Oinf__greatest) # label(axiom).  [clausify(517)].
2.06/2.80	1214 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),E))) # label(fact_359_min__max_Oinf__mono) # label(axiom).  [clausify(524)].
2.06/2.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),D))).  [resolve(1214,a,1095,a)].
2.06/2.80	1215 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_595_min__max_Oinf__Sup__absorb) # label(axiom).  [clausify(529)].
2.06/2.80	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)).  [resolve(1215,a,1095,a)].
2.06/2.80	1216 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_733_min__max_Oless__infI1) # label(axiom).  [clausify(531)].
2.06/2.80	1217 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_377_Min_Oeq__fold_H) # label(axiom).  [clausify(537)].
2.06/2.80	1218 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_greaterThan(A),B)),hAPP(A,fun(A,bool),ord_greaterThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_571_greaterThan__subset__iff) # label(axiom).  [clausify(538)].
2.06/2.80	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_greaterThan(int),A)),hAPP(int,fun(int,bool),ord_greaterThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1218,a,1095,a)].
2.06/2.80	1219 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_greaterThan(A),B)),hAPP(A,fun(A,bool),ord_greaterThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_571_greaterThan__subset__iff) # label(axiom).  [clausify(538)].
2.06/2.80	Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_greaterThan(int),A)),hAPP(int,fun(int,bool),ord_greaterThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1219,a,1095,a)].
2.06/2.80	1220 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_575_Max_Oinsert) # label(axiom).  [clausify(557)].
2.06/2.80	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)).  [resolve(1220,a,1095,a)].
2.06/2.80	1221 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f120(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_918_minf_I8_J) # label(axiom).  [clausify(558)].
2.06/2.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f120(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1221,a,1095,a)].
2.06/2.80	1222 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_554_min__max_Osup__absorb1) # label(axiom).  [clausify(560)].
2.06/2.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A).  [resolve(1222,a,1095,a)].
2.06/2.80	1223 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_790_linorder__neq__iff) # label(axiom).  [clausify(563)].
2.06/2.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) != ti(int,B).  [resolve(1223,a,1095,a)].
2.06/2.80	1224 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_790_linorder__neq__iff) # label(axiom).  [clausify(563)].
2.06/2.80	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A).  [resolve(1224,a,1095,a)].
2.06/2.80	1225 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_790_linorder__neq__iff) # label(axiom).  [clausify(563)].
2.06/2.80	1226 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_758_linorder__antisym__conv2) # label(axiom).  [clausify(570)].
2.06/2.80	1227 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_758_linorder__antisym__conv2) # label(axiom).  [clausify(570)].
2.06/2.81	1228 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_594_min__max_OSup__fin_Osingleton) # label(axiom).  [clausify(571)].
2.06/2.81	Derived: ti(int,A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))).  [resolve(1228,a,1095,a)].
2.06/2.81	1229 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_386_Max_Osingleton) # label(axiom).  [clausify(572)].
2.06/2.81	Derived: ti(int,A) = hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))).  [resolve(1229,a,1095,a)].
2.06/2.81	1230 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) # label(fact_472_min__max_OInf__fin_OF__eq) # label(axiom).  [clausify(597)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A).  [resolve(1230,a,1095,a)].
2.06/2.81	1231 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_354_min__max_Oinf__commute) # label(axiom).  [clausify(600)].
2.06/2.81	1232 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_365_min__max_Ole__infI1) # label(axiom).  [clausify(602)].
2.06/2.81	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B)).  [resolve(1232,a,1095,a)].
2.06/2.81	1233 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),hAPP(fun(A,bool),A,big_linorder_Max(A),C))) # label(fact_342_Max__mono) # label(axiom).  [clausify(613)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)),hAPP(fun(int,bool),int,big_linorder_Max(int),B))).  [resolve(1233,a,1095,a)].
2.06/2.81	1234 -linorder(A) | big_linorder_Max(A) = ti(fun(fun(A,bool),A),big_linorder_Max(A)) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom).  [clausify(614)].
2.06/2.81	Derived: big_linorder_Max(int) = ti(fun(fun(int,bool),int),big_linorder_Max(int)).  [resolve(1234,a,1095,a)].
2.06/2.81	1235 -linorder(A) | ord_max(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),min(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_573_dual__min) # label(axiom).  [clausify(617)].
2.06/2.81	Derived: ord_max(int) = hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),min(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))).  [resolve(1235,a,1095,a)].
2.06/2.81	1236 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_347_Min_Oidem) # label(axiom).  [clausify(626)].
2.06/2.81	1237 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B))) # label(fact_586_min__max_OInf__le__Sup) # label(axiom).  [clausify(630)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A))).  [resolve(1237,a,1095,a)].
2.06/2.81	1238 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_353_min__max_Oinf_Oleft__idem) # label(axiom).  [clausify(631)].
2.06/2.81	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B).  [resolve(1238,a,1095,a)].
2.06/2.81	1239 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),B) # label(fact_380_Min_Oremove) # label(axiom).  [clausify(634)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),A).  [resolve(1239,a,1095,a)].
2.06/2.81	1240 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_380_Min_Oremove) # label(axiom).  [clausify(634)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1240,a,1095,a)].
2.06/2.81	1241 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom).  [assumption].
2.06/2.81	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f4(nat,A,B,C)),f5(nat,A,B,C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f4(nat,A,B,C)),f6(nat,A,B,C))) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f4(nat,A,B,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f5(nat,A,B,C)),f6(nat,A,B,C))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)).  [resolve(1241,a,1096,a)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)).  [resolve(1241,a,1097,a)].
2.06/2.81	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)).  [resolve(1241,a,1098,a)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)).  [resolve(1241,a,1099,a)].
2.06/2.81	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(1241,a,1100,a)].
2.06/2.81	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(1241,a,1101,a)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)),B)).  [resolve(1241,a,1102,a)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)).  [resolve(1241,a,1103,a)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1241,a,1104,a)].
2.06/2.81	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)).  [resolve(1241,a,1105,a)].
2.06/2.81	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)).  [resolve(1241,a,1106,a)].
2.06/2.82	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,A,f23(nat,B,A))),hAPP(nat,nat,A,f24(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f23(nat,B,A)),f24(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),B)).  [resolve(1241,a,1107,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A).  [resolve(1241,a,1108,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f28(nat,A)),f29(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f28(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f29(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)),A)).  [resolve(1241,a,1109,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)).  [resolve(1241,a,1110,a)].
2.06/2.82	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)).  [resolve(1241,a,1111,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),B)).  [resolve(1241,a,1112,a)].
2.06/2.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))).  [resolve(1241,a,1113,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))).  [resolve(1241,a,1114,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),B))).  [resolve(1241,a,1115,a)].
2.06/2.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B).  [resolve(1241,a,1116,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A).  [resolve(1241,a,1117,a)].
2.06/2.82	Derived: ord_min(nat) = hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),max(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))).  [resolve(1241,a,1118,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A).  [resolve(1241,a,1119,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1241,a,1120,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f37(nat,A)),f38(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f37(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f38(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)),A)).  [resolve(1241,a,1121,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1241,a,1122,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),C)).  [resolve(1241,a,1123,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f42(nat,B,A)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)).  [resolve(1241,a,1124,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f42(nat,B,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)).  [resolve(1241,a,1125,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f43(nat,B,A)),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A).  [resolve(1241,a,1126,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f43(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A).  [resolve(1241,a,1127,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),f45(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1128,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),f45(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),f44(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1129,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,B,f45(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1130,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,B,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f44(nat,B,A)),f45(nat,B,A)))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1131,a)].
2.06/2.82	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)).  [resolve(1241,a,1132,a)].
2.06/2.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(1241,a,1133,a)].
2.06/2.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(1241,a,1134,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(1241,a,1135,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)).  [resolve(1241,a,1136,a)].
2.06/2.82	Derived: big_Inf_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Inf_fin(nat)).  [resolve(1241,a,1137,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)).  [resolve(1241,a,1138,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)),A)).  [resolve(1241,a,1139,a)].
2.06/2.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B)).  [resolve(1241,a,1140,a)].
2.06/2.82	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B).  [resolve(1241,a,1141,a)].
2.06/2.82	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)).  [resolve(1241,a,1142,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f57(nat,B,A)),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A).  [resolve(1241,a,1143,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f57(nat,B,A)),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A).  [resolve(1241,a,1144,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),C),A))).  [resolve(1241,a,1147,a)].
2.06/2.82	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A).  [resolve(1241,a,1148,a)].
2.06/2.82	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A).  [resolve(1241,a,1149,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),ord_max(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)).  [resolve(1241,a,1150,a)].
2.06/2.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))).  [resolve(1241,a,1151,a)].
2.06/2.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))).  [resolve(1241,a,1152,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))).  [resolve(1241,a,1153,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | ti(nat,A) = ti(nat,B).  [resolve(1241,a,1154,a)].
2.06/2.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | ti(nat,A) != ti(nat,B).  [resolve(1241,a,1155,a)].
2.06/2.82	Derived: big_Sup_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Sup_fin(nat)).  [resolve(1241,a,1157,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1241,a,1158,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)).  [resolve(1241,a,1159,a)].
2.06/2.82	Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))).  [resolve(1241,a,1160,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))).  [resolve(1241,a,1161,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f66(nat,B,C,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))).  [resolve(1241,a,1162,a)].
2.06/2.82	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f66(nat,B,C,A)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))).  [resolve(1241,a,1163,a)].
2.06/2.83	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))).  [resolve(1241,a,1164,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A).  [resolve(1241,a,1165,a)].
2.06/2.83	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)).  [resolve(1241,a,1166,a)].
2.06/2.83	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1241,a,1167,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A))).  [resolve(1241,a,1168,a)].
2.06/2.83	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f74(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1241,a,1169,a)].
2.06/2.83	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B)).  [resolve(1241,a,1171,a)].
2.06/2.83	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)).  [resolve(1241,a,1172,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)).  [resolve(1241,a,1175,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f89(nat,A)),f90(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f89(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f90(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),A)).  [resolve(1241,a,1177,a)].
2.06/2.83	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B).  [resolve(1241,a,1180,a)].
2.06/2.83	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),B).  [resolve(1241,a,1181,a)].
2.06/2.83	Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) != hAPP(nat,fun(nat,bool),ord_lessThan(nat),B).  [resolve(1241,a,1182,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A).  [resolve(1241,a,1183,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_max(nat)),A).  [resolve(1241,a,1184,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)).  [resolve(1241,a,1185,a)].
2.06/2.83	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A).  [resolve(1241,a,1186,a)].
2.06/2.83	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1241,a,1188,a)].
2.06/2.83	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,A,f97(nat,B,A))),hAPP(nat,nat,A,f98(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f97(nat,B,A)),f98(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),B)).  [resolve(1241,a,1189,a)].
2.06/2.83	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(1241,a,1190,a)].
2.06/2.83	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(1241,a,1191,a)].
2.06/2.83	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(1241,a,1192,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)).  [resolve(1241,a,1193,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)).  [resolve(1241,a,1195,a)].
2.06/2.83	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)))).  [resolve(1241,a,1196,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A).  [resolve(1241,a,1197,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)),A)).  [resolve(1241,a,1198,a)].
2.06/2.83	Derived: big_linorder_Min(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Min(nat)).  [resolve(1241,a,1199,a)].
2.06/2.83	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A).  [resolve(1241,a,1200,a)].
2.06/2.83	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))).  [resolve(1241,a,1201,a)].
2.06/2.83	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))).  [resolve(1241,a,1202,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)).  [resolve(1241,a,1203,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1241,a,1204,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)).  [resolve(1241,a,1205,a)].
2.06/2.83	Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))).  [resolve(1241,a,1206,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)).  [resolve(1241,a,1207,a)].
2.06/2.83	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),f113(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1208,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),f113(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f112(nat,B,A)),C)) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1209,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,B,f113(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1210,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,B,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f112(nat,B,A)),f113(nat,B,A)))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)).  [resolve(1241,a,1211,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),ord_min(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)).  [resolve(1241,a,1212,a)].
2.06/2.84	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),D))).  [resolve(1241,a,1214,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)).  [resolve(1241,a,1215,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1241,a,1218,a)].
2.06/2.84	Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1241,a,1219,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)).  [resolve(1241,a,1220,a)].
2.06/2.84	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f120(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1241,a,1221,a)].
2.06/2.84	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A).  [resolve(1241,a,1222,a)].
2.06/2.84	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B).  [resolve(1241,a,1223,a)].
2.06/2.84	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A).  [resolve(1241,a,1224,a)].
2.06/2.84	Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))).  [resolve(1241,a,1228,a)].
2.06/2.84	Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))).  [resolve(1241,a,1229,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A).  [resolve(1241,a,1230,a)].
2.06/2.84	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B)).  [resolve(1241,a,1232,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B))).  [resolve(1241,a,1233,a)].
2.06/2.84	Derived: big_linorder_Max(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Max(nat)).  [resolve(1241,a,1234,a)].
2.06/2.84	Derived: ord_max(nat) = hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),min(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))).  [resolve(1241,a,1235,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A))).  [resolve(1241,a,1237,a)].
2.06/2.84	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B).  [resolve(1241,a,1238,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A).  [resolve(1241,a,1239,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1241,a,1240,a)].
2.06/2.84	1242 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_793_lessThan__strict__subset__iff) # label(axiom).  [clausify(637)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(1242,a,1095,a)].
2.06/2.84	Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(1242,a,1241,a)].
2.06/2.84	1243 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_793_lessThan__strict__subset__iff) # label(axiom).  [clausify(637)].
2.06/2.84	Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(1243,a,1095,a)].
2.06/2.84	Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(1243,a,1241,a)].
2.06/2.84	1244 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_539_min__max_Osup__left__commute) # label(axiom).  [clausify(643)].
2.06/2.84	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)).  [resolve(1244,a,1095,a)].
2.06/2.84	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)).  [resolve(1244,a,1241,a)].
2.06/2.84	1245 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_max(A))) # label(fact_560_min__max_Ocomp__fun__idem__sup) # label(axiom).  [clausify(644)].
2.06/2.84	Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite_comp_fun_idem(int,int),ord_max(int))).  [resolve(1245,a,1095,a)].
2.06/2.84	Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_max(nat))).  [resolve(1245,a,1241,a)].
2.06/2.84	1246 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) # label(fact_468_min__max_OInf__fin_Oremove) # label(axiom).  [clausify(651)].
2.06/2.85	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A).  [resolve(1246,a,1095,a)].
2.06/2.85	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A).  [resolve(1246,a,1241,a)].
2.06/2.85	1247 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_468_min__max_OInf__fin_Oremove) # label(axiom).  [clausify(651)].
2.06/2.85	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1247,a,1095,a)].
2.06/2.85	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1247,a,1241,a)].
2.06/2.85	1248 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,B,f135(A,C,B))),hAPP(A,A,B,f136(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f135(A,C,B)),f136(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,big_linorder_Min(A),C)) # label(fact_392_Min_Ohom__commute) # label(axiom).  [clausify(664)].
