0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.14/0.35	% Computer   : n019.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 960
0.14/0.35	% DateTime   : Thu Jul  2 07:52:56 EDT 2020
0.14/0.35	% CPUTime    : 
1.44/1.70	============================== Prover9 ===============================
1.44/1.70	Prover9 (32) version 2009-11A, November 2009.
1.44/1.70	Process 10263 was started by sandbox2 on n019.cluster.edu,
1.44/1.70	Thu Jul  2 07:52:57 2020
1.44/1.70	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_10110_n019.cluster.edu".
1.44/1.70	============================== end of head ===========================
1.44/1.70	
1.44/1.70	============================== INPUT =================================
1.44/1.70	
1.44/1.70	% Reading from file /tmp/Prover9_10110_n019.cluster.edu
1.44/1.70	
1.44/1.70	set(prolog_style_variables).
1.44/1.70	set(auto2).
1.44/1.70	    % set(auto2) -> set(auto).
1.44/1.70	    % set(auto) -> set(auto_inference).
1.44/1.70	    % set(auto) -> set(auto_setup).
1.44/1.70	    % set(auto_setup) -> set(predicate_elim).
1.44/1.70	    % set(auto_setup) -> assign(eq_defs, unfold).
1.44/1.70	    % set(auto) -> set(auto_limits).
1.44/1.70	    % set(auto_limits) -> assign(max_weight, "100.000").
1.44/1.70	    % set(auto_limits) -> assign(sos_limit, 20000).
1.44/1.70	    % set(auto) -> set(auto_denials).
1.44/1.70	    % set(auto) -> set(auto_process).
1.44/1.70	    % set(auto2) -> assign(new_constants, 1).
1.44/1.70	    % set(auto2) -> assign(fold_denial_max, 3).
1.44/1.70	    % set(auto2) -> assign(max_weight, "200.000").
1.44/1.70	    % set(auto2) -> assign(max_hours, 1).
1.44/1.70	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
1.44/1.70	    % set(auto2) -> assign(max_seconds, 0).
1.44/1.70	    % set(auto2) -> assign(max_minutes, 5).
1.44/1.70	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
1.44/1.70	    % set(auto2) -> set(sort_initial_sos).
1.44/1.70	    % set(auto2) -> assign(sos_limit, -1).
1.44/1.70	    % set(auto2) -> assign(lrs_ticks, 3000).
1.44/1.70	    % set(auto2) -> assign(max_megs, 400).
1.44/1.70	    % set(auto2) -> assign(stats, some).
1.44/1.70	    % set(auto2) -> clear(echo_input).
1.44/1.70	    % set(auto2) -> set(quiet).
1.44/1.70	    % set(auto2) -> clear(print_initial_clauses).
1.44/1.70	    % set(auto2) -> clear(print_given).
1.44/1.70	assign(lrs_ticks,-1).
1.44/1.70	assign(sos_limit,10000).
1.44/1.70	assign(order,kbo).
1.44/1.70	set(lex_order_vars).
1.44/1.70	clear(print_given).
1.44/1.70	
1.44/1.70	% formulas(sos).  % not echoed (609 formulas)
1.44/1.70	
1.44/1.70	============================== end of input ==========================
1.44/1.70	
1.44/1.70	% From the command line: assign(max_seconds, 960).
1.44/1.70	
1.44/1.70	============================== PROCESS NON-CLAUSAL FORMULAS ==========
1.44/1.70	
1.44/1.70	% Formulas that are not ordinary clauses:
1.44/1.70	1 (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_71_in__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	2 (all X_b all A_2 all 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),B),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),bot_bot(fun(X_b,bool))) -> ti(X_b,A_2) = ti(X_b,B))) # label(fact_118_singleton__inject) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	3 (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_153_the__elem__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	4 (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_432_dense__le__bounded) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	5 (all Ts all G_1 (hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),Ts),G_1)) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),Ts)))) # label(fact_0_assms_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	6 (all X_a (monoid_add(X_a) -> plus_plus(X_a) = ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	7 (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_74_ext) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	8 (all X_a all X_b all 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)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	9 (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_70_equalityD2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	10 (all X_b all X_c all A_3 all B all F all X_1 (hAPP(X_c,X_b,F,X_1) = ti(X_b,B) -> (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),B),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_50_image__eqI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	11 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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,suc,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_190_card__Suc__Diff1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	12 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_447_less__zeroE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	13 (all X_a (preorder(X_a) -> (all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)))))) # label(fact_342_order__less__asym_H) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	14 (all X_a (ordere779506340up_add(X_a) -> (all C all D all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> 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_1),D)))))))) # label(fact_232_add__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	15 (all B_1_1 (hBOOL(B_1_1) <-> hBOOL(ti(bool,B_1_1)))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause).  [assumption].
1.44/1.70	16 (all I all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M))))) # label(fact_389_less__add__Suc1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	17 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_236_add__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	18 (all I all K all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)))) # label(fact_275_add__diff__assoc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	19 (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(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))))) # label(fact_420_psubsetD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	20 (all M_1 all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),Na) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)))) # label(fact_471_diff__is__0__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	21 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N) # label(fact_222_diff__Suc__1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	22 (all X_b all A_2 all A_3 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_122_insert__not__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	23 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) & Na != M_1)) # label(fact_327_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	24 (all X_b (ordere236663937imp_le(X_b) -> (all C_1 all A_2 all 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),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)))))) # label(fact_309_add__less__cancel__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	25 (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(X_b),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_28_finite__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	26 (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_101_le__funD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	27 (all X_c all X_b all C_1 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),C_1),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),C_1)),A_3)) & (bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3) -> 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),C_1)),A_3)))) # label(fact_134_image__constant__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	28 (all X_b (group_add(X_b) -> (all A_2 all B (ti(X_b,B) = ti(X_b,A_2) <-> zero_zero(X_b) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B))))) # label(fact_480_right__minus__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	29 (all L all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),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),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L))))) # label(fact_43_diff__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	30 (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].
1.44/1.70	31 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_285_card_Oinsert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	32 (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_3 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_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)))))) # label(fact_426_psubset__imp__ex__mem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	33 (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_135_linorder__le__cases) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	34 (all X_a (ordere216010020id_add(X_a) -> (all B_1 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_eq(X_a),zero_zero(X_a)),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_1)))))))) # label(fact_461_add__nonneg__nonneg) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	35 (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)) -> 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),A_3))) # label(fact_66_insert__absorb) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	36 (all X_b (zero(X_b) -> (all X_1 (zero_zero(X_b) = ti(X_b,X_1) <-> zero_zero(X_b) = ti(X_b,X_1))))) # label(fact_487_zero__reorient) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	37 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_163_finite__Diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	38 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_38_diff__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	39 (all X_c all X_b all X_d all F all G all 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) = 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))) # label(fact_83_image__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	40 (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_72_set__rev__mp) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	41 (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].
1.44/1.71	42 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(P))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	43 (all X_b all A_2 all A_3 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_123_empty__not__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	44 (all X_b (cancel_semigroup_add(X_b) -> (all B all A_2 all C_1 (ti(X_b,B) = ti(X_b,C_1) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2))))) # label(fact_247_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	45 (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)) & 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_68_set__eq__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	46 (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_413_not__psubset__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	47 (all X_b (linorder(X_b) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) | ti(X_b,X_1) = ti(X_b,Y_1))))) # label(fact_332_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	48 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(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_150_finite__induct) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	49 (all X_b all A_3 ((exists N_2 exists F_1 ti(fun(X_b,bool),A_3) = 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)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_418_finite__conv__nat__seg__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	50 (all X_a (ordere216010020id_add(X_a) -> (all B_1 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_eq(X_a),B_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_463_add__increasing) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	51 (all X_c (bot(X_c) -> ti(X_c,bot_bot(X_c)) = bot_bot(X_c))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	52 (all X_a (order(X_a) -> (all C all B_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)) -> (ti(X_a,C) = ti(X_a,B_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_347_xt1_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	53 (all X_c all X_b (order(X_b) & order(X_c) -> (all C_1 all F all B 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,B)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),B)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_2),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_2)),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,C_1)),A_2)))))))) # label(fact_433_xt4) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	54 (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_338_order__less__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	55 (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(fun(X_b,bool)),A_3),B_2)) | ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))) # label(fact_411_subset__iff__psubset__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	56 (all Nat_2 all Nat_3 (Nat_2 = Nat_3 <-> hAPP(nat,nat,suc,Nat_2) = hAPP(nat,nat,suc,Nat_3))) # label(fact_17_nat_Oinject) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	57 (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].
1.44/1.71	58 (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].
1.44/1.71	59 (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,X_2) = ti(X_b,A_2))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))))) # label(fact_214_theI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	60 (all N N != hAPP(nat,nat,suc,N)) # label(fact_19_n__not__Suc__n) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	61 (all X_b all X_c all B all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),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 (ti(X_b,B) = hAPP(X_c,X_b,F,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)))))) # label(fact_94_imageE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	62 (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_109_empty__Collect__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	63 (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].
1.44/1.71	64 (all X_b all C_1 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),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)),A_3),B_2))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)))) # label(fact_201_DiffD2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	65 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_32_le__SucI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	66 (all K_2 all M_1 all Na (Na = M_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na))) # label(fact_240_nat__add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	67 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B_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),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)))))) # label(fact_304_add__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	68 (all I all J_2 -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_2)),I))) # label(fact_303_not__add__less1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	69 (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].
1.44/1.71	70 (all I all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)) -> (hAPP(nat,nat,suc,I) != K -> -(all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hAPP(nat,nat,suc,J) != K))))) # label(fact_429_lessE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	71 (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_114_bot__apply) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	72 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B_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_1),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)))))) # label(fact_305_add__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	73 (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)) <-> 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_412_psubset__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	74 (all X_a (cancel_semigroup_add(X_a) -> (all B_1 all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),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_1))))) # label(fact_244_add__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	75 (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_340_order__less__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	76 (all X_b all A_2 all B 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),B),A_3))) -> (ti(X_b,B) != 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_54_insertE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	77 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_456_zero__le__one) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	78 (all X_b (order(X_b) -> (all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) | ti(X_b,Y_1) = ti(X_b,X_1) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)))))) # label(fact_367_order__le__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	79 (all X_b (preorder(X_b) -> (all Pa all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) -> hBOOL(Pa)))))) # label(fact_341_order__less__imp__triv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	80 (all I all K all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)) = 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_2))) # label(fact_279_diff__diff__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	81 (all M all 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),N)),M))) # label(fact_45_diff__le__self) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	82 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	83 (all X_b all A_2 all 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)) = 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))) # label(fact_59_insert__Collect) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	84 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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_1),C))))))) # label(fact_308_add__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	85 (all X_b all X_c all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2)))) # label(fact_444_finite__PlusD_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	86 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_458_zero__neq__one) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	87 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (N != hAPP(nat,nat,suc,M) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))))) # label(fact_316_Suc__lessI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	88 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_486_Zero__not__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	89 (all 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),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	90 (all X_c all X_b all A_3 all F all Z_1 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_1),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(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_1) = hAPP(X_c,X_b,G,X_2))) -> ti(X_b,Z_1) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_211_folding__image__simple_Oneutral) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	91 (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_165_Diff__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	92 (all K_2 all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) <-> 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_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na))))) # label(fact_258_nat__add__left__cancel__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	93 (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_182_image__diff__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	94 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_455_not__one__le__zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	95 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_396_Suc__leI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	96 (all X_b (order(X_b) -> (all Na all N_3 all F ((all N_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))))))) # label(fact_48_lift__Suc__mono__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	97 (all K all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K))))) # label(fact_315_less__trans__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	98 (all X_c all X_b (ord(X_c) & order(X_b) -> (all C_1 all F all B 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,B)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_2),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_2)),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,C_1)),A_2)))))))) # label(fact_430_xt6) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	99 (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(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_152_finite__less__ub) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	100 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_289_card__Diff1__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	101 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_276_le__add__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	102 (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_212_fun__diff__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	103 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) -> (M_1 = Na <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1)))))) # label(fact_397_le__less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	104 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all C_1 all 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),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)))))) # label(fact_310_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	105 (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_179_Diff__insert__absorb) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	106 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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,suc,hAPP(fun(X_b,bool),nat,finite_card(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(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))) # label(fact_8_card__insert__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	107 (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_100_le__fun__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	108 (all X_b all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(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_195_finite__empty__induct) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	109 (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_131_singleton__conv2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	110 (all X_b all C_2 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_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),C_2))))) # label(fact_77_subset__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	111 (all N 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),M)),N)) # label(fact_251_diff__add__inverse) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	112 (all Na all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)))) # label(fact_392_less__eq__Suc__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	113 (all M_1 all K_2 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_2)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2)))))) # label(fact_405_mono__nat__linear__lb) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	114 (all Pa all M_1 all Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1))) -> ((M_1 = Na -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1)))))) # label(fact_359_nat__less__cases) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	115 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_457_one__neq__zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	116 (all X_b all A_3 ((exists X_2 exists B_4 (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_2),B_4) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_4)))) <-> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_154_nonempty__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	117 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) <-> Na = M_1 | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)))) # label(fact_326_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	118 (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_187_folding__one_Osingleton) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	119 (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_113_bot__fun__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	120 (all X_a (monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))))) # label(fact_495_add__0__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	121 (all X_a undefined(X_a) = ti(X_a,undefined(X_a))) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	122 (all X_c finite_card(X_c) = ti(fun(fun(X_c,bool),nat),finite_card(X_c))) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	123 (all X_b (bot(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b))) <-> ti(X_b,A_2) = bot_bot(X_b))))) # label(fact_116_bot__unique) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	124 (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),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),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))))) # label(fact_129_Collect__conv__if2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	125 (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)),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))))) # label(fact_185_subset__insert__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	126 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) -> N = M))) # label(fact_318_less__antisym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	127 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_27_finite__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	128 (all N_1 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))))) # label(fact_383_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	129 (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)) -> (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) <-> ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3))))) # label(fact_64_insert__ident) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	130 (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_380_xt1_I7_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	131 (all X_b all A_3 ti(fun(X_b,bool),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)))) # label(fact_166_Diff__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	132 (all Pn all G_1 (hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),G_1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))),bot_bot(fun(x_a,bool))))) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),bot_bot(fun(x_a,bool))))))) # label(fact_149_assms_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	133 (all X_b all C_1 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),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)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))))) # label(fact_199_DiffE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	134 (all M all K all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))),M))) # label(fact_283_diff__Suc__diff__eq2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	135 (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_155_le__funI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	136 (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),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),A_3)) # label(fact_60_insert__absorb2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	137 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)))) # label(fact_320_Suc__less__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	138 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) -> (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) -> N = M))) # label(fact_473_diffs0__imp__equal) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	139 (all X_a (ord(X_a) -> (all C all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) -> (C = B_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_141_ord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	140 (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].
1.44/1.71	141 (all X_b all B all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),bot_bot(fun(X_b,bool))))) -> ti(X_b,B) = ti(X_b,A_2))) # label(fact_119_singletonE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	142 (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].