2.06/2.85	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,A,f135(int,B,A))),hAPP(int,int,A,f136(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f135(int,B,A)),f136(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,big_linorder_Min(int),B)).  [resolve(1248,a,1095,a)].
2.06/2.85	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,A,f135(nat,B,A))),hAPP(nat,nat,A,f136(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f135(nat,B,A)),f136(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)).  [resolve(1248,a,1241,a)].
2.06/2.85	1249 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_538_min__max_Osup_Oassoc) # label(axiom).  [clausify(669)].
2.06/2.85	1250 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_364_min__max_Ole__infI2) # label(axiom).  [clausify(688)].
2.06/2.85	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)).  [resolve(1250,a,1095,a)].
2.06/2.85	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)).  [resolve(1250,a,1241,a)].
2.06/2.85	1251 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_265_linorder__le__cases) # label(axiom).  [clausify(698)].
2.06/2.85	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1251,a,1095,a)].
2.06/2.85	1252 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_357_min__le__iff__disj) # label(axiom).  [clausify(699)].
2.06/2.85	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)).  [resolve(1252,a,1095,a)].
2.06/2.85	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(1252,a,1241,a)].
2.06/2.86	1253 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_357_min__le__iff__disj) # label(axiom).  [clausify(699)].
2.06/2.86	1254 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_357_min__le__iff__disj) # label(axiom).  [clausify(699)].
2.06/2.86	1255 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_362_min__max_Oinf__absorb2) # label(axiom).  [clausify(703)].
2.06/2.86	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A).  [resolve(1255,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A).  [resolve(1255,a,1241,a)].
2.06/2.86	1256 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_542_min__max_Osup_Oleft__idem) # label(axiom).  [clausify(704)].
2.06/2.86	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B).  [resolve(1256,a,1095,a)].
2.06/2.86	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B).  [resolve(1256,a,1241,a)].
2.06/2.86	1257 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f141(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_922_minf_I6_J) # label(axiom).  [clausify(706)].
2.06/2.86	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f141(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(1257,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f141(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(1257,a,1241,a)].
2.06/2.86	1258 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_469_min__max_OInf__fin_Oinsert__remove) # label(axiom).  [clausify(717)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)).  [resolve(1258,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)).  [resolve(1258,a,1241,a)].
2.06/2.86	1259 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_469_min__max_OInf__fin_Oinsert__remove) # label(axiom).  [clausify(717)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1259,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1259,a,1241,a)].
2.06/2.86	1260 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)) # label(fact_569_min__max_Ofold__sup__insert) # label(axiom).  [clausify(718)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)).  [resolve(1260,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)).  [resolve(1260,a,1241,a)].
2.06/2.86	1261 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_746_linorder__not__le) # label(axiom).  [clausify(719)].
2.06/2.86	1262 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_746_linorder__not__le) # label(axiom).  [clausify(719)].
2.06/2.86	1263 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f142(A,C,D,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),C)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B))) # label(fact_394_min__max_Oinf__le__fold__inf) # label(axiom).  [clausify(721)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f142(int,B,C,A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),B)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A))).  [resolve(1263,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f142(nat,B,C,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),B)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A))).  [resolve(1263,a,1241,a)].
2.06/2.86	1264 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f142(A,D,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),D),B))) # label(fact_394_min__max_Oinf__le__fold__inf) # label(axiom).  [clausify(721)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f142(int,C,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),C),A))).  [resolve(1264,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f142(nat,C,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),C),A))).  [resolve(1264,a,1241,a)].
2.06/2.86	1265 -linorder(A) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) # label(fact_338_fold1__antimono) # label(axiom).  [clausify(725)].
2.06/2.86	Derived: ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))).  [resolve(1265,a,1095,a)].
2.06/2.86	Derived: ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))).  [resolve(1265,a,1241,a)].
2.06/2.86	1266 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool)),hAPP(fun(fun(A,fun(A,bool)),fun(A,bool)),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool))),combb(fun(A,fun(A,bool)),fun(A,bool),A),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A))),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,bool)),fun(A,fun(A,bool))),hAPP(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),hAPP(fun(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))))),combb(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),A),combs(A,fun(A,bool),fun(A,bool))),hAPP(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),hAPP(fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),fun(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool))))),combb(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),A),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool))),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool)))),hAPP(fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool))))),combb(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),A),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj))),hAPP(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,A)),fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),hAPP(fun(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool))))),combb(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool))),A),combb(fun(A,A),fun(A,bool),A)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A)))),ord_min(A)))))),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(bool,bool),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),A),combb(bool,bool,A)),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),C)) # label(fact_592_min__max_Oinf__Sup2__distrib) # label(axiom).  [clausify(731)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool)),hAPP(fun(fun(int,fun(int,bool)),fun(int,bool)),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool))),combb(fun(int,fun(int,bool)),fun(int,bool),int),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int))),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,bool)),fun(int,fun(int,bool))),hAPP(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),hAPP(fun(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))))),combb(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),int),combs(int,fun(int,bool),fun(int,bool))),hAPP(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),hAPP(fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool))))),combb(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),int),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool))),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool)))),hAPP(fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool))))),combb(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),int),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,int)),fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),hAPP(fun(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),int),combb(fun(int,int),fun(int,bool),int)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),ord_min(int)))))),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),B))))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)).  [resolve(1266,a,1095,a)].
2.06/2.86	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,bool)),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool))),combb(fun(nat,fun(nat,bool)),fun(nat,bool),nat),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))))),combb(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),nat),combs(nat,fun(nat,bool),fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),hAPP(fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),nat),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool)))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool))))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),nat),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))))),combb(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),nat),combb(fun(nat,nat),fun(nat,bool),nat)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat)))),ord_min(nat)))))),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),nat),combb(bool,bool,nat)),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),B))))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),B)).  [resolve(1266,a,1241,a)].
2.06/2.87	1267 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) # label(fact_533_min__max_Osup__inf__absorb) # label(axiom).  [clausify(743)].
2.06/2.87	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)).  [resolve(1267,a,1095,a)].
2.06/2.87	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)).  [resolve(1267,a,1241,a)].
2.06/2.87	1268 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_752_not__leE) # label(axiom).  [clausify(747)].
2.06/2.87	1269 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_473_min__max_OInf__fin_Oinsert__idem) # label(axiom).  [clausify(749)].
2.06/2.87	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)).  [resolve(1269,a,1095,a)].
2.06/2.87	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)).  [resolve(1269,a,1241,a)].
2.06/2.87	1270 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B))) # label(fact_548_le__maxI2) # label(axiom).  [clausify(755)].
2.06/2.87	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A))).  [resolve(1270,a,1095,a)].
2.06/2.87	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A))).  [resolve(1270,a,1241,a)].
2.06/2.87	1271 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f152(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_919_pinf_I8_J) # label(axiom).  [clausify(764)].
2.06/2.87	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f152(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(1271,a,1095,a)].
2.06/2.87	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f152(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(1271,a,1241,a)].
2.06/2.87	1272 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),B) # label(fact_518_Max_Oremove) # label(axiom).  [clausify(765)].
2.06/2.87	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),A).  [resolve(1272,a,1095,a)].
2.06/2.87	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A).  [resolve(1272,a,1241,a)].
2.06/2.87	1273 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_518_Max_Oremove) # label(axiom).  [clausify(765)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))).  [resolve(1273,a,1095,a)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))).  [resolve(1273,a,1241,a)].
2.06/2.88	1274 -linorder(A) | ti(A,B) != ti(A,C) | hAPP(A,fun(A,bool),ord_greaterThan(A),B) = hAPP(A,fun(A,bool),ord_greaterThan(A),C) # label(fact_546_greaterThan__eq__iff) # label(axiom).  [clausify(769)].
2.06/2.88	Derived: ti(int,A) != ti(int,B) | hAPP(int,fun(int,bool),ord_greaterThan(int),A) = hAPP(int,fun(int,bool),ord_greaterThan(int),B).  [resolve(1274,a,1095,a)].
2.06/2.88	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B).  [resolve(1274,a,1241,a)].
2.06/2.88	1275 -linorder(A) | ti(A,B) = ti(A,C) | hAPP(A,fun(A,bool),ord_greaterThan(A),B) != hAPP(A,fun(A,bool),ord_greaterThan(A),C) # label(fact_546_greaterThan__eq__iff) # label(axiom).  [clausify(769)].
2.06/2.88	Derived: ti(int,A) = ti(int,B) | hAPP(int,fun(int,bool),ord_greaterThan(int),A) != hAPP(int,fun(int,bool),ord_greaterThan(int),B).  [resolve(1275,a,1095,a)].
2.06/2.88	Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A) != hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B).  [resolve(1275,a,1241,a)].
2.06/2.88	1276 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_603_min__max_OSup__fin_Oeq__fold_H) # label(axiom).  [clausify(777)].
2.06/2.88	1277 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_541_min__max_Osup__left__idem) # label(axiom).  [clausify(782)].
2.06/2.88	1278 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f154(A,C,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom).  [clausify(788)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f154(int,B,A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))).  [resolve(1278,a,1095,a)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f154(nat,B,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))).  [resolve(1278,a,1241,a)].
2.06/2.88	1279 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f154(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom).  [clausify(788)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f154(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))).  [resolve(1279,a,1095,a)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f154(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))).  [resolve(1279,a,1241,a)].
2.06/2.88	1280 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom).  [clausify(788)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))).  [resolve(1280,a,1095,a)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))).  [resolve(1280,a,1241,a)].
2.06/2.88	1281 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_536_Max_Oidem) # label(axiom).  [clausify(791)].
2.06/2.88	1282 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_840_strict__below__fold1__iff) # label(axiom).  [clausify(806)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).  [resolve(1282,a,1095,a)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(1282,a,1241,a)].
2.06/2.88	1283 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f156(A,C,B)),B)) # label(fact_840_strict__below__fold1__iff) # label(axiom).  [clausify(806)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f156(int,B,A)),A)).  [resolve(1283,a,1095,a)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f156(nat,B,A)),A)).  [resolve(1283,a,1241,a)].
2.06/2.88	1284 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),f156(A,C,B))) # label(fact_840_strict__below__fold1__iff) # label(axiom).  [clausify(806)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),f156(int,B,A))).  [resolve(1284,a,1095,a)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),f156(nat,B,A))).  [resolve(1284,a,1241,a)].
2.06/2.88	1285 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_361_min__max_Ole__infI) # label(axiom).  [clausify(814)].
2.06/2.88	1286 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool)),hAPP(fun(fun(A,fun(A,bool)),fun(A,bool)),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool))),combb(fun(A,fun(A,bool)),fun(A,bool),A),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A))),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,bool)),fun(A,fun(A,bool))),hAPP(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),hAPP(fun(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))))),combb(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),A),combs(A,fun(A,bool),fun(A,bool))),hAPP(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),hAPP(fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),fun(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool))))),combb(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),A),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool))),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool)))),hAPP(fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool))))),combb(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),A),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj))),hAPP(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,A)),fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),hAPP(fun(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool))))),combb(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool))),A),combb(fun(A,A),fun(A,bool),A)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A)))),ord_max(A)))))),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(bool,bool),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),A),combb(bool,bool,A)),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),C)) # label(fact_587_min__max_Osup__Inf2__distrib) # label(axiom).  [clausify(815)].
2.06/2.88	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool)),hAPP(fun(fun(int,fun(int,bool)),fun(int,bool)),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool))),combb(fun(int,fun(int,bool)),fun(int,bool),int),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int))),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,bool)),fun(int,fun(int,bool))),hAPP(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),hAPP(fun(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))))),combb(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),int),combs(int,fun(int,bool),fun(int,bool))),hAPP(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),hAPP(fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool))))),combb(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),int),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool))),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool)))),hAPP(fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool))))),combb(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),int),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,int)),fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),hAPP(fun(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),int),combb(fun(int,int),fun(int,bool),int)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),ord_max(int)))))),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),B))))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)).  [resolve(1286,a,1095,a)].
2.06/2.89	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,bool)),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool))),combb(fun(nat,fun(nat,bool)),fun(nat,bool),nat),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))))),combb(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),nat),combs(nat,fun(nat,bool),fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),hAPP(fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),nat),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool)))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool))))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),nat),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))))),combb(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),nat),combb(fun(nat,nat),fun(nat,bool),nat)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat)))),ord_max(nat)))))),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),nat),combb(bool,bool,nat)),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),B))))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),B)).  [resolve(1286,a,1241,a)].
2.06/2.89	1287 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_756_leD) # label(axiom).  [clausify(835)].
2.06/2.89	1288 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_min(A))) # label(fact_373_min__max_Ocomp__fun__idem__inf) # label(axiom).  [clausify(840)].
2.06/2.89	Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite_comp_fun_idem(int,int),ord_min(int))).  [resolve(1288,a,1095,a)].
2.06/2.89	Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_min(nat))).  [resolve(1288,a,1241,a)].
2.06/2.89	1289 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_530_min__max_Oinf__sup__distrib1) # label(axiom).  [clausify(842)].
2.06/2.89	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)).  [resolve(1289,a,1095,a)].
2.06/2.89	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)).  [resolve(1289,a,1241,a)].
2.06/2.89	1290 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_552_min__max_Ole__supI2) # label(axiom).  [clausify(848)].
2.06/2.89	1291 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))) # label(fact_547_le__maxI1) # label(axiom).  [clausify(851)].
2.06/2.89	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B))).  [resolve(1291,a,1095,a)].
2.06/2.89	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B))).  [resolve(1291,a,1241,a)].
2.06/2.89	1292 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_713_min__max_Oless__supI1) # label(axiom).  [clausify(852)].
2.06/2.89	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))).  [resolve(1292,a,1095,a)].
2.06/2.89	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))).  [resolve(1292,a,1241,a)].
2.06/2.90	1293 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_550_min__max_Ole__sup__iff) # label(axiom).  [clausify(865)].
2.06/2.90	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)).  [resolve(1293,a,1095,a)].
2.06/2.90	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(1293,a,1241,a)].
2.06/2.90	1294 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_550_min__max_Ole__sup__iff) # label(axiom).  [clausify(865)].
2.06/2.90	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)).  [resolve(1294,a,1095,a)].
2.06/2.90	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)).  [resolve(1294,a,1241,a)].
2.06/2.90	1295 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_550_min__max_Ole__sup__iff) # label(axiom).  [clausify(865)].
2.06/2.90	1296 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_570_min__max_Osup__Inf__absorb) # label(axiom).  [clausify(866)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)).  [resolve(1296,a,1095,a)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)).  [resolve(1296,a,1241,a)].
2.06/2.90	1297 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_max(A)),B) # label(fact_572_Max_OF__eq) # label(axiom).  [clausify(885)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_max(int)),A).  [resolve(1297,a,1095,a)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_max(nat)),A).  [resolve(1297,a,1241,a)].
2.06/2.90	1298 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_788_linorder__less__linear) # label(axiom).  [clausify(891)].