1.44/1.71	143 (all X_b all 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)),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),B),B_2))))) # label(fact_88_subset__insertI2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	144 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_11_Suc__diff__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	145 (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_96_image__subsetI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	146 (all X_b zero_zero(nat) = hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool)))) # label(fact_451_card_Oempty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	147 (all Na all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1))) <-> M_1 = Na))) # label(fact_319_not__less__less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	148 (all X_b all X_c (order(X_c) & order(X_b) -> (all F all C_1 all A_2 all B (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,B)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> 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_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)))))))) # label(fact_439_order__less__le__subst2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	149 (all X_a (ord(X_a) -> (all C all A_1 all B_1 (B_1 = A_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_344_ord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	150 (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].
1.44/1.71	151 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> 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_1),D)))))))) # label(fact_387_add__le__less__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	152 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> N = M))) # label(fact_20_le__antisym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	153 (all I_1 all Pa all K_2 (hBOOL(hAPP(nat,bool,Pa,K_2)) -> ((all N_2 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,Pa,N_2)))) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_2),I_1)))))) # label(fact_55_zero__induct__lemma) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	154 (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].
1.44/1.71	155 (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_352_termination__basic__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	156 (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),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))))) # label(fact_205_set__diff__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	157 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B_1 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_1) -> ti(X_a,B_1) = ti(X_a,C))))) # label(fact_246_add__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	158 (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].
1.44/1.71	159 (all 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)) = finite2073411215e_idem(X_b)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	160 (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_348_order__less__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	161 (all Na (Na = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat))))) # label(fact_489_le__0__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	162 (all X_b (order(X_b) -> (all Na all M_1 all F ((all N_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M_1)))))))) # label(fact_422_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	163 (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_294_termination__basic__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	164 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> 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_1),D)))))))) # label(fact_388_add__less__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	165 (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_369_not__leE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	166 (all I all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K)) -> -(all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> K != hAPP(nat,nat,suc,J))))) # label(fact_428_Suc__lessE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	167 (all M all K all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) -> 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,suc,J_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))))) # label(fact_284_diff__Suc__diff__eq1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	168 (all X_b all X_c 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_127_empty__is__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	169 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = M) # label(fact_250_diff__add__inverse2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	170 (all M_1 all Na (M_1 = hAPP(nat,nat,suc,Na) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,Na))))) # label(fact_34_le__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	171 (all X_b (linorder(X_b) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) <-> ti(X_b,X_1) = ti(X_b,Y_1)))))) # label(fact_334_linorder__antisym__conv3) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	172 (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)) & -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)) <-> 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)))))) # label(fact_414_less__fun__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	173 (all 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),fequal(X_a),X),Y)))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	174 (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].
1.44/1.71	175 (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_349_xt1_I10_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	176 (all I all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N)) -> I = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I)))) # label(fact_42_diff__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	177 (all M all N all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K))) # label(fact_37_Suc__diff__diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	178 (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(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)) != 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),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,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,A_3)))))) # label(fact_174_folding__one_Oremove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	179 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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),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)))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))) # label(fact_225_card_Oremove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	180 (all X_b (zero(X_b) -> zero_zero(X_b) = ti(X_b,zero_zero(X_b)))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	181 (all X all Y all 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)) = 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))) # label(fact_242_nat__add__left__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	182 (all X_c all X_b all C_1 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_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),C_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),C_1),bot_bot(fun(X_c,bool))))) # label(fact_133_image__constant) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	183 (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_350_order__less__asym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	184 (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].
1.44/1.72	185 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_290_lessI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	186 (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_333_linorder__less__linear) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	187 (all M all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> 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_2))))) # label(fact_299_trans__less__add2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	188 (all X_b all X_c all Z_1 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_1),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 (ti(X_b,Z_1) = hAPP(X_c,X_b,F,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)))))) # label(fact_79_image__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	189 (all X_c all X_b (order(X_c) & order(X_b) -> (all C_1 all F all B all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),hAPP(X_b,X_c,F,B))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),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_2)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_435_xt5) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	190 (all X_b (order(X_b) -> (all X_1 all Y_1 (ti(X_b,Y_1) = ti(X_b,X_1) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)))))) # label(fact_146_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	191 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_417_card__psubset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	192 (all X_c all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_4_card__image__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	193 (all L all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))))) # label(fact_328_diff__less__mono2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	194 (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_381_order__le__less__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	195 (all X_c all X_b all F 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),A_3) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_125_image__is__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	196 (all K all L all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L)) -> 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_2),L)))))) # label(fact_262_add__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	197 (all X_b all B all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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),bot_bot(fun(X_b,bool))))) <-> ti(X_b,A_2) = ti(X_b,B))) # label(fact_121_singleton__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	198 (all X_a (order(X_a) -> (all C all A_1 all B_1 (ti(X_a,B_1) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_345_xt1_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	199 (all Na all K_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) <-> 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_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2))))))) # label(fact_39_le__diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	200 (all Nat_1 hAPP(nat,nat,suc,Nat_1) != zero_zero(nat)) # label(fact_483_nat_Osimps_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	201 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	202 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_312_Suc__less__SucD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	203 (all X_a (order(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)))))) # label(fact_343_xt1_I9_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	204 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> S != T_3)) # label(fact_358_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	205 (all X_a (ordere216010020id_add(X_a) -> (all B_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_464_add__increasing2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	206 (all K_2 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_2),I_1) <-> K_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)))) # label(fact_272_le__imp__diff__is__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	207 (all Na all K_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) <-> 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_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2))))))) # label(fact_403_less__diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	208 (all X_b all C_2 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_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),C_2))))) # label(fact_408_subset__psubset__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	209 (all M all N (M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_22_eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	210 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))))) # label(fact_496_add_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	211 (all X_b all Pa all A_2 ((-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),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))) & (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),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))))) # label(fact_128_Collect__conv__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	212 (all I all K all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)))) # label(fact_271_diff__add__assoc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	213 (all M all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> 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_2),M))))) # label(fact_300_trans__less__add1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	214 (all K all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_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),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K))))) # label(fact_261_add__le__mono1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	215 (all X_b all C_1 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),C_1),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)),A_3),B_2))))) # label(fact_204_Diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	216 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_235_add__Suc__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	217 (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))))) -> bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_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),X_1),bot_bot(fun(X_b,bool))))) # label(fact_132_subset__singletonD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	218 (all X_b all Q_1 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_1)))))) # label(fact_10_finite__Collect__conjI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	219 (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)),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) = 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_177_Diff__insert2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	220 (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(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,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_158_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	221 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B_1 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_1) -> ti(X_a,C) = ti(X_a,B_1))))) # label(fact_245_add__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	222 (all X_c all X_b (order(X_b) & order(X_c) -> (all C_1 all F all B all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,B))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),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_2)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_436_xt7) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	223 (all X_b all Pa all A_3 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(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_148_finite__subset__induct) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	224 (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].
1.44/1.72	225 (all M_1 all Na (Na != M_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)))) # label(fact_354_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	226 (all M all K 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),M),K)),N)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N))))) # label(fact_265_add__leE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	227 (all X_b all X_c all A_3 all B_2 (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) <-> hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))))) # label(fact_441_finite__Plus__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	228 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_353_less__not__refl) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	229 (all X_b all Pa ((exists X_2 ((all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2)) -> ti(X_b,Y_2) = ti(X_b,X_2))) & 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_215_theI_H) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	230 (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)),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) = 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_203_Diff__idemp) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	231 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_478_diff__self) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	232 (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_361_bot__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	233 (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_382_xt1_I8_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	234 (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_374_order__less__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	235 (all X_c all X_b all X_1 all A_3 all F all Z_1 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_1),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(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,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_196_folding__image__simple_Oremove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	236 (all X_b all D_2 all B_2 all A_3 all C_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),C_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)),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_2),D_2)))))) # label(fact_172_Diff__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	237 (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)))),finite1357897459simple(X_b,X_c)) = finite1357897459simple(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	238 (all X_b all 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),B_2)) -> ti(X_b,A_2) = ti(X_b,B)) -> 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),B),B_2))))) # label(fact_53_insertCI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	239 (all X_b all 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),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),B),B_2))))) # label(fact_65_insertI2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	240 (all X_b all A_2 all 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) = 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)))) # label(fact_58_insert__compr) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	241 (all X_b all X_c (order(X_b) & order(X_c) -> (all C_1 all A_2 all F all B (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,B))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_2)) -> 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_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))))))))) # label(fact_434_order__le__less__subst1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	242 (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_115_le__bot) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	243 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(X_b),A_3))))) # label(fact_29_rev__finite__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	244 (all K_2 all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na))))) # label(fact_301_nat__add__left__cancel__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	245 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_24_le__refl) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	246 (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_373_leD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	247 (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_126_image__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	248 (all M all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) -> 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_2))))) # label(fact_260_trans__le__add2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	249 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))))) # label(fact_291_Suc__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	250 (all L all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),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),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))))) # label(fact_44_diff__le__mono2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	251 (all X_b all A_2 all Pa ((exists X_2 ((all Y_2 (hBOOL(hAPP(X_b,bool,Pa,Y_2)) -> ti(X_b,X_2) = ti(X_b,Y_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_216_the1__equality) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	252 (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_67_subset__refl) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	253 (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_57_insertI1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	254 (all X_b all Y_1 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_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)),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_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))))) # label(fact_288_card__Diff2__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	255 (all X_b all X_c (order(X_c) & order(X_b) -> (all F all C_1 all A_2 all B (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_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,F,Y_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)))))))) # label(fact_438_order__le__less__subst2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	256 (all X_a (group_add(X_a) -> (all A_1 all B_1 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_1)),B_1)))) # label(fact_267_add__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	257 (all M M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))) # label(fact_475_minus__nat_Odiff__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	258 (all M all K 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),M),K)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_264_add__leD1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	259 (all M all 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),N)),hAPP(nat,nat,suc,M)))) # label(fact_399_diff__less__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	260 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = N))) # label(fact_314_less__SucE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	261 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_477_diff__0__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	262 (all X_b (order(X_b) -> (all Na all N_3 all F ((all N_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))))))) # label(fact_419_lift__Suc__mono__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	263 (all Na hAPP(nat,nat,suc,Na) = 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_eq(nat)),Na)))) # label(fact_13_card__Collect__le__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	264 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_398_Suc__le__lessD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	265 (all X_b (cancel_semigroup_add(X_b) -> (all A_2 all B all C_1 (ti(X_b,C_1) = ti(X_b,B) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1))))) # label(fact_248_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	266 (all X_2 hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)) = hAPP(nat,fun(nat,bool),ord_less(nat),X_2)) # label(fact_404_less__eq__Suc__le__raw) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	267 (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].
1.44/1.72	268 (all Na all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_1)))) # label(fact_33_Suc__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	269 (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(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)),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))))) # label(fact_170_insert__Diff__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	270 (all X_c all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2)) -> hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)))))) # label(fact_442_finite__Plus) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	271 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(Q) | hBOOL(P))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	272 (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_69_equalityD1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	273 (all X_b (linorder(X_b) -> (all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)))))) # label(fact_363_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	274 (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_1_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	275 (all X_b all C_2 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_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),C_2))))) # label(fact_409_psubset__subset__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	276 (all I_1 all J_1 all K_2 (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_2)),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_2))))) # label(fact_401_less__diff__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	277 (all X_c all X_b (minus(X_b) -> (all A_3 all B_2 all 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)) = 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)))) # label(fact_213_minus__apply) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	278 (all K_2 hBOOL(hAPP(fun(nat,bool),bool,finite_finite(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_2))))) # label(fact_292_finite__Collect__less__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	279 (all X_b all C_1 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),bot_bot(fun(X_b,bool))))) # label(fact_108_empty__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	280 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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)))))) = 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_224_card_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	281 (all K all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_253_diff__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	282 (all X_a (order(X_a) -> (all A_1 all B_1 (ti(X_a,B_1) != ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))))))) # label(fact_371_order__neq__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	283 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_482_Zero__neq__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	284 (all X_b all X_2 all 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))) = 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)) # label(fact_82_insert__compr__raw) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	285 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | hBOOL(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	286 (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_167_empty__Diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	287 (all X_c all X_b all H all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(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_2_finite__imageI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	288 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_356_less__irrefl__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	289 (all M_1 all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na) = hAPP(nat,nat,suc,zero_zero(nat)) <-> Na = hAPP(nat,nat,suc,zero_zero(nat)) & zero_zero(nat) = M_1 | hAPP(nat,nat,suc,zero_zero(nat)) = M_1 & Na = zero_zero(nat))) # label(fact_468_one__is__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	290 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	291 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_448_le0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	292 (all X all Y (X != 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),Y),X))))) # label(fact_355_linorder__neqE__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	293 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all C_1 all B (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) <-> 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),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1))))))) # label(fact_228_add__le__cancel__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	294 (all X_b all Y_3 ti(fun(X_b,bool),Y_3) = 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_3)) # label(fact_84_image__ident) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	295 (all N 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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K))))) # label(fact_40_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	296 (all X_c all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(X_c),B_2))))) # label(fact_46_finite__surj) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	297 (all I all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I))))) # label(fact_390_less__add__Suc2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	298 (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_95_subsetI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	299 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(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_160_finite__ne__induct) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	300 (all N hAPP(nat,nat,suc,N) != N) # label(fact_18_Suc__n__not__n) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	301 (all X_a (ord(X_a) -> (all C all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) -> (C = B_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_346_ord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	302 (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_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_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)))) # label(fact_91_insert__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	303 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na))))) # label(fact_393_less__Suc__eq__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	304 (all X_c all X_b all X_1 all A_3 all F all Z_1 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_1),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(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_197_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	305 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) <-> (exists K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) = Na))) # label(fact_257_le__iff__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	306 (all N_1 ((exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) -> 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(nat),N_1)))) # label(fact_98_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	307 (all X_c (minus(X_c) -> ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c)) = minus_minus(X_c))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	308 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_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),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))))))) # label(fact_307_add__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	309 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N) = hAPP(nat,nat,suc,N)) # label(fact_281_Suc__eq__plus1__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	310 (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].