2.06/2.90	1299 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f166(A,C,B)),B)) # label(fact_390_fold1__below__iff) # label(axiom).  [clausify(897)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f166(int,B,A)),A)).  [resolve(1299,a,1095,a)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f166(nat,B,A)),A)).  [resolve(1299,a,1241,a)].
2.06/2.90	1300 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f166(A,C,B)),C)) # label(fact_390_fold1__below__iff) # label(axiom).  [clausify(897)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f166(int,B,A)),B)).  [resolve(1300,a,1095,a)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f166(nat,B,A)),B)).  [resolve(1300,a,1241,a)].
2.06/2.90	1301 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_390_fold1__below__iff) # label(axiom).  [clausify(897)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)).  [resolve(1301,a,1095,a)].
2.06/2.90	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),B)).  [resolve(1301,a,1241,a)].
2.06/2.90	1302 -linorder(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_549_min__max_Ole__iff__sup) # label(axiom).  [clausify(902)].
2.06/2.90	Derived: ti(int,A) != hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1302,a,1095,a)].
2.06/2.90	Derived: ti(nat,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1302,a,1241,a)].
2.73/2.92	1303 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_549_min__max_Ole__iff__sup) # label(axiom).  [clausify(902)].
2.73/2.92	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1303,a,1095,a)].
2.73/2.92	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(1303,a,1241,a)].
2.73/2.92	1304 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_352_min__max_Oinf__left__idem) # label(axiom).  [clausify(909)].
2.73/2.92	1305 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_786_linorder__neqE) # label(axiom).  [clausify(913)].
2.73/2.92	1306 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_558_min__max_Ole__supE) # label(axiom).  [clausify(929)].
2.73/2.92	1307 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_558_min__max_Ole__supE) # label(axiom).  [clausify(929)].
2.73/2.92	1308 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_351_min__max_Oinf_Oleft__commute) # label(axiom).  [clausify(933)].
2.73/2.92	1309 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_553_min__max_Osup__absorb2) # label(axiom).  [clausify(938)].
2.73/2.92	1310 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_555_min__max_Ole__supI) # label(axiom).  [clausify(945)].
2.73/2.92	1311 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))) # label(fact_561_min__max_Odistrib__inf__le) # label(axiom).  [clausify(956)].
2.73/2.92	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)))).  [resolve(1311,a,1095,a)].
2.73/2.92	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)))).  [resolve(1311,a,1241,a)].
2.73/2.92	1312 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_711_less__max__iff__disj) # label(axiom).  [clausify(963)].
2.73/2.92	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(1312,a,1095,a)].
2.73/2.92	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(1312,a,1241,a)].
2.73/2.92	1313 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_711_less__max__iff__disj) # label(axiom).  [clausify(963)].
2.73/2.92	1314 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_711_less__max__iff__disj) # label(axiom).  [clausify(963)].
2.73/2.92	1315 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_577_Max_Oeq__fold_H) # label(axiom).  [clausify(966)].
2.73/2.92	1316 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_540_min__max_Osup_Oleft__commute) # label(axiom).  [clausify(967)].
2.73/2.92	1317 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_476_min__max_OInf__fin_Oeq__fold_H) # label(axiom).  [clausify(969)].
2.73/2.92	1318 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom).  [clausify(972)].
2.73/2.92	1319 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom).  [clausify(972)].
2.73/2.92	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(1319,a,1095,a)].
2.73/2.92	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).  [resolve(1319,a,1241,a)].
2.73/2.92	1320 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom).  [clausify(972)].
2.73/2.92	1321 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_474_min__max_OInf__fin_Oinsert) # label(axiom).  [clausify(973)].
2.73/2.92	1322 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B)) # label(fact_388_min__max_Ofold__inf__insert) # label(axiom).  [clausify(979)].
2.73/2.92	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A)).  [resolve(1322,a,1095,a)].
2.73/2.93	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A)).  [resolve(1322,a,1241,a)].
2.73/2.93	1323 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) # label(fact_532_min__max_Oinf__sup__absorb) # label(axiom).  [clausify(985)].
2.73/2.93	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)).  [resolve(1323,a,1095,a)].
2.73/2.93	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)).  [resolve(1323,a,1241,a)].
2.73/2.93	1324 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_574_Max__insert) # label(axiom).  [clausify(1010)].
2.73/2.93	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)).  [resolve(1324,a,1095,a)].
2.73/2.93	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)).  [resolve(1324,a,1241,a)].
2.73/2.93	1325 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,B,f180(A,C,B))),hAPP(A,A,B,f181(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f180(A,C,B)),f181(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,big_linorder_Max(A),C)) # label(fact_579_Max_Ohom__commute) # label(axiom).  [clausify(1020)].
2.73/2.93	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,A,f180(int,B,A))),hAPP(int,int,A,f181(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f180(int,B,A)),f181(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,big_linorder_Max(int),B)).  [resolve(1325,a,1095,a)].
2.73/2.93	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,A,f180(nat,B,A))),hAPP(nat,nat,A,f181(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f180(nat,B,A)),f181(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B)).  [resolve(1325,a,1241,a)].
2.81/3.01	1326 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),B)) # label(fact_369_min__max_Oinf__le1) # label(axiom).  [clausify(1044)].
2.81/3.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),A)).  [resolve(1326,a,1095,a)].
2.81/3.01	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),A)).  [resolve(1326,a,1241,a)].
2.81/3.01	1327 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),E))) # label(fact_557_min__max_Osup__mono) # label(axiom).  [clausify(1045)].
2.81/3.01	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),D))).  [resolve(1327,a,1095,a)].
2.81/3.01	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),D))).  [resolve(1327,a,1241,a)].
2.81/3.01	1328 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_551_min__max_Ole__supI1) # label(axiom).  [clausify(1061)].
2.81/3.01	1329 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B))) # label(fact_381_Max__ge) # label(axiom).  [clausify(1076)].
2.81/3.01	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A))).  [resolve(1329,a,1095,a)].
2.81/3.01	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A))).  [resolve(1329,a,1241,a)].
2.81/3.01	1330 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f189(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f190(A,B,C,D)),f191(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f189(A,B,C,D)),f190(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f189(A,B,C,D)),f191(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_582_min__max_Odistrib__imp1) # label(axiom).  [clausify(1085)].
2.81/3.01	1331 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.81/3.01	1332 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_726_add__less__imp__less__right) # label(axiom).  [clausify(4)].
2.81/3.01	1333 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_730_add__less__cancel__left) # label(axiom).  [clausify(125)].
2.81/3.03	1334 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_730_add__less__cancel__left) # label(axiom).  [clausify(125)].
2.81/3.03	1335 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_294_add__le__imp__le__left) # label(axiom).  [clausify(141)].
2.81/3.03	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(1331,a,1332,a)].
2.81/3.03	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))).  [resolve(1331,a,1333,a)].
2.81/3.03	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))).  [resolve(1331,a,1334,a)].
2.81/3.03	1336 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_370_min__add__distrib__left) # label(axiom).  [clausify(341)].
2.81/3.03	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(1336,a,1331,a)].
2.81/3.03	1337 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_534_max__add__distrib__left) # label(axiom).  [clausify(504)].
2.81/3.03	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(1337,a,1331,a)].
2.81/3.03	1338 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_725_add__less__imp__less__left) # label(axiom).  [clausify(520)].
2.81/3.03	1339 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.81/3.03	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(1339,a,1332,a)].
2.81/3.03	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))).  [resolve(1339,a,1333,a)].
2.81/3.03	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))).  [resolve(1339,a,1334,a)].
2.81/3.06	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)).  [resolve(1339,a,1335,a)].
2.81/3.06	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)).  [resolve(1339,a,1336,a)].
2.81/3.06	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)).  [resolve(1339,a,1337,a)].
2.81/3.06	1340 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_295_add__le__imp__le__right) # label(axiom).  [clausify(744)].
2.81/3.06	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)).  [resolve(1340,a,1331,a)].
2.81/3.06	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)).  [resolve(1340,a,1339,a)].
2.81/3.06	1341 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_299_add__le__cancel__left) # label(axiom).  [clausify(898)].
2.81/3.06	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))).  [resolve(1341,a,1331,a)].
2.81/3.06	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))).  [resolve(1341,a,1339,a)].
2.81/3.06	1342 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_299_add__le__cancel__left) # label(axiom).  [clausify(898)].
2.81/3.06	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))).  [resolve(1342,a,1331,a)].
2.81/3.06	1343 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_731_add__less__cancel__right) # label(axiom).  [clausify(957)].
2.81/3.06	1344 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_731_add__less__cancel__right) # label(axiom).  [clausify(957)].
2.81/3.06	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(1344,a,1331,a)].
2.89/3.14	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(1344,a,1339,a)].
2.89/3.14	1345 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_300_add__le__cancel__right) # label(axiom).  [clausify(991)].
2.89/3.14	1346 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_300_add__le__cancel__right) # label(axiom).  [clausify(991)].
2.89/3.14	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)).  [resolve(1346,a,1331,a)].
2.89/3.14	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)).  [resolve(1346,a,1339,a)].
2.89/3.14	1347 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom).  [assumption].
2.89/3.14	1348 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_884_power__less__imp__less__exp) # label(axiom).  [clausify(5)].
2.89/3.14	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(1347,a,1348,a)].
2.89/3.14	1349 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom).  [assumption].
2.89/3.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(1349,a,1348,a)].
2.89/3.14	1350 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_883_power__strict__increasing) # label(axiom).  [clausify(50)].
2.89/3.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))).  [resolve(1350,a,1347,a)].
2.89/3.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))).  [resolve(1350,a,1349,a)].
2.89/3.14	1351 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_878_one__le__power) # label(axiom).  [clausify(107)].
2.89/3.14	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))).  [resolve(1351,a,1347,a)].
2.89/3.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))).  [resolve(1351,a,1349,a)].
2.89/3.14	1352 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_846_power__increasing__iff) # label(axiom).  [clausify(114)].
2.89/3.14	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(1352,a,1347,a)].
2.89/3.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(1352,a,1349,a)].
2.89/3.14	1353 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_846_power__increasing__iff) # label(axiom).  [clausify(114)].
2.89/3.14	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(1353,a,1347,a)].
2.89/3.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(1353,a,1349,a)].
2.89/3.14	1354 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_881_power__less__power__Suc) # label(axiom).  [clausify(120)].
2.89/3.14	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))).  [resolve(1354,a,1347,a)].
2.89/3.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))).  [resolve(1354,a,1349,a)].
2.89/3.16	1355 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C != D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_879_power__inject__exp) # label(axiom).  [clausify(250)].
2.89/3.16	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B != C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C).  [resolve(1355,a,1347,a)].
2.89/3.16	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B != C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C).  [resolve(1355,a,1349,a)].
2.89/3.16	1356 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C = D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_879_power__inject__exp) # label(axiom).  [clausify(250)].
2.89/3.16	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B = C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C).  [resolve(1356,a,1347,a)].
2.89/3.16	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B = C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C).  [resolve(1356,a,1349,a)].
2.89/3.16	1357 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_973_of__nat__0__less__iff) # label(axiom).  [clausify(319)].
2.89/3.16	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))).  [resolve(1357,a,1349,a)].
2.89/3.16	1358 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_973_of__nat__0__less__iff) # label(axiom).  [clausify(319)].
2.89/3.16	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))).  [resolve(1358,a,1349,a)].
2.89/3.16	1359 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_823_less__1__mult) # label(axiom).  [clausify(321)].
2.89/3.16	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(1359,a,1347,a)].
2.89/3.16	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))).  [resolve(1359,a,1349,a)].
2.89/3.16	1360 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_885_power__strict__increasing__iff) # label(axiom).  [clausify(453)].
2.89/3.16	1361 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_885_power__strict__increasing__iff) # label(axiom).  [clausify(453)].
2.89/3.17	1362 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_882_power__gt1__lemma) # label(axiom).  [clausify(487)].
2.89/3.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))).  [resolve(1362,a,1347,a)].
2.89/3.17	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))).  [resolve(1362,a,1349,a)].
2.89/3.17	1363 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_822_less__add__one) # label(axiom).  [clausify(502)].
2.89/3.17	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int)))).  [resolve(1363,a,1347,a)].
2.89/3.17	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))).  [resolve(1363,a,1349,a)].
2.89/3.17	1364 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_819_of__nat__less__imp__less) # label(axiom).  [clausify(519)].
2.89/3.17	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(1364,a,1349,a)].
2.89/3.17	1365 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_817_of__nat__less__iff) # label(axiom).  [clausify(649)].
2.89/3.17	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))).  [resolve(1365,a,1349,a)].
2.89/3.17	1366 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_817_of__nat__less__iff) # label(axiom).  [clausify(649)].
2.89/3.17	1367 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_964_zero__less__power) # label(axiom).  [clausify(671)].
2.89/3.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))).  [resolve(1367,a,1347,a)].
2.89/3.17	1368 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_977_pos__add__strict) # label(axiom).  [clausify(678)].
2.89/3.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))).  [resolve(1368,a,1347,a)].
3.01/3.19	1369 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_659_of__nat__le__iff) # label(axiom).  [clausify(808)].
3.01/3.19	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))).  [resolve(1369,a,1349,a)].
3.01/3.19	1370 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_659_of__nat__le__iff) # label(axiom).  [clausify(808)].
3.01/3.19	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))).  [resolve(1370,a,1349,a)].
3.01/3.19	1371 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_886_power__increasing) # label(axiom).  [clausify(826)].
3.01/3.19	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))).  [resolve(1371,a,1347,a)].
3.01/3.19	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))).  [resolve(1371,a,1349,a)].
3.01/3.19	1372 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_967_power__strict__mono) # label(axiom).  [clausify(919)].
3.01/3.19	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C))).  [resolve(1372,a,1347,a)].
3.01/3.19	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))).  [resolve(1372,a,1349,a)].
3.01/3.19	1373 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_818_less__imp__of__nat__less) # label(axiom).  [clausify(951)].
3.01/3.19	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))).  [resolve(1373,a,1347,a)].
3.03/3.28	1374 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | ti(A,B) = ti(A,D) # label(fact_966_power__eq__imp__eq__base) # label(axiom).  [clausify(958)].
3.03/3.28	Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(int,A) = ti(int,C).  [resolve(1374,a,1347,a)].
3.03/3.28	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(nat,A) = ti(nat,C).  [resolve(1374,a,1349,a)].
3.03/3.28	1375 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_939_power__less__imp__less__base) # label(axiom).  [clausify(994)].
3.03/3.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(1375,a,1347,a)].
3.03/3.28	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(1375,a,1349,a)].
3.03/3.28	1376 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_845_power__le__imp__le__exp) # label(axiom).  [clausify(1026)].
3.03/3.28	1377 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))) # label(fact_942_zero__less__two) # label(axiom).  [clausify(1083)].
3.03/3.28	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)))).  [resolve(1377,a,1347,a)].
3.03/3.28	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)))).  [resolve(1377,a,1349,a)].
3.03/3.28	1378 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom).  [assumption].
3.03/3.28	1379 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_487_equation__minus__iff) # label(axiom).  [clausify(12)].