1.44/1.72	311 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	312 (all I all K all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),K))) # label(fact_270_add__diff__assoc2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	313 (all G_1 all C_1 (hBOOL(hAPP(com,bool,wt,C_1)) -> ((all X_2 (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_2),u)) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X_2)),bot_bot(fun(x_a,bool))))))) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,C_1)),bot_bot(fun(x_a,bool)))))))) # label(fact_99_assms_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	314 (all P all Q (hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	315 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_415_psubset__card__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	316 (all X_a (linordered_semidom(X_a) -> (all B_1 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_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_454_pos__add__strict) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	317 (all X_c all X_b all A_3 all B_2 (hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2) = bot_bot(fun(sum_sum(X_b,X_c),bool)) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) & bot_bot(fun(X_c,bool)) = ti(fun(X_c,bool),B_2))) # label(fact_445_Plus__eq__empty__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	318 (all X_c all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2)) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2))))) # label(fact_440_card__Plus) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	319 (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_423_less__add__one) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	320 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	321 (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(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,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)) = 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,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,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_folding__one_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	322 (all M_1 all Na ((exists K_1 Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)))) # label(fact_391_less__iff__Suc__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	323 (all M all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) -> 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_2),M))))) # label(fact_259_trans__le__add1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	324 (all X_b all A_2 (bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_2) | (exists A_4 exists A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_4)) & ti(fun(X_b,bool),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_5),A_4))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2)))) # label(fact_151_finite_Osimps) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	325 (all Na all K_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na)) -> (M_1 = Na <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2))))) # label(fact_41_eq__diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	326 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c)) = finite_comp_fun_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	327 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(nat,nat,suc,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),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_191_card__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	328 (all X_b insert(X_b) = ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b))) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	329 (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_138_order__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	330 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1)) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)))) # label(fact_35_not__less__eq__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	331 (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_130_singleton__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	332 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_6_card__seteq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	333 (all X_a (ord(X_a) -> ord_less(X_a) = ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	334 (all Nat zero_zero(nat) != hAPP(nat,nat,suc,Nat)) # label(fact_485_nat_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	335 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_30_Suc__leD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	336 (all X_b all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat))) # label(fact_450_card__infinite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	337 (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_268_comp__fun__idem__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	338 (all X_b all X_c all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_443_finite__PlusD_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	339 (all X_c all X_b all 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(X_b,X_c,F,X_1) = ti(X_c,B) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),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_81_rev__image__eqI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	340 (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_173_Diff__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	341 (all T_2 all T_1 (finite_finite_1(T_2) & finite_finite_1(T_1) -> finite_finite_1(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	342 (all X_b all A_2 all C_2 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_2),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_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),D_2))))) # label(fact_89_insert__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	343 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)))) # label(fact_256_le__add1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	344 (all X_b all A_3 all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(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_181_finite__Diff__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	345 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_317_less__SucI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	346 (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_209_the__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	347 (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].
1.44/1.72	348 (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(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_162_folding__one_Oinsert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	349 (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(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_2 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_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_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_2),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_194_folding__one_Oclosed) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	350 (all X_b (ordere236663937imp_le(X_b) -> (all C_1 all A_2 all B (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),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)))))) # label(fact_229_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	351 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1)),Na)))) # label(fact_227_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	352 (all X_b all C_1 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),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)),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)))) # label(fact_202_DiffD1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	353 (all K all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> 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_2),K))))) # label(fact_298_add__less__mono1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	354 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)))) # label(fact_493_add__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	355 (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_410_psubset__imp__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	356 (all X_c all X_b all X_1 all A_3 all F all Z_1 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_1),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(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,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_207_folding__image__simple_Oinsert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	357 (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_286_termination__basic__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	358 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B all C_1 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1))))))) # label(fact_311_diff__eq__diff__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	359 (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_330_order__less__irrefl) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	360 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) # label(fact_280_Suc__eq__plus1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	361 (all X_b member(X_b) = ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))) # label(tsy_c_member_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	362 (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_97_order__refl) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	363 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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)))))) & (-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)))))))) # label(fact_219_card__Diff__singleton__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	364 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_490_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	365 (all X_c all X_b all B_2 all A_3 ((hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2))) & (-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))) -> hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = zero_zero(nat)))) # label(fact_446_card__Plus__conv__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	366 (all X_a (linordered_idom(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_424_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	367 (all X_b all A_2 all B all A_3 (ti(X_b,B) = 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),B),A_3))))) # label(fact_62_insert__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	368 (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_85_subset__insertI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	369 (all X_b (ab_group_add(X_b) -> (all A_2 all B all C_1 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) -> (ti(X_b,C_1) = ti(X_b,D_1) <-> ti(X_b,A_2) = ti(X_b,B)))))) # label(fact_186_diff__eq__diff__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	370 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B all C_1 all D_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),D_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))))))) # label(fact_157_diff__eq__diff__less__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	371 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> M != N)) # label(fact_357_less__not__refl2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	372 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) = zero_zero(nat)) # label(fact_469_diff__add__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	373 (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_51_equalityI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	374 (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_137_xt1_I5_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	375 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_325_less__imp__le__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	376 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) # label(fact_470_diff__is__0__eq_H) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	377 (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_176_Diff__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	378 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,suc,N) = M))) # label(fact_31_le__SucE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	379 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(X_b),A_3))))) # label(fact_168_finite__Diff2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	380 (all X_a (group_add(X_a) -> (all A_1 all B_1 ti(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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B_1)),B_1)))) # label(fact_266_diff__add__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	381 (all M_1 all Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1))))) # label(fact_322_not__less__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	382 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B_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),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)))))) # label(fact_234_add__le__imp__le__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	383 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_9_card__insert__disjoint) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	384 (all M all K 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),M),K)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)))) # label(fact_263_add__leD2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	385 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_313_Suc__lessD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	386 (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_117_bot__least) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	387 (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_184_diff__single__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	388 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	389 (all T_2 all T_1 (finite_finite_1(T_2) & finite_finite_1(T_1) -> finite_finite_1(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	390 (all X_b all A_3 all F all Na (ti(fun(X_b,bool),A_3) = 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)),Na))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)))) # label(fact_384_nat__seg__image__imp__finite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	391 (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_136_xt1_I6_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	392 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_395_le__imp__less__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	393 (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_220_one__reorient) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	394 (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_226_comp__fun__idem__remove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	395 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_3_finite_OinsertI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	396 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)))) # label(fact_23_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	397 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_476_diff__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	398 (all X_b all A_2 all B all C_1 all D_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),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),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),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),D_1),bot_bot(fun(X_b,bool)))) <-> ti(X_b,D_1) = ti(X_b,A_2) & ti(X_b,B) = ti(X_b,C_1) | ti(X_b,B) = ti(X_b,D_1) & ti(X_b,A_2) = ti(X_b,C_1))) # label(fact_120_doubleton__eq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	399 (all M all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) -> 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),M)),K))))) # label(fact_277_le__add__diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	400 (all X_b (order(X_b) -> (all Y_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) <-> ti(X_b,X_1) = ti(X_b,Y_1)))))) # label(fact_144_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	401 (all M all N all K all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_296_less__add__eq__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	402 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_237_add__Suc__shift) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	403 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	404 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B_1 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_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),plus_plus(X_a),A_1),B_1)),C)))) # label(fact_249_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	405 (all X_b all C_2 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_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),C_2))))) # label(fact_421_psubset__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	406 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_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_1),C))))))) # label(fact_230_add__right__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	407 (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(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),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)))))) # label(fact_416_psubset__insert__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	408 (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].
1.44/1.73	409 (all Pn (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn),u)) -> hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))))) # label(fact_156_assms_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	410 (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_364_linorder__le__less__linear) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	411 (all M all N (M = N | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_323_less__or__eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	412 (all X_b (linord219039673up_add(X_b) -> (all A_2 (zero_zero(X_b) = ti(X_b,A_2) <-> 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))))) # label(fact_494_double__zero__sym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	413 (all K all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K))))) # label(fact_21_le__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	414 (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].
1.44/1.73	415 (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].