3.03/3.28	1380 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_487_equation__minus__iff) # label(axiom).  [clausify(12)].
3.03/3.28	1381 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_488_minus__equation__iff) # label(axiom).  [clausify(14)].
3.11/3.33	1382 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_488_minus__equation__iff) # label(axiom).  [clausify(14)].
3.11/3.33	1383 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C) # label(fact_221_diff__add__cancel) # label(axiom).  [clausify(102)].
3.11/3.33	1384 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) # label(fact_222_add__diff__cancel) # label(axiom).  [clausify(130)].
3.11/3.33	1385 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_503_add__minus__cancel) # label(axiom).  [clausify(186)].
3.11/3.33	Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A).  [resolve(1378,a,1379,a)].
3.11/3.33	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),B).  [resolve(1378,a,1383,a)].
3.11/3.33	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B).  [resolve(1378,a,1384,a)].
3.11/3.33	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),A)).  [resolve(1378,a,1385,a)].
3.11/3.33	1386 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_511_diff__minus__eq__add) # label(axiom).  [clausify(431)].
3.11/3.33	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),hAPP(int,int,uminus_uminus(int),B)).  [resolve(1386,a,1378,a)].
3.11/3.33	1387 -group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_502_minus__add) # label(axiom).  [clausify(481)].
3.11/3.33	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)).  [resolve(1387,a,1378,a)].
3.11/3.33	1388 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)) # label(fact_504_minus__add__cancel) # label(axiom).  [clausify(628)].
3.11/3.33	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)).  [resolve(1388,a,1378,a)].
3.11/3.33	1389 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,B) = ti(A,C) # label(fact_489_neg__equal__iff__equal) # label(axiom).  [clausify(629)].
3.11/3.33	Derived: hAPP(int,int,uminus_uminus(int),A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B).  [resolve(1389,a,1378,a)].
3.11/3.33	1390 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,B) != ti(A,C) # label(fact_489_neg__equal__iff__equal) # label(axiom).  [clausify(629)].
3.11/3.33	Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) != ti(int,B).  [resolve(1390,a,1378,a)].
3.11/3.33	1391 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_486_minus__minus) # label(axiom).  [clausify(654)].
3.11/3.33	Derived: ti(int,A) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),A)).  [resolve(1391,a,1378,a)].
3.11/3.33	1392 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) # label(fact_514_diff__def) # label(axiom).  [clausify(1041)].
3.11/3.33	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B).  [resolve(1392,a,1378,a)].
3.19/3.40	1393 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_836_less__add__iff1) # label(axiom).  [clausify(242)].
3.19/3.40	1394 ordered_ring(int) # label(arity_Int_Oint___Rings_Oordered__ring) # label(axiom).  [assumption].
3.19/3.40	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))).  [resolve(1393,a,1394,a)].
3.19/3.40	1395 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_836_less__add__iff1) # label(axiom).  [clausify(242)].
3.19/3.40	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))).  [resolve(1395,a,1394,a)].
3.19/3.40	1396 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_325_le__add__iff2) # label(axiom).  [clausify(345)].
3.19/3.40	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,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),D),A)),B)),E))).  [resolve(1396,a,1394,a)].
3.19/3.40	1397 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_325_le__add__iff2) # label(axiom).  [clausify(345)].
3.19/3.40	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,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),D),A)),B)),E))).  [resolve(1397,a,1394,a)].
3.19/3.44	1398 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_837_less__add__iff2) # label(axiom).  [clausify(415)].
3.19/3.44	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,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),D),A)),B)),E))).  [resolve(1398,a,1394,a)].
3.19/3.44	1399 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_837_less__add__iff2) # label(axiom).  [clausify(415)].
3.19/3.44	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,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),D),A)),B)),E))).  [resolve(1399,a,1394,a)].
3.19/3.44	1400 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_324_le__add__iff1) # label(axiom).  [clausify(968)].
3.19/3.44	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))).  [resolve(1400,a,1394,a)].
3.19/3.44	1401 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_324_le__add__iff1) # label(axiom).  [clausify(968)].
3.19/3.44	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))).  [resolve(1401,a,1394,a)].
3.43/3.64	1402 -power(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom).  [clausify(685)].
3.43/3.64	1403 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom).  [assumption].
3.43/3.64	Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)).  [resolve(1402,a,1403,a)].
3.43/3.64	1404 -power(A) | power_power(A) = hAPP(fun(A,fun(A,A)),fun(A,fun(nat,A)),hAPP(A,fun(fun(A,fun(A,A)),fun(A,fun(nat,A))),power_1(A),one_one(A)),times_times(A)) # label(fact_916_power__power__power) # label(axiom).  [clausify(947)].
3.43/3.64	Derived: power_power(int) = hAPP(fun(int,fun(int,int)),fun(int,fun(nat,int)),hAPP(int,fun(fun(int,fun(int,int)),fun(int,fun(nat,int))),power_1(int),one_one(int)),times_times(int)).  [resolve(1404,a,1403,a)].
3.43/3.64	1405 power(nat) # label(arity_Nat_Onat___Power_Opower) # label(axiom).  [assumption].
3.43/3.64	Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)).  [resolve(1405,a,1402,a)].
3.43/3.64	Derived: power_power(nat) = hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),hAPP(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat))),power_1(nat),one_one(nat)),times_times(nat)).  [resolve(1405,a,1404,a)].
3.43/3.64	1406 -power(A) | ti(fun(A,fun(nat,A)),power_power(A)) = power_power(A) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom).  [clausify(1053)].
3.43/3.64	Derived: ti(fun(int,fun(nat,int)),power_power(int)) = power_power(int).  [resolve(1406,a,1403,a)].
3.43/3.64	Derived: ti(fun(nat,fun(nat,nat)),power_power(nat)) = power_power(nat).  [resolve(1406,a,1405,a)].
3.43/3.64	1407 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
3.43/3.64	1408 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_728_add__strict__left__mono) # label(axiom).  [clausify(25)].
3.43/3.64	1409 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_821_add__le__less__mono) # label(axiom).  [clausify(108)].
3.43/3.64	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))).  [resolve(1407,a,1409,a)].
3.43/3.64	1410 -ordere223160158up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | ti(fun(B,bool),C) = bot_bot(fun(B,bool)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f108(B,A,D,E,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_847_setsum__strict__mono) # label(axiom).  [clausify(478)].
3.43/3.64	Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f108(A,int,C,D,B)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))).  [resolve(1410,a,1407,a)].
3.43/3.67	1411 -ordere223160158up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | ti(fun(B,bool),C) = bot_bot(fun(B,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,D,f108(B,A,D,E,C))),hAPP(B,A,E,f108(B,A,D,E,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_847_setsum__strict__mono) # label(axiom).  [clausify(478)].
3.43/3.67	Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,C,f108(A,int,C,D,B))),hAPP(A,int,D,f108(A,int,C,D,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))).  [resolve(1411,a,1407,a)].
3.43/3.67	1412 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_820_add__less__le__mono) # label(axiom).  [clausify(532)].
3.43/3.67	1413 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
3.43/3.67	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))).  [resolve(1413,a,1409,a)].
3.43/3.67	Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f108(A,nat,C,D,B)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))).  [resolve(1413,a,1410,a)].
3.43/3.67	Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(A,nat,C,f108(A,nat,C,D,B))),hAPP(A,nat,D,f108(A,nat,C,D,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))).  [resolve(1413,a,1411,a)].
3.43/3.67	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))).  [resolve(1413,a,1412,a)].
3.43/3.67	1414 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_729_add__strict__right__mono) # label(axiom).  [clausify(869)].
3.43/3.67	1415 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_727_add__strict__mono) # label(axiom).  [clausify(903)].
3.43/3.67	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))).  [resolve(1415,a,1407,a)].
3.58/3.76	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))).  [resolve(1415,a,1413,a)].
3.58/3.76	1416 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
3.58/3.76	1417 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_984_mult__pos__pos) # label(axiom).  [clausify(27)].
3.58/3.76	1418 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_988_zero__less__mult__pos2) # label(axiom).  [clausify(146)].
3.58/3.76	1419 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_993_mult__strict__left__mono) # label(axiom).  [clausify(147)].
3.58/3.76	1420 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_987_zero__less__mult__pos) # label(axiom).  [clausify(368)].
3.58/3.76	1421 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_985_mult__pos__neg) # label(axiom).  [clausify(458)].
3.58/3.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(1416,a,1417,a)].
3.58/3.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(1416,a,1418,a)].
3.58/3.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)).  [resolve(1416,a,1420,a)].
3.58/3.76	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))).  [resolve(1416,a,1421,a)].
3.58/3.76	1422 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
3.58/3.76	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))).  [resolve(1422,a,1417,a)].
3.73/3.98	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(1422,a,1418,a)].
3.73/3.98	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(1422,a,1419,a)].
3.73/3.98	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)).  [resolve(1422,a,1420,a)].
3.73/3.98	1423 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_986_mult__pos__neg2) # label(axiom).  [clausify(733)].
3.73/3.98	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),zero_zero(int))).  [resolve(1423,a,1416,a)].
3.73/3.98	1424 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_990_mult__neg__pos) # label(axiom).  [clausify(893)].
3.73/3.98	1425 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_992_mult__strict__right__mono) # label(axiom).  [clausify(1056)].
3.73/3.98	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))).  [resolve(1425,a,1416,a)].
3.73/3.98	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))).  [resolve(1425,a,1422,a)].
3.73/3.98	1426 ring(int) # label(arity_Int_Oint___Rings_Oring) # label(axiom).  [assumption].
3.73/3.98	1427 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_507_minus__mult__commute) # label(axiom).  [clausify(31)].
3.73/3.98	1428 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) # label(fact_508_minus__mult__minus) # label(axiom).  [clausify(128)].
3.73/3.98	1429 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) # label(fact_220_eq__add__iff1) # label(axiom).  [clausify(179)].
3.80/4.03	1430 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) # label(fact_220_eq__add__iff1) # label(axiom).  [clausify(179)].
3.80/4.03	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,uminus_uminus(int),B)).  [resolve(1426,a,1427,a)].
3.80/4.03	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B).  [resolve(1426,a,1428,a)].
3.80/4.03	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(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),D),A)),B)),E).  [resolve(1426,a,1429,a)].
3.80/4.03	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(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),D),A)),B)),E).  [resolve(1426,a,1430,a)].
3.80/4.03	1431 -ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_506_minus__mult__left) # label(axiom).  [clausify(413)].
3.80/4.03	1432 -ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_505_minus__mult__right) # label(axiom).  [clausify(684)].
3.80/4.03	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,uminus_uminus(int),B)).  [resolve(1432,a,1426,a)].
3.80/4.03	1433 -ring(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool))))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(B,A,E,D)) # label(fact_174_setsum__diff1__ring) # label(axiom).  [clausify(1025)].
3.80/4.03	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(A,int,D,C)).  [resolve(1433,a,1426,a)].
3.80/4.03	1434 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,F) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D) # label(fact_219_eq__add__iff2) # label(axiom).  [clausify(1046)].
3.90/4.10	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,E) = 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),D)),B)),C).  [resolve(1434,a,1426,a)].
3.90/4.10	1435 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,F) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D) # label(fact_219_eq__add__iff2) # label(axiom).  [clausify(1046)].
3.90/4.10	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,E) != 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),D)),B)),C).  [resolve(1435,a,1426,a)].
3.90/4.10	1436 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
3.90/4.10	1437 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom).  [clausify(46)].
3.90/4.10	1438 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom).  [clausify(57)].
3.90/4.10	1439 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_724_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom).  [clausify(106)].
3.90/4.10	Derived: 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))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A).  [resolve(1436,a,1437,a)].
3.90/4.10	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)).  [resolve(1436,a,1438,a)].
3.90/4.10	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(1436,a,1439,a)].
3.90/4.10	1440 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom).  [clausify(158)].
3.90/4.10	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)).  [resolve(1440,a,1436,a)].
3.90/4.10	1441 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom).  [clausify(173)].
3.90/4.11	1442 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom).  [clausify(207)].
3.90/4.11	1443 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_251_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom).  [clausify(236)].
3.90/4.11	1444 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom).  [clausify(257)].
3.90/4.11	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)).  [resolve(1444,a,1436,a)].
3.90/4.11	1445 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_732_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom).  [clausify(388)].
3.90/4.11	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B).  [resolve(1445,a,1436,a)].
3.90/4.11	1446 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom).  [clausify(389)].
3.90/4.11	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A).  [resolve(1446,a,1436,a)].
3.90/4.11	1447 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom).  [clausify(397)].
3.90/4.11	1448 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) # label(fact_816_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom).  [clausify(455)].
3.90/4.11	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(1448,a,1436,a)].
3.90/4.11	1449 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom).  [clausify(527)].
3.90/4.11	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A).  [resolve(1449,a,1436,a)].
3.93/4.13	1450 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),semiring_1_of_nat(A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),B))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,semiring_1_of_nat(A),B)),one_one(A))) # label(fact_677_gauss__sum) # label(axiom).  [clausify(573)].
3.93/4.13	Derived: 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))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),semiring_1_of_nat(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),one_one(nat))).  [resolve(1450,a,1436,a)].
3.93/4.13	1451 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom).  [clausify(587)].
3.93/4.13	1452 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom).  [clausify(593)].
3.93/4.13	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B).  [resolve(1452,a,1436,a)].
3.93/4.13	1453 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom).  [clausify(603)].
3.93/4.13	1454 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)) # label(fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom).  [clausify(619)].
3.93/4.13	1455 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom).  [clausify(676)].
3.93/4.13	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(1455,a,1436,a)].
3.93/4.13	1456 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom).  [clausify(709)].
3.93/4.13	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)).  [resolve(1456,a,1436,a)].
3.93/4.13	1457 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom).  [clausify(758)].
3.94/4.14	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)).  [resolve(1457,a,1436,a)].
3.94/4.14	1458 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom).  [clausify(881)].
3.94/4.14	1459 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom).  [clausify(900)].
3.94/4.14	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)).  [resolve(1459,a,1436,a)].
3.94/4.14	1460 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
3.94/4.14	Derived: 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))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A).  [resolve(1460,a,1437,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)).  [resolve(1460,a,1438,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)).  [resolve(1460,a,1440,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)).  [resolve(1460,a,1441,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A).  [resolve(1460,a,1442,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)).  [resolve(1460,a,1444,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B).  [resolve(1460,a,1445,a)].
3.94/4.14	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A).  [resolve(1460,a,1446,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)).  [resolve(1460,a,1448,a)].
3.94/4.14	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A).  [resolve(1460,a,1449,a)].
3.94/4.14	Derived: 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))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),A)),one_one(int))).  [resolve(1460,a,1450,a)].
3.94/4.15	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B).  [resolve(1460,a,1452,a)].
3.94/4.15	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)).  [resolve(1460,a,1455,a)].
3.94/4.15	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)).  [resolve(1460,a,1456,a)].
3.94/4.15	Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)).  [resolve(1460,a,1457,a)].
3.94/4.15	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)).  [resolve(1460,a,1459,a)].
3.94/4.15	1461 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom).  [clausify(935)].
3.94/4.15	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B).  [resolve(1461,a,1436,a)].
3.94/4.15	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B).  [resolve(1461,a,1460,a)].
3.94/4.15	1462 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),plus_plus(A),B)),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),D))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),one_one(nat)))),C)))) # label(fact_656_arith__series__general) # label(axiom).  [clausify(950)].
3.94/4.15	Derived: 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))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),plus_plus(nat),A)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),semiring_1_of_nat(nat))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))).  [resolve(1462,a,1436,a)].
4.02/4.23	Derived: 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))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),hAPP(int,fun(int,int),plus_plus(int),A)),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))).  [resolve(1462,a,1460,a)].
4.02/4.23	1463 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom).  [clausify(1027)].
4.02/4.23	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B).  [resolve(1463,a,1436,a)].
4.02/4.23	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B).  [resolve(1463,a,1460,a)].
4.02/4.23	1464 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom).  [clausify(1054)].
4.02/4.23	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)).  [resolve(1464,a,1436,a)].
4.02/4.23	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)).  [resolve(1464,a,1460,a)].
4.02/4.23	1465 -comm_semiring_1(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom).  [clausify(1060)].
4.02/4.23	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)).  [resolve(1465,a,1436,a)].
4.02/4.23	Derived: ti(int,A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)).  [resolve(1465,a,1460,a)].
4.02/4.23	1466 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom).  [assumption].
4.02/4.23	1467 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool)))))) # label(fact_176_setprod_Oremove) # label(axiom).  [clausify(53)].
4.02/4.23	1468 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_643_setprod_Oinfinite) # label(axiom).  [clausify(59)].
4.02/4.23	1469 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_198_setprod_Oinsert) # label(axiom).  [clausify(60)].
4.02/4.23	1470 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)) # label(fact_186_setprod__timesf) # label(axiom).  [clausify(71)].
4.02/4.23	1471 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f34(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_653_setprod__mono__one__left) # label(axiom).  [clausify(105)].
4.02/4.23	1472 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | one_one(A) != hAPP(B,A,E,f34(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_653_setprod__mono__one__left) # label(axiom).  [clausify(105)].
4.02/4.23	1473 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f39(B,A,E,F,C,D)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),D) # label(fact_253_setprod_OF__cong) # label(axiom).  [clausify(127)].
4.02/4.23	1474 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f39(B,A,E,F,C,D)) != hAPP(B,A,F,f39(B,A,E,F,C,D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),D) # label(fact_253_setprod_OF__cong) # label(axiom).  [clausify(127)].
4.02/4.23	1475 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_644_setprod__delta_H) # label(axiom).  [clausify(132)].
4.02/4.23	1476 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) # label(fact_644_setprod__delta_H) # label(axiom).  [clausify(132)].
4.02/4.23	1477 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f49(B,A,E,F,C,D)),D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) # label(fact_252_setprod__cong) # label(axiom).  [clausify(165)].
4.02/4.23	1478 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f49(B,A,F,E,C,D)) != hAPP(B,A,F,f49(B,A,F,E,C,D)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C) # label(fact_252_setprod__cong) # label(axiom).  [clausify(165)].
4.02/4.23	1479 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f51(B,A,C,D)),D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_655_setprod__1_H) # label(axiom).  [clausify(176)].
4.02/4.23	1480 -comm_monoid_mult(A) | one_one(A) != hAPP(B,A,C,f51(B,A,C,D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_655_setprod__1_H) # label(axiom).  [clausify(176)].
4.02/4.23	1481 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),bot_bot(fun(B,bool))) # label(fact_641_setprod__empty) # label(axiom).  [clausify(178)].
4.02/4.23	1482 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_627_mult_Ocomm__neutral) # label(axiom).  [clausify(200)].
4.02/4.23	1483 -comm_monoid_mult(A) | big_co302546470etprod(B,A) = ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co302546470etprod(B,A)) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom).  [clausify(261)].
4.02/4.23	1484 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f76(B,A,D,C)),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_654_setprod_Oneutral) # label(axiom).  [clausify(314)].
4.02/4.23	1485 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) != hAPP(B,A,D,f76(B,A,D,C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_654_setprod_Oneutral) # label(axiom).  [clausify(314)].
4.02/4.23	1486 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_197_setprod__insert) # label(axiom).  [clausify(325)].
4.02/4.23	1487 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f85(C,A,D,E,F,B)),f87(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f88(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom).  [clausify(349)].
4.02/4.23	1488 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f85(C,A,D,E,F,B)),f87(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f88(C,A,D,E,F,B))),hAPP(C,A,E,f88(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom).  [clausify(349)].
4.02/4.23	1489 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f84(C,A,D,E,F,B)),f86(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f88(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom).  [clausify(349)].
4.02/4.23	1490 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f84(C,A,D,E,F,B)),f86(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f88(C,A,D,E,F,B))),hAPP(C,A,E,f88(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom).  [clausify(349)].
4.02/4.23	1491 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f84(C,A,D,E,F,B)),f85(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f86(C,A,D,E,F,B)),f87(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f88(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom).  [clausify(349)].
4.02/4.23	1492 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f84(C,A,D,E,F,B)),f85(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f86(C,A,D,E,F,B)),f87(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f88(C,A,D,E,F,B))),hAPP(C,A,E,f88(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom).  [clausify(349)].
4.02/4.23	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))).  [resolve(1466,a,1467,a)].
4.02/4.24	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B).  [resolve(1466,a,1468,a)].
4.02/4.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B)).  [resolve(1466,a,1469,a)].
4.02/4.24	Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D)).  [resolve(1466,a,1470,a)].
4.02/4.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f34(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C).  [resolve(1466,a,1471,a)].
4.02/4.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f34(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C).  [resolve(1466,a,1472,a)].
4.02/4.24	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f39(A,nat,D,E,B,C)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),C).  [resolve(1466,a,1473,a)].
4.02/4.24	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f39(A,nat,D,E,B,C)) != hAPP(A,nat,E,f39(A,nat,D,E,B,C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),C).  [resolve(1466,a,1474,a)].
4.02/4.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C).  [resolve(1466,a,1475,a)].
4.02/4.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B).  [resolve(1466,a,1476,a)].
4.02/4.24	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f49(A,nat,D,E,B,C)),C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B).  [resolve(1466,a,1477,a)].
4.02/4.24	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f49(A,nat,E,D,B,C)) != hAPP(A,nat,E,f49(A,nat,E,D,B,C)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B).  [resolve(1466,a,1478,a)].
4.02/4.24	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f51(A,nat,B,C)),C)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C).  [resolve(1466,a,1479,a)].
4.02/4.24	Derived: one_one(nat) != hAPP(A,nat,B,f51(A,nat,B,C)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C).  [resolve(1466,a,1480,a)].
4.02/4.24	Derived: one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),bot_bot(fun(A,bool))).  [resolve(1466,a,1481,a)].
4.02/4.24	Derived: big_co302546470etprod(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co302546470etprod(A,nat)).  [resolve(1466,a,1483,a)].
4.02/4.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f76(A,nat,C,B)),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B).  [resolve(1466,a,1484,a)].
4.02/4.24	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) != hAPP(A,nat,C,f76(A,nat,C,B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B).  [resolve(1466,a,1485,a)].
4.02/4.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f85(B,nat,C,D,E,A)),f87(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f88(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))).  [resolve(1466,a,1487,a)].
4.02/4.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f85(B,nat,C,D,E,A)),f87(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f88(B,nat,C,D,E,A))),hAPP(B,nat,D,f88(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))).  [resolve(1466,a,1488,a)].
4.02/4.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f84(B,nat,C,D,E,A)),f86(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f88(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))).  [resolve(1466,a,1489,a)].
4.02/4.25	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f84(B,nat,C,D,E,A)),f86(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f88(B,nat,C,D,E,A))),hAPP(B,nat,D,f88(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))).  [resolve(1466,a,1490,a)].
4.02/4.25	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f84(B,nat,C,D,E,A)),f85(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f86(B,nat,C,D,E,A)),f87(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f88(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))).  [resolve(1466,a,1491,a)].
4.02/4.25	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f84(B,nat,C,D,E,A)),f85(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f86(B,nat,C,D,E,A)),f87(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f88(B,nat,C,D,E,A))),hAPP(B,nat,D,f88(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))).  [resolve(1466,a,1492,a)].
4.02/4.25	1493 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),D)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_838_setprod__constant) # label(axiom).  [clausify(450)].
4.02/4.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(fun(A,bool),nat,finite_card(A),B)).  [resolve(1493,a,1466,a)].
4.02/4.25	1494 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_872_power__mult__distrib) # label(axiom).  [clausify(475)].
4.02/4.25	1495 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,D,E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),bot_bot(fun(B,bool)))))) # label(fact_175_setprod_Oinsert__remove) # label(axiom).  [clausify(576)].
4.02/4.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,C,D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))).  [resolve(1495,a,1466,a)].
4.02/4.25	1496 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_678_setprod__gen__delta) # label(axiom).  [clausify(585)].
4.02/4.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(fun(A,bool),nat,finite_card(A),B)).  [resolve(1496,a,1466,a)].
4.02/4.25	1497 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(B,bool),nat,finite_card(B),C)),one_one(nat)))) # label(fact_678_setprod__gen__delta) # label(axiom).  [clausify(585)].
4.02/4.25	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))).  [resolve(1497,a,1466,a)].
4.02/4.26	1498 -semiring_1(A) | -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,nat),fun(B,A),hAPP(fun(nat,A),fun(fun(B,nat),fun(B,A)),combb(nat,A,B),semiring_1_of_nat(A)),C)),D) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),D)) # label(fact_666_of__nat__setprod) # label(axiom).  [clausify(786)].
4.02/4.26	Derived: -semiring_1(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),semiring_1_of_nat(nat)),B)),C) = hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)).  [resolve(1498,b,1466,a)].
4.02/4.26	1499 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),one_one(A))),C) # label(fact_622_setprod__1) # label(axiom).  [clausify(790)].
4.02/4.26	Derived: one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),one_one(nat))),B).  [resolve(1499,a,1466,a)].
4.02/4.26	1500 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_194_setprod_Odistrib) # label(axiom).  [clausify(823)].
4.02/4.26	1501 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_645_setprod__delta) # label(axiom).  [clausify(843)].
4.02/4.26	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C).  [resolve(1501,a,1466,a)].
4.02/4.27	1502 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) # label(fact_645_setprod__delta) # label(axiom).  [clausify(843)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B).  [resolve(1502,a,1466,a)].
4.09/4.27	1503 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f167(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_209_setprod_Ocong) # label(axiom).  [clausify(901)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f167(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B).  [resolve(1503,a,1466,a)].
4.09/4.27	1504 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f167(B,A,E,D,C)) != hAPP(B,A,E,f167(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) # label(fact_209_setprod_Ocong) # label(axiom).  [clausify(901)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f167(A,nat,D,C,B)) != hAPP(A,nat,D,f167(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B).  [resolve(1504,a,1466,a)].
4.09/4.27	1505 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom).  [assumption].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))).  [resolve(1505,a,1467,a)].
4.09/4.27	Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B).  [resolve(1505,a,1468,a)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B)).  [resolve(1505,a,1469,a)].
4.09/4.27	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)).  [resolve(1505,a,1470,a)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f34(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C).  [resolve(1505,a,1471,a)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(int) != hAPP(A,int,D,f34(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C).  [resolve(1505,a,1472,a)].
4.09/4.27	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f39(A,int,D,E,B,C)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),C).  [resolve(1505,a,1473,a)].
4.09/4.27	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f39(A,int,D,E,B,C)) != hAPP(A,int,E,f39(A,int,D,E,B,C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),C).  [resolve(1505,a,1474,a)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B) = hAPP(A,int,D,C).  [resolve(1505,a,1475,a)].
4.09/4.27	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B).  [resolve(1505,a,1476,a)].
4.09/4.27	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f49(A,int,D,E,B,C)),C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B).  [resolve(1505,a,1477,a)].
4.09/4.28	Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f49(A,int,E,D,B,C)) != hAPP(A,int,E,f49(A,int,E,D,B,C)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B).  [resolve(1505,a,1478,a)].
4.09/4.28	Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f51(A,int,B,C)),C)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C).  [resolve(1505,a,1479,a)].
4.09/4.28	Derived: one_one(int) != hAPP(A,int,B,f51(A,int,B,C)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C).  [resolve(1505,a,1480,a)].
4.09/4.28	Derived: one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),bot_bot(fun(A,bool))).  [resolve(1505,a,1481,a)].
4.09/4.28	Derived: big_co302546470etprod(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co302546470etprod(A,int)).  [resolve(1505,a,1483,a)].
4.09/4.28	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f76(A,int,C,B)),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B).  [resolve(1505,a,1484,a)].
4.09/4.28	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) != hAPP(A,int,C,f76(A,int,C,B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B).  [resolve(1505,a,1485,a)].
4.09/4.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f85(B,int,C,D,E,A)),f87(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f88(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))).  [resolve(1505,a,1487,a)].
4.09/4.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f85(B,int,C,D,E,A)),f87(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f88(B,int,C,D,E,A))),hAPP(B,int,D,f88(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))).  [resolve(1505,a,1488,a)].
4.09/4.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f84(B,int,C,D,E,A)),f86(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f88(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))).  [resolve(1505,a,1489,a)].
4.09/4.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f84(B,int,C,D,E,A)),f86(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f88(B,int,C,D,E,A))),hAPP(B,int,D,f88(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))).  [resolve(1505,a,1490,a)].
4.09/4.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f84(B,int,C,D,E,A)),f85(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f86(B,int,C,D,E,A)),f87(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f88(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))).  [resolve(1505,a,1491,a)].
4.09/4.28	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f84(B,int,C,D,E,A)),f85(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f86(B,int,C,D,E,A)),f87(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f88(B,int,C,D,E,A))),hAPP(B,int,D,f88(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))).  [resolve(1505,a,1492,a)].
4.09/4.28	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),C)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(fun(A,bool),nat,finite_card(A),B)).  [resolve(1505,a,1493,a)].
4.09/4.28	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,C,D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))).  [resolve(1505,a,1495,a)].
4.09/4.28	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(fun(A,bool),nat,finite_card(A),B)).  [resolve(1505,a,1496,a)].
4.09/4.28	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))).  [resolve(1505,a,1497,a)].
4.09/4.29	Derived: one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),one_one(int))),B).  [resolve(1505,a,1499,a)].
4.09/4.29	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B) = hAPP(A,int,D,C).  [resolve(1505,a,1501,a)].
4.09/4.29	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B).  [resolve(1505,a,1502,a)].
4.09/4.29	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f167(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B).  [resolve(1505,a,1503,a)].
4.09/4.29	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f167(A,int,D,C,B)) != hAPP(A,int,D,f167(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B).  [resolve(1505,a,1504,a)].
4.09/4.29	1506 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_642_setprod__infinite) # label(axiom).  [clausify(999)].