1.44/1.73	416 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N))) # label(fact_36_Suc__n__not__le__n) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	417 (all X_b (linord219039673up_add(X_b) -> (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,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_eq(X_b),A_2),zero_zero(X_b))))))) # label(fact_460_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	418 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),bot_bot(fun(X_b,bool))))) # label(fact_104_finite_OemptyI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	419 (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) = 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)))))) # label(fact_178_insert__Diff__single) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	420 (all X_b all A_3 all B ((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),B),bot_bot(fun(X_b,bool))))) -> ti(X_b,B) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),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)),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),B),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),B),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(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),B),bot_bot(fun(X_b,bool))))))))) # label(fact_217_flat__lub__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	421 (all X_b all A_2 all 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),A_2),A_3)))) # label(fact_106_equals0D) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	422 (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_103_emptyE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	423 (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_368_leI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	424 (all X_b (finite_finite_1(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_14_finite__code) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	425 (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_379_order__less__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	426 (all I all J_2 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_2)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)))) # label(fact_295_add__lessD1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	427 (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)),one_one(X_a))))) # label(fact_452_zero__less__one) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	428 (all X_b bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse))) # label(fact_112_empty__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	429 (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)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_164_folding__one__idem_Oidem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	430 (all M all K all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))) # label(fact_254_diff__cancel2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	431 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_189_diff__card__le__card__Diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	432 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite(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_1_finite__Collect__subsets) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	433 (all X all Y (hAPP(nat,nat,suc,Y) = hAPP(nat,nat,suc,X) -> X = Y)) # label(fact_16_Suc__inject) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	434 (all X_b all F1 all F2 all Nat_2 hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),hAPP(nat,nat,suc,Nat_2)) = hAPP(nat,X_b,F2,Nat_2)) # label(fact_282_nat__case__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	435 (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_105_empty__subsetI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	436 (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(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))))) # label(fact_52_subsetD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	437 (all I all J_2 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),K)),J_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_2)),K)) # label(fact_25_diff__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	438 (all C all A_1 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B_1)) -> (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_1),C)))))) # label(fact_402_diff__less__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	439 (all K all L all I all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) -> 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_2),L)))))) # label(fact_297_add__less__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	440 (all X_b all X_1 all Y_1 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_1)))) = ti(X_b,X_1)) & (-hBOOL(Pa) -> ti(X_b,Y_1) = 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_1))))))) # label(fact_208_If__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	441 (all K_2 hBOOL(hAPP(fun(nat,bool),bool,finite_finite(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_2))))) # label(fact_12_finite__Collect__le__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	442 (all P (fTrue = ti(bool,P) | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	443 (all X_a (order(X_a) -> (all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) -> (ti(X_a,A_1) != ti(X_a,B_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))))))) # label(fact_377_order__le__neq__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	444 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_453_not__one__less__zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	445 (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_335_linorder__neqE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	446 (all Pa all I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite(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_386_finite__M__bounded__by__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	447 (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_287_termination__basic__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	448 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) # label(fact_243_nat__add__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	449 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)))) # label(fact_394_Suc__le__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	450 (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].
1.44/1.73	451 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B_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_1),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)))))) # label(fact_233_add__le__imp__le__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	452 (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(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_183_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	453 (all J_2 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_2),I)),I))) # label(fact_302_not__add__less2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	454 (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_431_dense__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	455 (all X_c all X_b all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(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,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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))))))))))) # label(fact_49_pigeonhole__infinite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	456 (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_376_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	457 (all X_b all A_3 ((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))) <-> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_110_ex__in__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	458 (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_293_termination__basic__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	459 (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].
1.44/1.73	460 (all X_b all F1 all F2 ti(X_b,F1) = hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),zero_zero(nat))) # label(fact_491_nat__case__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	461 (all X_a (ord(X_a) -> (all C all A_1 all B_1 (A_1 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_143_ord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	462 (all X_b (linorder(X_b) -> (all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) -> (ti(X_b,X_1) = ti(X_b,Y_1) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))))))) # label(fact_375_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	463 (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].
1.44/1.73	464 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (N != M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_324_le__neq__implies__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	465 (all X_a (order(X_a) -> (all C all B_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1)) -> (ti(X_a,C) = ti(X_a,B_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_140_xt1_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	466 (all X_b all B_2 all C_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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)),A_3),B_2)))))) # label(fact_200_DiffI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	467 (all I_1 all K_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),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),I_1),K_2)),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_2)))))) # label(fact_274_le__diff__conv2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	468 (all X_a (order(X_a) -> (all B_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1)) -> (ti(X_a,B_1) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1))))))) # label(fact_378_xt1_I11_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	469 (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_161_the__elem__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	470 (all X_b ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b)) = nat_case(X_b)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	471 (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)) -> -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_78_equalityE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	472 (all X_b (finite_finite_1(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))))) # label(fact_15_finite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	473 (all M_1 all Na (M_1 = Na | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na))))) # label(fact_321_less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	474 (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_336_less__imp__neq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	475 (all M_1 all K_2 all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2) <-> M_1 = Na)) # label(fact_239_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	476 (all X_c all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_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)),C_3),A_3)) & 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),C_3) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_3))))))) # label(fact_47_finite__subset__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	477 (all M all N 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),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K)) # label(fact_241_nat__add__assoc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	478 (all X_b (linorder(X_b) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) <-> ti(X_b,Y_1) = ti(X_b,X_1)))))) # label(fact_370_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	479 (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_147_linorder__linear) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	480 (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].
1.44/1.73	481 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	482 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_474_diff__self__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	483 (all X_a (order(X_a) -> (all A_1 all B_1 (ti(X_a,A_1) != ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1))))))) # label(fact_372_xt1_I12_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	484 (all X_b (linorder(X_b) -> (all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) <-> ti(X_b,X_1) != ti(X_b,Y_1))))) # label(fact_331_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	485 (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].