4.09/4.29	1507 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),bot_bot(fun(B,bool))) # label(fact_640_setprod_Oempty) # label(axiom).  [clausify(1013)].
4.09/4.29	1508 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_630_mult__1) # label(axiom).  [clausify(1018)].
4.09/4.29	1509 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f182(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_652_setprod__mono__one__right) # label(axiom).  [clausify(1031)].
4.09/4.29	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f182(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C).  [resolve(1509,a,1466,a)].
4.21/4.41	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f182(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C).  [resolve(1509,a,1505,a)].
4.21/4.41	1510 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | one_one(A) != hAPP(B,A,E,f182(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_652_setprod__mono__one__right) # label(axiom).  [clausify(1031)].
4.21/4.41	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f182(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C).  [resolve(1510,a,1466,a)].
4.21/4.41	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(int) != hAPP(A,int,D,f182(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C).  [resolve(1510,a,1505,a)].
4.21/4.41	1511 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom).  [assumption].
4.21/4.41	1512 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_873_power__commutes) # label(axiom).  [clausify(58)].
4.21/4.41	1513 -monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_629_mult__1__right) # label(axiom).  [clausify(90)].
4.21/4.41	1514 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom).  [assumption].
4.21/4.41	1515 -monoid_mult(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),one_one(A)),B) # label(fact_874_power__one) # label(axiom).  [clausify(661)].
4.21/4.41	Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),one_one(int)),A).  [resolve(1515,a,1511,a)].
4.21/4.41	Derived: one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),one_one(nat)),A).  [resolve(1515,a,1514,a)].
4.21/4.41	1516 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) # label(fact_880_power__add) # label(axiom).  [clausify(766)].
4.21/4.41	1517 -monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_632_mult__1__left) # label(axiom).  [clausify(793)].
4.21/4.41	1518 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_876_power__mult) # label(axiom).  [clausify(800)].
4.21/4.41	1519 -monoid_mult(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_877_power__one__right) # label(axiom).  [clausify(1068)].
4.41/4.62	1520 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom).  [assumption].
4.41/4.62	1521 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B)) # label(fact_940_mult__right__le__one__le) # label(axiom).  [clausify(66)].
4.41/4.62	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A)).  [resolve(1520,a,1521,a)].
4.41/4.62	1522 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_979_even__less__0__iff) # label(axiom).  [clausify(789)].
4.41/4.62	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(1522,a,1520,a)].
4.41/4.62	1523 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_979_even__less__0__iff) # label(axiom).  [clausify(789)].
4.41/4.62	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))).  [resolve(1523,a,1520,a)].
4.41/4.62	1524 -linordered_idom(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_769_linorder__neqE__linordered__idom) # label(axiom).  [clausify(807)].
4.41/4.62	1525 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B)) # label(fact_941_mult__left__le__one__le) # label(axiom).  [clausify(895)].
4.41/4.62	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A)).  [resolve(1525,a,1520,a)].
4.41/4.62	1526 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom).  [assumption].
4.41/4.62	1527 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_495_minus__le__iff) # label(axiom).  [clausify(72)].
4.41/4.62	1528 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_495_minus__le__iff) # label(axiom).  [clausify(72)].
4.41/4.62	1529 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_304_diff__eq__diff__less__eq) # label(axiom).  [clausify(111)].
4.41/4.62	1530 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_304_diff__eq__diff__less__eq) # label(axiom).  [clausify(111)].
4.41/4.62	1531 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_494_neg__le__iff__le) # label(axiom).  [clausify(118)].
4.41/4.62	1532 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_494_neg__le__iff__le) # label(axiom).  [clausify(118)].
4.41/4.62	1533 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_768_diff__eq__diff__less) # label(axiom).  [clausify(313)].
4.41/4.62	1534 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_768_diff__eq__diff__less) # label(axiom).  [clausify(313)].
4.41/4.62	1535 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),ord_greaterThan(A),B)) = hAPP(A,fun(A,bool),ord_lessThan(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_517_image__uminus__greaterThan) # label(axiom).  [clausify(384)].
4.41/4.62	1536 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_493_le__imp__neg__le) # label(axiom).  [clausify(477)].
4.41/4.62	1537 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_535_max__diff__distrib__left) # label(axiom).  [clausify(499)].
4.41/4.62	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),A)).  [resolve(1526,a,1527,a)].
4.41/4.62	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)).  [resolve(1526,a,1529,a)].
4.41/4.62	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)).  [resolve(1526,a,1530,a)].
4.41/4.62	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1526,a,1531,a)].
4.41/4.62	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(1526,a,1532,a)].
4.41/4.62	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)).  [resolve(1526,a,1533,a)].
4.41/4.62	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)).  [resolve(1526,a,1534,a)].
4.41/4.63	Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),ord_greaterThan(int),A)) = hAPP(int,fun(int,bool),ord_lessThan(int),hAPP(int,int,uminus_uminus(int),A)).  [resolve(1526,a,1535,a)].
4.41/4.63	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B).  [resolve(1526,a,1537,a)].
4.41/4.63	1538 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_834_image__uminus__atLeastAtMost) # label(axiom).  [clausify(554)].
4.41/4.63	Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)).  [resolve(1538,a,1526,a)].
4.41/4.63	1539 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),ord_lessThan(A),B)) = hAPP(A,fun(A,bool),ord_greaterThan(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_516_image__uminus__lessThan) # label(axiom).  [clausify(690)].
4.41/4.63	Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),ord_lessThan(int),A)) = hAPP(int,fun(int,bool),ord_greaterThan(int),hAPP(int,int,uminus_uminus(int),A)).  [resolve(1539,a,1526,a)].
4.41/4.63	1540 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_496_le__minus__iff) # label(axiom).  [clausify(710)].
4.41/4.63	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,uminus_uminus(int),A))).  [resolve(1540,a,1526,a)].
4.41/4.63	1541 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_496_le__minus__iff) # label(axiom).  [clausify(710)].
4.41/4.63	1542 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_808_neg__less__iff__less) # label(axiom).  [clausify(734)].
4.41/4.63	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(1542,a,1526,a)].
4.41/4.63	1543 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_808_neg__less__iff__less) # label(axiom).  [clausify(734)].
4.41/4.63	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(1543,a,1526,a)].
4.41/4.63	1544 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_371_min__diff__distrib__left) # label(axiom).  [clausify(770)].
4.54/4.75	Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B).  [resolve(1544,a,1526,a)].
4.54/4.75	1545 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_810_less__minus__iff) # label(axiom).  [clausify(877)].
4.54/4.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,uminus_uminus(int),A))).  [resolve(1545,a,1526,a)].
4.54/4.75	1546 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_810_less__minus__iff) # label(axiom).  [clausify(877)].
4.54/4.75	1547 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_809_minus__less__iff) # label(axiom).  [clausify(923)].
4.54/4.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),B)),A)).  [resolve(1547,a,1526,a)].
4.54/4.75	1548 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_809_minus__less__iff) # label(axiom).  [clausify(923)].
4.54/4.75	1549 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_298_add__right__mono) # label(axiom).  [clausify(544)].
4.54/4.75	1550 ordere779506340up_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
4.54/4.75	1551 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
4.54/4.75	1552 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_297_add__left__mono) # label(axiom).  [clausify(548)].
4.54/4.75	1553 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_296_add__mono) # label(axiom).  [clausify(832)].
4.54/4.75	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))).  [resolve(1553,a,1550,a)].
4.54/4.75	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))).  [resolve(1553,a,1551,a)].
4.54/4.76	1554 -ordere779506340up_add(A) | -semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f168(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,finite_card(B),E))),D))) # label(fact_665_setsum__bounded) # label(axiom).  [clausify(911)].
4.54/4.76	Derived: -semiring_1(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f168(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))).  [resolve(1554,a,1550,a)].
4.54/4.76	Derived: -semiring_1(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f168(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))).  [resolve(1554,a,1551,a)].
4.54/4.76	1555 -ordere779506340up_add(A) | -semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f168(B,A,C,D,E))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,finite_card(B),E))),D))) # label(fact_665_setsum__bounded) # label(axiom).  [clausify(911)].
4.54/4.76	Derived: -semiring_1(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f168(A,int,B,C,D))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))).  [resolve(1555,a,1550,a)].
4.54/4.76	Derived: -semiring_1(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f168(A,nat,B,C,D))),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))).  [resolve(1555,a,1551,a)].
4.54/4.76	1556 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f171(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_333_setsum__mono) # label(axiom).  [clausify(939)].
4.54/4.76	Derived: -comm_monoid_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f171(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))).  [resolve(1556,b,1550,a)].
4.54/4.76	Derived: -comm_monoid_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f171(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))).  [resolve(1556,b,1551,a)].
4.54/4.76	1557 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f171(B,A,C,D,E))),hAPP(B,A,D,f171(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_333_setsum__mono) # label(axiom).  [clausify(939)].
5.13/5.31	Derived: -comm_monoid_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f171(A,int,B,C,D))),hAPP(A,int,C,f171(A,int,B,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))).  [resolve(1557,b,1550,a)].
5.13/5.31	Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f171(A,nat,B,C,D))),hAPP(A,nat,C,f171(A,nat,B,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))).  [resolve(1557,b,1551,a)].
5.13/5.31	1558 -comm_ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) # label(fact_512_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom).  [clausify(148)].
5.13/5.31	1559 comm_ring_1(int) # label(arity_Int_Oint___Rings_Ocomm__ring__1) # label(axiom).  [assumption].
5.13/5.31	1560 -comm_ring_1(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B) # label(fact_639_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom).  [clausify(1078)].
5.13/5.31	Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A).  [resolve(1560,a,1559,a)].
5.13/5.31	1561 -cancel146912293up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_227_add__imp__eq) # label(axiom).  [clausify(306)].
5.13/5.31	1562 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
5.13/5.31	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) = ti(int,C).  [resolve(1561,a,1562,a)].
5.13/5.31	1563 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
5.13/5.31	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) = ti(nat,C).  [resolve(1563,a,1561,a)].
5.13/5.31	1564 -one(A) | ti(A,one_one(A)) = one_one(A) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom).  [clausify(606)].
5.13/5.31	1565 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom).  [assumption].
5.13/5.31	Derived: ti(int,one_one(int)) = one_one(int).  [resolve(1564,a,1565,a)].
5.13/5.31	1566 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom).  [assumption].
5.13/5.31	Derived: ti(nat,one_one(nat)) = one_one(nat).  [resolve(1566,a,1564,a)].
5.13/5.31	1567 -ab_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_233_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom).  [clausify(260)].
5.13/5.31	1568 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
5.13/5.31	1569 -ab_semigroup_add(A) | ti(fun(A,fun(A,A)),plus_plus(A)) = plus_plus(A) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom).  [clausify(512)].
5.13/5.31	Derived: ti(fun(nat,fun(nat,nat)),plus_plus(nat)) = plus_plus(nat).  [resolve(1569,a,1568,a)].
5.13/5.31	1570 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
5.13/5.31	Derived: ti(fun(int,fun(int,int)),plus_plus(int)) = plus_plus(int).  [resolve(1570,a,1569,a)].
5.13/5.31	1571 -linord893533164strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_994_comm__mult__strict__left__mono) # label(axiom).  [clausify(599)].
5.43/5.67	1572 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
5.43/5.67	1573 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
5.43/5.67	1574 -linordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),zero_zero(A))) # label(fact_980_not__square__less__zero) # label(axiom).  [clausify(880)].
5.43/5.67	1575 linordered_ring(int) # label(arity_Int_Oint___Rings_Olinordered__ring) # label(axiom).  [assumption].
5.43/5.67	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),zero_zero(int))).  [resolve(1574,a,1575,a)].
5.43/5.67	1576 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
5.43/5.67	1577 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_230_add__right__cancel) # label(axiom).  [clausify(124)].
5.43/5.67	1578 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) != ti(A,D) # label(fact_230_add__right__cancel) # label(axiom).  [clausify(124)].
5.43/5.67	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C).  [resolve(1576,a,1577,a)].
5.43/5.67	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) != ti(nat,C).  [resolve(1576,a,1578,a)].
5.43/5.67	1579 -cancel_semigroup_add(A) | ti(fun(A,fun(A,A)),plus_plus(A)) = plus_plus(A) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(399)].
5.43/5.67	1580 -cancel_semigroup_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) # label(fact_231_add__left__cancel) # label(axiom).  [clausify(430)].
5.43/5.67	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B).  [resolve(1580,a,1576,a)].
5.43/5.67	1581 -cancel_semigroup_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) # label(fact_231_add__left__cancel) # label(axiom).  [clausify(430)].
5.43/5.67	1582 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_228_add__left__imp__eq) # label(axiom).  [clausify(473)].
5.43/5.67	1583 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
5.43/5.67	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) = ti(int,C).  [resolve(1583,a,1577,a)].
5.43/5.67	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) != ti(int,C).  [resolve(1583,a,1578,a)].
5.43/5.67	Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B).  [resolve(1583,a,1580,a)].
5.43/5.67	1584 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_226_add__right__imp__eq) # label(axiom).  [clausify(1071)].
5.43/5.67	1585 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)) # label(fact_223_crossproduct__eq) # label(axiom).  [clausify(846)].
5.43/5.67	1586 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom).  [assumption].
5.43/5.67	1587 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom).  [assumption].
5.43/5.67	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),A)).  [resolve(1585,a,1586,a)].
5.43/5.67	Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),A)).  [resolve(1585,a,1587,a)].
5.43/5.67	1588 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_223_crossproduct__eq) # label(axiom).  [clausify(846)].
5.43/5.67	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(1588,a,1586,a)].
5.43/5.67	Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)).  [resolve(1588,a,1587,a)].
5.43/5.67	1589 -semiri456707255roduct(A) | ti(A,B) = ti(A,C) | ti(A,D) = ti(A,E) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)) # label(fact_223_crossproduct__eq) # label(axiom).  [clausify(846)].
5.43/5.67	Derived: ti(nat,A) = ti(nat,B) | ti(nat,C) = ti(nat,D) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),B)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),A)).  [resolve(1589,a,1586,a)].
5.43/5.67	Derived: ti(int,A) = ti(int,B) | ti(int,C) = ti(int,D) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),A)).  [resolve(1589,a,1587,a)].
5.43/5.67	1590 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,D) != ti(A,B) # label(fact_249_crossproduct__noteq) # label(axiom).  [clausify(988)].
5.43/5.67	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,C) != ti(nat,A).  [resolve(1590,a,1586,a)].
5.63/5.89	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,C) != ti(int,A).  [resolve(1590,a,1587,a)].
5.63/5.89	1591 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_249_crossproduct__noteq) # label(axiom).  [clausify(988)].
5.63/5.89	1592 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,D) = ti(A,B) | ti(A,C) = ti(A,E) # label(fact_249_crossproduct__noteq) # label(axiom).  [clausify(988)].
5.63/5.89	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,C) = ti(nat,A) | ti(nat,B) = ti(nat,D).  [resolve(1592,a,1586,a)].
5.63/5.89	Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,C) = ti(int,A) | ti(int,B) = ti(int,D).  [resolve(1592,a,1587,a)].
5.63/5.89	1593 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom).  [assumption].
5.63/5.89	1594 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),uminus_uminus(A)),C)),D) = hAPP(A,A,uminus_uminus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)) # label(fact_510_setsum__negf) # label(axiom).  [clausify(168)].
5.63/5.89	1595 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) # label(fact_513_ab__diff__minus) # label(axiom).  [clausify(264)].
5.63/5.89	1596 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,D,B)),hAPP(nat,A,D,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) # label(fact_934_setsum__natinterval__difff) # label(axiom).  [clausify(624)].
5.63/5.89	1597 -ab_group_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | zero_zero(A) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) # label(fact_934_setsum__natinterval__difff) # label(axiom).  [clausify(624)].
5.63/5.89	1598 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) != ti(A,D) | ti(A,C) = ti(A,B) # label(fact_247_diff__eq__diff__eq) # label(axiom).  [clausify(635)].
5.63/5.89	1599 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) = ti(A,D) | ti(A,C) != ti(A,B) # label(fact_247_diff__eq__diff__eq) # label(axiom).  [clausify(635)].
5.63/5.89	1600 -ab_group_add(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom).  [clausify(677)].
5.63/5.89	1601 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)) # label(fact_329_setsum__diff) # label(axiom).  [clausify(689)].
5.63/5.89	1602 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),minus_minus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_190_setsum__subtractf) # label(axiom).  [clausify(752)].
5.63/5.89	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),uminus_uminus(int)),B)),C) = hAPP(int,int,uminus_uminus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)).  [resolve(1593,a,1594,a)].
5.63/5.89	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,C,A)),hAPP(nat,int,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))).  [resolve(1593,a,1596,a)].
5.63/5.89	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | zero_zero(int) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)).  [resolve(1593,a,1597,a)].
5.72/5.90	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) != ti(int,C) | ti(int,B) = ti(int,A).  [resolve(1593,a,1598,a)].
5.72/5.90	Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) = ti(int,C) | ti(int,B) != ti(int,A).  [resolve(1593,a,1599,a)].
5.72/5.90	Derived: zero_zero(int) = ti(int,zero_zero(int)).  [resolve(1593,a,1600,a)].
5.72/5.90	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)).  [resolve(1593,a,1601,a)].
5.72/5.90	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),minus_minus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)).  [resolve(1593,a,1602,a)].
5.72/5.90	1603 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) # label(fact_492_minus__diff__eq) # label(axiom).  [clausify(921)].
5.72/5.90	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A).  [resolve(1603,a,1593,a)].
5.72/5.90	1604 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool))))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(B,A,E,D)) # label(fact_173_setsum__diff1) # label(axiom).  [clausify(986)].
5.72/5.90	1605 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool))))) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_173_setsum__diff1) # label(axiom).  [clausify(986)].
5.72/5.90	Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool))))) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B).  [resolve(1605,a,1593,a)].
5.82/6.00	1606 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_501_minus__add__distrib) # label(axiom).  [clausify(1035)].
5.82/6.00	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)).  [resolve(1606,a,1593,a)].
5.82/6.00	1607 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom).  [assumption].
5.82/6.00	1608 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_989_mult__less__cancel__left__neg) # label(axiom).  [clausify(195)].
5.82/6.00	1609 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_989_mult__less__cancel__left__neg) # label(axiom).  [clausify(195)].
5.82/6.00	1610 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom).  [clausify(295)].
5.82/6.00	1611 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom).  [clausify(295)].
5.82/6.00	1612 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom).  [clausify(295)].
5.82/6.00	1613 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom).  [clausify(295)].
5.82/6.00	1614 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom).  [clausify(295)].
5.82/6.00	1615 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom).  [clausify(295)].
5.82/6.01	1616 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_983_mult__less__cancel__left__pos) # label(axiom).  [clausify(323)].
5.82/6.01	1617 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_983_mult__less__cancel__left__pos) # label(axiom).  [clausify(323)].
5.82/6.01	1618 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom).  [clausify(369)].
5.82/6.01	1619 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom).  [clausify(369)].
5.82/6.01	1620 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom).  [clausify(369)].
5.82/6.01	1621 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom).  [clausify(369)].
5.82/6.01	1622 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom).  [clausify(369)].
5.82/6.01	1623 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom).  [clausify(369)].
5.82/6.01	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)).  [resolve(1607,a,1608,a)].
5.82/6.01	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)).  [resolve(1607,a,1609,a)].
5.82/6.01	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))).  [resolve(1607,a,1610,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))).  [resolve(1607,a,1612,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))).  [resolve(1607,a,1613,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(1607,a,1614,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))).  [resolve(1607,a,1615,a)].
5.82/6.01	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).  [resolve(1607,a,1616,a)].
5.82/6.01	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))).  [resolve(1607,a,1619,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))).  [resolve(1607,a,1620,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))).  [resolve(1607,a,1621,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))).  [resolve(1607,a,1622,a)].
5.82/6.01	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))).  [resolve(1607,a,1623,a)].
5.82/6.01	1624 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_991_mult__neg__neg) # label(axiom).  [clausify(860)].
5.92/6.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(1624,a,1607,a)].
5.92/6.11	1625 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_996_mult__strict__left__mono__neg) # label(axiom).  [clausify(914)].
5.92/6.11	1626 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_995_mult__strict__right__mono__neg) # label(axiom).  [clausify(974)].
5.92/6.11	1627 ab_semigroup_mult(int) # label(arity_Int_Oint___Groups_Oab__semigroup__mult) # label(axiom).  [assumption].
5.92/6.11	1628 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),E),bot_bot(fun(A,bool)))))),D)) # label(fact_143_fold__graph__permute__diff) # label(axiom).  [clausify(213)].
5.92/6.11	1629 -ab_semigroup_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_243_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom).  [clausify(407)].
5.92/6.11	Derived: -hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),A),B),C)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),D),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),D),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),D),bot_bot(fun(int,bool)))))),C)).  [resolve(1627,a,1628,a)].
5.92/6.11	1630 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom).  [assumption].
5.92/6.11	Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),D),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),D),bot_bot(fun(nat,bool)))))),C)).  [resolve(1630,a,1628,a)].
5.92/6.12	1631 -ab_semigroup_mult(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite100568337ommute(A,A),times_times(A))) # label(fact_192_comp__fun__commute) # label(axiom).  [clausify(528)].
5.92/6.12	Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite100568337ommute(int,int),times_times(int))).  [resolve(1631,a,1627,a)].
5.92/6.12	Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite100568337ommute(nat,nat),times_times(nat))).  [resolve(1631,a,1630,a)].
5.92/6.12	1632 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f133(A,B)),f134(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f133(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f134(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)),B)) # label(fact_154_fold1__in) # label(axiom).  [clausify(650)].
5.92/6.12	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f133(int,A)),f134(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f133(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f134(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),A)),A)).  [resolve(1632,a,1627,a)].
5.92/6.12	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f133(nat,A)),f134(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f133(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f134(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)),A)).  [resolve(1632,a,1630,a)].
5.92/6.12	1633 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_150_fold__graph__insert__swap) # label(axiom).  [clausify(653)].
5.92/6.12	Derived: -hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),A),B),C)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),D),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),C))).  [resolve(1633,a,1627,a)].
5.92/6.14	Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),C))).  [resolve(1633,a,1630,a)].
5.92/6.14	1634 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),times_times(A)),C),B) # label(fact_205_fold1__eq__fold) # label(axiom).  [clausify(922)].
5.92/6.14	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),times_times(int)),B),A).  [resolve(1634,a,1627,a)].
5.92/6.14	Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),times_times(nat)),B),A).  [resolve(1634,a,1630,a)].
5.92/6.14	1635 -ab_semigroup_mult(A) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)) # label(fact_125_fold1__insert) # label(axiom).  [clausify(1064)].
5.92/6.14	Derived: ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),A)).  [resolve(1635,a,1627,a)].
5.92/6.14	Derived: ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)).  [resolve(1635,a,1630,a)].
6.02/6.23	1636 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom).  [clausify(1087)].
6.02/6.23	1637 semiring_0(int) # label(arity_Int_Oint___Rings_Osemiring__0) # label(axiom).  [assumption].
6.02/6.23	1638 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,A),fun(B,fun(C,A)),hAPP(fun(B,fun(fun(C,A),fun(C,A))),fun(fun(C,A),fun(B,fun(C,A))),combc(B,fun(C,A),fun(C,A)),hAPP(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A))),hAPP(fun(fun(A,A),fun(fun(C,A),fun(C,A))),fun(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A)))),combb(fun(A,A),fun(fun(C,A),fun(C,A)),B),combb(A,A,C)),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D))),E))),F)),V6) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),V6)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F)) # label(fact_187_setsum__product) # label(axiom).  [clausify(240)].
6.02/6.23	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,int),fun(A,fun(B,int)),hAPP(fun(A,fun(fun(B,int),fun(B,int))),fun(fun(B,int),fun(A,fun(B,int))),combc(A,fun(B,int),fun(B,int)),hAPP(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int))),hAPP(fun(fun(int,int),fun(fun(B,int),fun(B,int))),fun(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int)))),combb(fun(int,int),fun(fun(B,int),fun(B,int)),A),combb(int,int,B)),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C))),D))),E)),F) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),F)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E)).  [resolve(1637,a,1638,a)].
6.02/6.23	1639 semiring_0(nat) # label(arity_Nat_Onat___Rings_Osemiring__0) # label(axiom).  [assumption].
6.02/6.23	Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,nat),fun(A,fun(B,nat)),hAPP(fun(A,fun(fun(B,nat),fun(B,nat))),fun(fun(B,nat),fun(A,fun(B,nat))),combc(A,fun(B,nat),fun(B,nat)),hAPP(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat))),hAPP(fun(fun(nat,nat),fun(fun(B,nat),fun(B,nat))),fun(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat)))),combb(fun(nat,nat),fun(fun(B,nat),fun(B,nat)),A),combb(nat,nat,B)),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C))),D))),E)),F) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),F)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E)).  [resolve(1639,a,1638,a)].
6.12/6.35	1640 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_188_setsum__left__distrib) # label(axiom).  [clausify(825)].
6.12/6.35	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),C).  [resolve(1640,a,1637,a)].
6.12/6.35	Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),C).  [resolve(1640,a,1639,a)].
6.12/6.35	1641 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_189_setsum__right__distrib) # label(axiom).  [clausify(1077)].
6.12/6.35	Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),hAPP(int,fun(int,int),times_times(int),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)).  [resolve(1641,a,1637,a)].
6.12/6.35	Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),hAPP(nat,fun(nat,nat),times_times(nat),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D)).  [resolve(1641,a,1639,a)].
6.12/6.35	1642 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,B) = ti(A,C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_509_square__eq__iff) # label(axiom).  [clausify(878)].
6.12/6.35	1643 idom(int) # label(arity_Int_Oint___Rings_Oidom) # label(axiom).  [assumption].
6.12/6.35	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,A) = ti(int,B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A).  [resolve(1642,a,1643,a)].
6.12/6.35	1644 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,B) != ti(A,C) # label(fact_509_square__eq__iff) # label(axiom).  [clausify(878)].
6.12/6.35	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,A) != ti(int,B).  [resolve(1644,a,1643,a)].
6.12/6.35	1645 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_509_square__eq__iff) # label(axiom).  [clausify(878)].
6.22/6.48	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,B) != hAPP(int,int,uminus_uminus(int),A).  [resolve(1645,a,1643,a)].
6.22/6.48	1646 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom).  [clausify(584)].
6.22/6.48	1647 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
6.22/6.48	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(1646,a,1647,a)].
6.22/6.48	1648 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom).  [clausify(584)].
6.22/6.48	1649 -linord219039673up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_481_minus__Min__eq__Max) # label(axiom).  [clausify(655)].
6.22/6.48	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),A)) = hAPP(int,int,uminus_uminus(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)).  [resolve(1649,a,1647,a)].
6.22/6.48	1650 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_563_minus__min__eq__max) # label(axiom).  [clausify(830)].
6.22/6.48	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)).  [resolve(1650,a,1647,a)].
6.22/6.48	1651 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_564_minus__max__eq__min) # label(axiom).  [clausify(1024)].
6.22/6.48	Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)).  [resolve(1651,a,1647,a)].
6.22/6.48	1652 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(1047)].
6.22/6.48	1653 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(1047)].
6.22/6.48	1654 -linord219039673up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_480_minus__Max__eq__Min) # label(axiom).  [clausify(1067)].
6.33/6.58	Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),A)) = hAPP(int,int,uminus_uminus(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)).  [resolve(1654,a,1647,a)].
6.33/6.58	1655 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_945_add__nonneg__pos) # label(axiom).  [clausify(401)].
6.33/6.58	1656 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
6.33/6.58	1657 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
6.33/6.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))).  [resolve(1655,a,1656,a)].
6.33/6.58	1658 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_944_add__pos__nonneg) # label(axiom).  [clausify(423)].
6.33/6.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))).  [resolve(1658,a,1656,a)].
6.33/6.58	1659 -ordere216010020id_add(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom).  [clausify(488)].
6.33/6.58	Derived: zero_zero(nat) = ti(nat,zero_zero(nat)).  [resolve(1659,a,1657,a)].
6.33/6.58	1660 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_976_add__pos__pos) # label(axiom).  [clausify(746)].
6.33/6.58	1661 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_978_add__neg__neg) # label(axiom).  [clausify(809)].
6.33/6.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))).  [resolve(1661,a,1656,a)].
6.33/6.58	1662 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_947_add__strict__increasing2) # label(axiom).  [clausify(854)].
6.33/6.58	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))).  [resolve(1662,a,1656,a)].
6.33/6.58	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))).  [resolve(1662,a,1657,a)].
6.61/6.79	1663 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_948_add__neg__nonpos) # label(axiom).  [clausify(904)].
6.61/6.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))).  [resolve(1663,a,1656,a)].
6.61/6.79	1664 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_946_add__strict__increasing) # label(axiom).  [clausify(934)].
6.61/6.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))).  [resolve(1664,a,1656,a)].
6.61/6.79	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))).  [resolve(1664,a,1657,a)].
6.61/6.79	1665 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_949_add__nonpos__neg) # label(axiom).  [clausify(1088)].
6.61/6.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))).  [resolve(1665,a,1656,a)].
6.61/6.79	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))).  [resolve(1665,a,1657,a)].
6.61/6.79	1666 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) != hAPP(nat,A,semiring_1_of_nat(A),C) | B = C # label(fact_658_of__nat__eq__iff) # label(axiom).  [clausify(582)].
6.61/6.79	1667 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom).  [assumption].
6.61/6.79	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B.  [resolve(1666,a,1667,a)].
6.61/6.79	1668 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(nat,A,semiring_1_of_nat(A),C) | B != C # label(fact_658_of__nat__eq__iff) # label(axiom).  [clausify(582)].
6.61/6.79	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B.  [resolve(1668,a,1667,a)].
6.61/6.79	1669 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom).  [assumption].