1.44/1.73	486 (all X_b all X_c all X_1 all Z_1 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),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1))) # label(fact_238_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	487 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_481_Suc__neq__Zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	488 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_449_zero__less__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	489 (all X_c all X_b all F all A_2 all 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)) = 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))) # label(fact_90_image__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	490 (all X_b all B_2 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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(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))) = 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)))))) # label(fact_223_card__Diff__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	491 (all X_b finite_finite(X_b) = ti(fun(fun(X_b,bool),bool),finite_finite(X_b))) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	492 (all X_b all X_1 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),X_1),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),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2)))) # label(fact_86_insert__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	493 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)))) # label(fact_255_le__add2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	494 (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_93_image__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	495 (all I all K all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),K))) # label(fact_269_diff__add__assoc2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	496 (all N all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_3)) -> (exists M_2 M_3 = hAPP(nat,nat,suc,M_2)))) # label(fact_56_Suc__le__D) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	497 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_192_card__Diff1__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	498 (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)) -> 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),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_180_insert__Diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	499 (all X_b (ab_group_add(X_b) -> (all A_2 all B (zero_zero(X_b) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) <-> ti(X_b,B) = ti(X_b,A_2))))) # label(fact_479_eq__iff__diff__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	500 (all Na all N_1 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1)))) # label(fact_425_bounded__nat__set__is__finite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	501 (all X_b (ordere216010020id_add(X_b) -> (all Y_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),X_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),Y_1)) -> (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_1) = zero_zero(X_b) <-> ti(X_b,Y_1) = zero_zero(X_b) & zero_zero(X_b) = ti(X_b,X_1))))))) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	502 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_400_add__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	503 (all X_b all X_c (order(X_b) & order(X_c) -> (all C_1 all A_2 all F all B (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,B))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),B),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_2)) -> 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_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))))))))) # label(fact_437_order__less__le__subst1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	504 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_5_card__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	505 (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_73_set__mp) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	506 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_218_card__Diff__singleton) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	507 (all X_a (order(X_a) -> (all C all A_1 all B_1 (ti(X_a,A_1) = ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_142_xt1_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	508 (all X_b all Pa ti(fun(X_b,bool),Pa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) # label(fact_76_Collect__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	509 (all M_1 all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na) = hAPP(nat,nat,suc,zero_zero(nat)) <-> zero_zero(nat) = M_1 & hAPP(nat,nat,suc,zero_zero(nat)) = Na | M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & zero_zero(nat) = Na)) # label(fact_467_add__is__1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	510 (all X_a (ordere216010020id_add(X_a) -> (all B_1 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_eq(X_a),B_1),zero_zero(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),plus_plus(X_a),A_1),B_1)),zero_zero(X_a)))))))) # label(fact_465_add__nonpos__nonpos) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	511 (all Na Na = 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)),Na)))) # label(fact_385_card__Collect__less__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	512 (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_198_the__sym__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	513 (all X_b (order(X_b) -> (all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) & ti(X_b,Y_1) != ti(X_b,X_1) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)))))) # label(fact_365_order__less__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	514 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (exists K_1 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1))))) # label(fact_407_less__imp__Suc__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	515 (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_139_order__antisym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	516 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_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),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))))))) # label(fact_231_add__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	517 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_7_card__insert__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	518 (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_80_imageI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	519 (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(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),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_159_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	520 (all X_b (preorder(X_b) -> (all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) & -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)))))) # label(fact_366_less__le__not__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	521 (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_75_mem__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	522 (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_351_linorder__cases) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	523 (all Pa 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,Pa,J_1)) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I_2))) -> hBOOL(hAPP(nat,bool,Pa,I_2))))) -> hBOOL(hAPP(nat,bool,Pa,I_1)))))) # label(fact_406_inc__induct) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	524 (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(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_169_insert__Diff1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	525 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_188_card__Diff__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	526 (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_102_le__funE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	527 (all J_1 all K_2 all 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_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),J_1),K_2)),I_1)))) # label(fact_278_le__diff__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	528 (all X_b all X_c sum_Plus(X_b,X_c) = ti(fun(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool))),sum_Plus(X_b,X_c))) # label(tsy_c_Sum__Type_OPlus_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	529 (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_337_order__less__not__sym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	530 (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].
1.44/1.73	531 (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,X_2) = ti(X_b,A_2))) -> ti(X_b,A_2) = hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))) # label(fact_210_the__equality) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	532 (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_107_Collect__empty__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.73	533 (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_111_all__not__in__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	534 (all I all J_2 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_2),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_2)),K)) # label(fact_252_diff__diff__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	535 (all X_b all Y_1 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,A_3,X_1)) | ti(X_b,X_1) = ti(X_b,Y_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_1),A_3),X_1)))) # label(fact_63_insert__code) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	536 (all X_a (monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)))) # label(fact_492_add__0__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	537 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> 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_1),D)))))))) # label(fact_306_add__strict__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	538 (all X_a (cancel_semigroup_add(X_a) -> plus_plus(X_a) = ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	539 (all X_b all X_c all B_2 all F all A_3 ((exists 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)) & 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) = 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),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_92_subset__image__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	540 (all X_b (linorder(X_b) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)))))) # label(fact_362_linorder__not__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	541 (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_360_not__less__bot) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	542 (all X_c all X_b all F all Z_1 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_1),G),F_2)) -> ti(X_b,Z_1) = hAPP(fun(X_c,bool),X_b,F_2,bot_bot(fun(X_c,bool))))) # label(fact_206_folding__image__simple_Oempty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	543 (all X_b all X_1 all Y_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),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_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),Y_1),A_3))) # label(fact_61_insert__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	544 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(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_eq(X_b),zero_zero(X_b)),A_2)))))) # label(fact_459_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	545 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_221_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	546 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))) # label(fact_273_le__add__diff__inverse2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	547 (all X_b all N_1 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_2 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_2)) = hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_1)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_1) -> 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_1)) = hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_2,N_1))))))) # label(fact_193_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	548 (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_87_subset__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	549 (all N all J_2 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),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_2),N)),K)))) # label(fact_329_less__imp__diff__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	550 (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_145_order__eq__refl) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	551 (all I_1 all J_1 all F ((all I_2 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J))))) -> (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_427_less__mono__imp__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	552 (all X_b all C_2 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_2)) -> ti(fun(X_b,bool),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),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_2),A_3))))) # label(fact_171_double__diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	553 (all X_b all Pa all Q_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_1)))))) # label(fact_26_finite__Collect__disjI) # label(axiom) # label(non_clause).  [assumption].
1.54/1.81	554 (all X_b 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),bot_bot(fun(X_b,bool)))))) # label(fact_124_subset__empty) # label(axiom) # label(non_clause).  [assumption].
1.54/1.81	555 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_484_Suc__not__Zero) # label(axiom) # label(non_clause).  [assumption].
1.54/1.81	556 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all B (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) <-> 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),minus_minus(X_b),A_2),B)),zero_zero(X_b))))))) # label(fact_466_le__iff__diff__le__0) # label(axiom) # label(non_clause).  [assumption].
1.54/1.81	557 (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_339_order__less__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
1.54/1.81	
1.54/1.81	============================== end of process non-clausal formulas ===
1.54/1.81	
1.54/1.81	============================== PROCESS INITIAL CLAUSES ===============
1.54/1.81	
1.54/1.81	============================== PREDICATE ELIMINATION =================
1.54/1.81	558 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom).  [assumption].
1.54/1.81	559 -monoid_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom).  [clausify(6)].
1.54/1.81	Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)).  [resolve(558,a,559,a)].
1.54/1.81	560 -monoid_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) # label(fact_495_add__0__right) # label(axiom).  [clausify(120)].
1.54/1.81	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)).  [resolve(560,a,558,a)].
1.54/1.81	561 -monoid_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) # label(fact_492_add__0__left) # label(axiom).  [clausify(536)].
1.54/1.81	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A).  [resolve(561,a,558,a)].
1.54/1.81	562 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
1.54/1.81	563 -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_232_add__mono) # label(axiom).  [clausify(14)].
1.54/1.81	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(562,a,563,a)].
1.54/1.81	564 -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_230_add__right__mono) # label(axiom).  [clausify(406)].
1.54/1.81	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),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))).  [resolve(564,a,562,a)].
1.54/1.81	565 -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_231_add__left__mono) # label(axiom).  [clausify(516)].
1.54/1.81	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(565,a,562,a)].
1.57/1.83	566 -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_309_add__less__cancel__left) # label(axiom).  [clausify(24)].
1.57/1.83	567 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
1.57/1.83	568 -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_309_add__less__cancel__left) # label(axiom).  [clausify(24)].
1.57/1.83	569 -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_304_add__less__imp__less__left) # label(axiom).  [clausify(67)].
1.57/1.83	570 -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_305_add__less__imp__less__right) # label(axiom).  [clausify(72)].
1.57/1.83	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(570,a,567,a)].
1.57/1.83	571 -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_310_add__less__cancel__right) # label(axiom).  [clausify(104)].
1.57/1.83	572 -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_310_add__less__cancel__right) # label(axiom).  [clausify(104)].
1.57/1.83	573 -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),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_228_add__le__cancel__right) # label(axiom).  [clausify(293)].
1.57/1.83	574 -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),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_228_add__le__cancel__right) # label(axiom).  [clausify(293)].
1.57/1.83	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),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))).  [resolve(574,a,567,a)].
1.57/1.83	575 -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_229_add__le__cancel__left) # label(axiom).  [clausify(350)].
1.57/1.83	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),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(575,a,567,a)].