6.61/6.79	Derived: hAPP(nat,int,semiring_1_of_nat(int),A) != hAPP(nat,int,semiring_1_of_nat(int),B) | A = B.  [resolve(1669,a,1666,a)].
6.61/6.79	Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(nat,int,semiring_1_of_nat(int),B) | A != B.  [resolve(1669,a,1668,a)].
6.61/6.79	1670 -semiring(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom).  [clausify(829)].
6.61/6.79	1671 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom).  [assumption].
6.94/7.12	1672 semiring(int) # label(arity_Int_Oint___Rings_Osemiring) # label(axiom).  [assumption].
6.94/7.12	1673 -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),E)) # label(fact_224_combine__common__factor) # label(axiom).  [clausify(1066)].
6.94/7.12	Derived: 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),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),D)).  [resolve(1673,a,1671,a)].
6.94/7.12	Derived: 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),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),D)).  [resolve(1673,a,1672,a)].
6.94/7.12	1674 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom).  [assumption].
6.94/7.12	1675 -ring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,semiring_1_of_nat(A),C)),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) # label(fact_663_of__nat__diff) # label(axiom).  [clausify(595)].
6.94/7.12	1676 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),C)),B) # label(fact_887_power__minus) # label(axiom).  [clausify(1048)].
6.94/7.12	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),B)),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)).  [resolve(1674,a,1675,a)].
6.94/7.12	Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),B)),A).  [resolve(1674,a,1676,a)].
6.94/7.12	1677 -comm_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_250_comm__semiring__class_Odistrib) # label(axiom).  [clausify(1079)].
6.94/7.12	1678 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom).  [assumption].
6.94/7.12	1679 comm_semiring(int) # label(arity_Int_Oint___Rings_Ocomm__semiring) # label(axiom).  [assumption].
6.94/7.12	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)).  [resolve(1677,a,1678,a)].
6.94/7.12	1680 -ring_11004092258visors(A) | one_one(A) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) | ti(A,B) = one_one(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_638_square__eq__1__iff) # label(axiom).  [clausify(838)].
6.94/7.12	1681 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
6.94/7.12	Derived: one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) | ti(int,A) = one_one(int) | ti(int,A) = hAPP(int,int,uminus_uminus(int),one_one(int)).  [resolve(1680,a,1681,a)].
8.64/8.84	1682 -ring_11004092258visors(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) | ti(A,B) != one_one(A) # label(fact_638_square__eq__1__iff) # label(axiom).  [clausify(838)].
8.64/8.84	Derived: one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) | ti(int,A) != one_one(int).  [resolve(1682,a,1681,a)].
8.64/8.84	1683 -ring_11004092258visors(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) | ti(A,B) != hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_638_square__eq__1__iff) # label(axiom).  [clausify(838)].
8.64/8.84	Derived: one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) | ti(int,A) != hAPP(int,int,uminus_uminus(int),one_one(int)).  [resolve(1683,a,1681,a)].
8.64/8.84	
8.64/8.84	============================== end predicate elimination =============
8.64/8.84	
8.64/8.84	Auto_denials:  (non-Horn, no changes).
8.64/8.84	
8.64/8.84	Term ordering decisions:
8.64/8.84	Function symbol KB weights:  bool=1. nat=1. int=1. state=1. com=1. fconj=1. vname=1. fdisj=1. fimplies=1. ass=1. fNot=1. semi=1. fFalse=1. fTrue=1. skip=1. update=1. b=1. c=1. g=1. p=1. x_a=1. fun=1. ti=1. big_co1399186613setsum=1. big_co302546470etprod=1. image=1. finite_fold=1. finite_fold_graph=1. finite100568337ommute=1. combk=1. finite_comp_fun_idem=1. finite1357897459simple=1. finite908156982e_idem=1. fold_graph=1. hoare_1759541758le_rec=1. hoare_225284258e_case=1. f21=1. f22=1. f28=1. f29=1. f37=1. f38=1. f65=1. f67=1. f69=1. f72=1. f74=1. f89=1. f90=1. f99=1. f109=1. f110=1. f111=1. f114=1. f115=1. f116=1. f120=1. f121=1. f122=1. f123=1. f133=1. f134=1. f140=1. f141=1. f150=1. f151=1. f152=1. f165=1. f175=1. f183=1. ord_less_eq=1. ord_less=1. hoare_2118899576triple=1. plus_plus=1. finite_finite_1=1. bot_bot=1. times_times=1. insert=1. member=1. minus_minus=1. ord_min=1. ord_max=1. one_one=1. semiring_1_of_nat=1. zero_zero=1. uminus_uminus=1. power_power=1. collect=1. big_linorder_Max=1. finite_card=1. big_linorder_Min=1. big_Inf_fin=1. big_Sup_fin=1. finite_fold1=1. ord_atLeastAtMost=1. fequal=1. hoare_759811442triple=1. hoare_1301688828derivs=1. ord_lessThan=1. fEx=1. ord_greaterThan=1. if=1. the=1. finite_fold1Set=1. finite_folding_one=1. finite2073411215e_idem=1. max=1. min=1. power_1=1. combi=1. ord_gr1471790799AtMost=1. partial_flat_lub=1. the_elem=1. big_semilattice_big=1. undefined=1. f68=1. f73=1. f104=1. f105=1. f160=1. f161=1. f172=1. f173=1. combb=1. combc=1. combs=1. f12=1. f23=1. f24=1. f25=1. f35=1. f36=1. f42=1. f43=1. f44=1. f45=1. f46=1. f50=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f75=1. f80=1. f81=1. f93=1. f94=1. f95=1. f97=1. f98=1. f112=1. f113=1. f117=1. f128=1. f129=1. f130=1. f132=1. f135=1. f136=1. f145=1. f147=1. f148=1. f149=1. f153=1. f154=1. f156=1. f162=1. f166=1. f176=1. f177=1. f178=1. f180=1. f181=1. f186=1. hAPP=1. f4=1. f5=1. f6=1. f9=1. f10=1. f11=1. f48=1. f51=1. f66=1. f71=1. f76=1. f79=1. f118=1. f138=1. f139=1. f142=1. f157=1. f158=1. f159=1. f179=1. f1=1. f2=1. f13=1. f14=1. f30=1. f34=1. f96=1. f108=1. f119=1. f125=1. f126=1. f127=1. f131=1. f137=1. f155=1. f163=1. f164=1. f167=1. f168=1. f171=1. f182=1. f184=1. f185=1. f187=1. f7=1. f8=1. f15=1. f16=1. f17=1. f18=1. f19=1. f26=1. f27=1. f31=1. f32=1. f33=1. f39=1. f40=1. f41=1. f47=1. f49=1. f77=1. f78=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f91=1. f92=1. f102=1. f103=1. f106=1. f107=1. f143=1. f144=1. f146=1. f170=1. f188=1. f3=1. f60=1. f61=1. f62=1. f70=1. f124=1. f169=1.
8.64/8.84	
8.64/8.84	============================== end of process initial clauses ========
8.64/8.84	
8.64/8.84	============================== CLAUSES FOR SEARCH ====================
8.64/8.84	
8.64/8.84	============================== end of clauses for search =============
8.64/8.84	
8.64/8.84	============================== SEARCH ================================
8.64/8.84	
8.64/8.84	% Starting search at 5.51 seconds.
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115.91/116.10	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 7.12 sec).
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115.91/116.10	Low Water (displace): id=6632, wt=200.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=6642, wt=199.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=6496, wt=196.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=5310, wt=195.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=6538, wt=193.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=16343, wt=25.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=16345, wt=21.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=16347, wt=18.000
115.91/116.10	
115.91/116.10	Low Water (displace): id=22220, wt=16.000
115.91/116.10	
115.91/116.10	Low Water (keep): wt=31.000, iters=3551
115.91/116.10	
115.91/116.10	Low Water (keep): wt=30.000, iters=3457
115.91/116.10	
115.91/116.10	Low Water (keep): wt=29.000, iters=3336
115.91/116.10	
115.91/116.10	Low Water (keep): wt=28.000, iters=3335
115.91/116.10	
115.91/116.10	Low Water (keep): wt=27.000, iters=3414
115.91/116.10	
115.91/116.10	Low Water (keep): wt=26.000, iters=3335
115.91/116.10	
115.91/116.10	Low Water (keep): wt=25.000, iters=3414
115.91/116.10	
115.91/116.10	Low Water (keep): wt=24.000, iters=3340
115.91/116.10	
115.91/116.10	Low Water (keep): wt=23.000, iters=3333
115.91/116.10	
115.91/116.10	============================== STATISTICS ============================
115.91/116.10	
115.91/116.10	Given=9987. Generated=2143789. Kept=164927. proofs=0.
115.91/116.10	Usable=8306. Sos=9999. Demods=1381. Limbo=34, Disabled=148923. Hints=0.
115.91/116.10	Kept_by_rule=0, Deleted_by_rule=68599.
115.91/116.10	Forward_subsumed=307162. Back_subsumed=139.
115.91/116.10	Sos_limit_deleted=1603101. Sos_displaced=140954. Sos_removed=0.
115.91/116.10	New_demodulators=3291 (0 lex), Back_demodulated=5089. Back_unit_deleted=405.
115.91/116.10	Demod_attempts=125819318. Demod_rewrites=674543.
115.91/116.10	Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
115.91/116.10	Nonunit_fsub_feature_tests=1923531. Nonunit_bsub_feature_tests=14062.
115.91/116.10	Megabytes=419.43.
115.91/116.10	User_CPU=112.52, System_CPU=1.31, Wall_clock=114.
115.91/116.10	
115.91/116.10	Megs malloced by palloc(): 400.
115.91/116.10	  type (bytes each)        gets      frees     in use      bytes
115.91/116.10	chunk ( 104)             104642     104642          0      0.0 K
115.91/116.10	string_buf (   8)         91033      91033          0      0.0 K
115.91/116.10	token (  20)             228364     228364          0      0.0 K
115.91/116.10	pterm (  16)             161428     161428          0      0.0 K
115.91/116.10	hashtab (   8)             1090       1090          0      0.0 K
115.91/116.10	hashnode (   8)            4982       4982          0      0.0 K
115.91/116.10	term (  20)           166104773  156658320    9446453 184501.0 K
115.91/116.10	      term arg arrays:                                 41176.3 K
115.91/116.10	attribute (  12)           7906        172       7734     90.6 K
115.91/116.10	ilist (   8)          652991319  652162470     828849   6475.4 K
115.91/116.10	plist (   8)            8018897    7817893     201004   1570.3 K
115.91/116.10	i2list (  12)           7323460    7323460          0      0.0 K
115.91/116.10	just (  12)             2680313    2492222     188091   2204.2 K
115.91/116.10	parajust (  16)          629816     536606      93210   1456.4 K
115.91/116.10	instancejust (   8)           0          0          0      0.0 K
115.91/116.10	ivyjust (  24)                0          0          0      0.0 K
115.91/116.10	formula (  28)            52534      34616      17918    489.9 K
115.91/116.10	    formula arg arrays:                                   61.5 K
115.91/116.10	topform (  52)          2147447    1978862     168585   8561.0 K
115.91/116.10	clist_pos (  20)         495359     326716     168643   3293.8 K
115.91/116.10	clist (  16)                  8          1          7      0.1 K
115.91/116.10	context ( 808)         11845111   11845109          2      1.6 K
115.91/116.10	trail (  12)           15301299   15301297          2      0.0 K
115.91/116.10	ac_match_pos (70044)          0          0          0      0.0 K
115.91/116.10	ac_match_free_vars_pos (20020)
115.91/116.10	                              0          0          0      0.0 K
115.91/116.10	btm_state (  60)              0          0          0      0.0 K
115.91/116.10	btu_state (  60)              0          0          0      0.0 K
115.91/116.10	ac_position (285432)          0          0          0      0.0 K
115.91/116.10	fpa_trie (  20)         3114481    2853675     260806   5093.9 K
115.91/116.10	fpa_state (  28)       13084911   13084911          0      0.0 K
115.91/116.10	fpa_index (  12)             10          0         10      0.1 K
115.91/116.10	fpa_chunk (  20)        4477663    4354909     122754   2397.5 K
115.91/116.10	fpa_list (  16)         2914977          0    2914977  45546.5 K
115.91/116.10	      fpa_list chunks:                                 11361.3 K
115.91/116.10	discrim (  12)          3003310    2888421     114889   1346.4 K
115.91/116.10	discrim_pos (  16)       853169     853169          0      0.0 K
115.91/116.10	flat2 (  32)           58185776   58185776          0      0.0 K
115.91/116.10	flat (  48)                   0          0          0      0.0 K
115.91/116.10	flatterm (  32)       150672159  150672159          0      0.0 K
115.91/116.10	mindex (  28)                13          0         13      0.4 K
115.91/116.10	mindex_pos (  56)       5941496    5941496          0      0.0 K
115.91/116.10	lindex (  12)                 5          0          5      0.1 K
115.91/116.10	clash (  40)                  0          0          0      0.0 K
115.91/116.10	di_tree (  12)         31403806   24033357    7370449  86372.4 K
115.91/116.10	avl_node (  20)          327905     307907      19998    390.6 K
115.91/116.10	
115.91/116.10	Memory report, 20 @ 20 = 400 megs (400.00 megs used).
115.91/116.10	List   1, length       4,      0.0 K
115.91/116.10	List   2, length    1072,      8.4 K
115.91/116.10	List   3, length  431164,   5052.7 K
115.91/116.10	List   7, length     159,      4.3 K
115.91/116.10	List   8, length     216,      6.8 K
115.91/116.10	List  10, length      15,      0.6 K
115.91/116.10	List  11, length      22,      0.9 K
115.91/116.10	List  12, length       3,      0.1 K
115.91/116.10	List  14, length       2,      0.1 K
115.91/116.10	List  16, length    8524,    532.8 K
115.91/116.10	List  26, length    1087,    110.4 K
115.91/116.10	List  32, length    2761,    345.1 K
115.91/116.10	List  64, length     586,    146.5 K
115.91/116.10	List 128, length       1,      0.5 K
115.91/116.10	List 202, length       2,      1.6 K
115.91/116.10	List 256, length       2,      2.0 K
115.91/116.10	
115.91/116.10	============================== SELECTOR REPORT =======================
115.91/116.10	Sos_deleted=1603101, Sos_displaced=140954, Sos_size=9999
115.91/116.10	  SELECTOR       PART   PRIORITY      ORDER       SIZE   SELECTED
115.91/116.10	         I 2147483647       high        age          0       1389
115.91/116.10	         H          1       high     weight          0          0
115.91/116.10	         A          1        low        age       9999        956
115.91/116.10	         F          4        low     weight        463       3822
115.91/116.10	         T          4        low     weight       9536       3820
115.91/116.10	============================== end of selector report ================
115.91/116.10	
115.91/116.10	============================== end of statistics =====================
115.91/116.10	
115.91/116.10	Exiting with failure.
115.91/116.10	
115.91/116.10	Process 11658 exit (max_megs) Thu Aug 29 15:13:58 2019
115.91/116.10	Prover9 interrupted
115.91/116.11	EOF