1.57/1.83	576 -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_229_add__le__cancel__left) # label(axiom).  [clausify(350)].
1.64/1.91	577 -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_234_add__le__imp__le__left) # label(axiom).  [clausify(382)].
1.64/1.91	578 -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_233_add__le__imp__le__right) # label(axiom).  [clausify(451)].
1.64/1.91	579 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom).  [clausify(180)].
1.64/1.91	580 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom).  [assumption].
1.64/1.91	Derived: zero_zero(nat) = ti(nat,zero_zero(nat)).  [resolve(579,a,580,a)].
1.64/1.91	581 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom).  [assumption].
1.64/1.91	582 -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_135_linorder__le__cases) # label(axiom).  [clausify(33)].
1.64/1.91	583 -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,C) = ti(A,B) # label(fact_332_not__less__iff__gr__or__eq) # label(axiom).  [clausify(47)].
1.64/1.91	584 -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_332_not__less__iff__gr__or__eq) # label(axiom).  [clausify(47)].
1.64/1.91	585 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_332_not__less__iff__gr__or__eq) # label(axiom).  [clausify(47)].
1.64/1.91	586 -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_369_not__leE) # label(axiom).  [clausify(165)].
1.64/1.91	587 -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_334_linorder__antisym__conv3) # label(axiom).  [clausify(171)].
1.64/1.91	588 -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_334_linorder__antisym__conv3) # label(axiom).  [clausify(171)].
1.64/1.91	589 -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_333_linorder__less__linear) # label(axiom).  [clausify(186)].
1.64/1.91	590 -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_373_leD) # label(axiom).  [clausify(246)].
1.64/1.91	591 -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_363_linorder__not__le) # label(axiom).  [clausify(273)].
1.64/1.91	592 -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_363_linorder__not__le) # label(axiom).  [clausify(273)].
1.64/1.91	593 -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_364_linorder__le__less__linear) # label(axiom).  [clausify(410)].
1.64/1.91	594 -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_368_leI) # label(axiom).  [clausify(423)].
1.64/1.91	595 -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_335_linorder__neqE) # label(axiom).  [clausify(445)].
1.64/1.92	596 -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_375_linorder__antisym__conv2) # label(axiom).  [clausify(462)].
1.64/1.92	597 -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_375_linorder__antisym__conv2) # label(axiom).  [clausify(462)].
1.64/1.92	598 -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),B),C)) | ti(A,C) = ti(A,B) # label(fact_370_linorder__antisym__conv1) # label(axiom).  [clausify(478)].
1.64/1.92	599 -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),B),C)) | ti(A,C) != ti(A,B) # label(fact_370_linorder__antisym__conv1) # label(axiom).  [clausify(478)].
1.64/1.92	600 -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_147_linorder__linear) # label(axiom).  [clausify(479)].
1.64/1.92	601 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_331_linorder__neq__iff) # label(axiom).  [clausify(484)].
1.64/1.92	602 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_331_linorder__neq__iff) # label(axiom).  [clausify(484)].
1.64/1.92	603 -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,C) = ti(A,B) # label(fact_331_linorder__neq__iff) # label(axiom).  [clausify(484)].
1.64/1.92	604 -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_351_linorder__cases) # label(axiom).  [clausify(522)].
1.64/1.92	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(581,a,582,a)].
1.64/1.92	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)) | ti(nat,B) = ti(nat,A).  [resolve(581,a,583,a)].
1.64/1.92	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(581,a,584,a)].
1.64/1.92	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A).  [resolve(581,a,585,a)].
1.64/1.92	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),B),A)).  [resolve(581,a,586,a)].
1.64/1.92	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),B),A)).  [resolve(581,a,590,a)].
1.64/1.92	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(581,a,597,a)].
1.64/1.92	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_eq(nat),A),B)) | ti(nat,B) != ti(nat,A).  [resolve(581,a,599,a)].
1.64/1.92	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B).  [resolve(581,a,602,a)].
1.64/1.92	605 -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_362_linorder__not__less) # label(axiom).  [clausify(540)].
1.64/1.92	606 -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_362_linorder__not__less) # label(axiom).  [clausify(540)].
1.64/1.92	607 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.64/1.92	608 -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_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_461_add__nonneg__nonneg) # label(axiom).  [clausify(34)].
1.64/1.95	609 -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_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_463_add__increasing) # label(axiom).  [clausify(50)].
1.64/1.95	610 -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_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B))) # label(fact_464_add__increasing2) # label(axiom).  [clausify(205)].
1.64/1.95	611 -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_eq(A),zero_zero(A)),C)) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) | zero_zero(A) = ti(A,C) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom).  [clausify(501)].
1.64/1.95	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_eq(nat),zero_zero(nat)),B)) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) | zero_zero(nat) = ti(nat,B).  [resolve(611,a,607,a)].
1.64/1.95	612 -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_eq(A),zero_zero(A)),C)) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) | zero_zero(A) = ti(A,B) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom).  [clausify(501)].
1.64/1.95	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_eq(nat),zero_zero(nat)),B)) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) | zero_zero(nat) = ti(nat,A).  [resolve(612,a,607,a)].
1.64/1.95	613 -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_eq(A),zero_zero(A)),C)) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) | zero_zero(A) != ti(A,C) | zero_zero(A) != ti(A,B) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom).  [clausify(501)].
1.64/1.95	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_eq(nat),zero_zero(nat)),B)) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) | zero_zero(nat) != ti(nat,B) | zero_zero(nat) != ti(nat,A).  [resolve(613,a,607,a)].
1.64/1.95	614 -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_eq(A),C),zero_zero(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)),zero_zero(A))) # label(fact_465_add__nonpos__nonpos) # label(axiom).  [clausify(510)].
1.64/1.95	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_eq(nat),B),zero_zero(nat))) | 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)),zero_zero(nat))).  [resolve(614,a,607,a)].
1.64/1.95	615 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
1.64/1.95	616 -cancel_semigroup_add(A) | ti(A,B) != ti(A,C) | 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_247_add__right__cancel) # label(axiom).  [clausify(44)].
1.64/1.95	617 -cancel_semigroup_add(A) | ti(A,B) = ti(A,C) | 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_247_add__right__cancel) # label(axiom).  [clausify(44)].
1.72/2.01	618 -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_244_add__right__imp__eq) # label(axiom).  [clausify(74)].
1.72/2.01	619 -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_246_add__left__imp__eq) # label(axiom).  [clausify(157)].
1.72/2.01	Derived: ti(nat,A) != ti(nat,B) | 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(615,a,616,a)].
1.72/2.01	Derived: ti(nat,A) = ti(nat,B) | 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(615,a,617,a)].
1.72/2.01	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(615,a,619,a)].
1.72/2.01	620 -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_248_add__left__cancel) # label(axiom).  [clausify(265)].
1.72/2.01	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(620,a,615,a)].
1.72/2.01	621 -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_248_add__left__cancel) # label(axiom).  [clausify(265)].
1.72/2.01	622 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom).  [clausify(538)].
1.72/2.01	623 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom).  [assumption].
1.72/2.01	624 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom).  [clausify(63)].
1.72/2.01	Derived: one_one(nat) = ti(nat,one_one(nat)).  [resolve(623,a,624,a)].
1.72/2.01	625 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.72/2.01	626 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_456_zero__le__one) # label(axiom).  [clausify(77)].
1.72/2.01	627 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_455_not__one__le__zero) # label(axiom).  [clausify(94)].
1.72/2.01	628 -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_454_pos__add__strict) # label(axiom).  [clausify(316)].
1.72/2.01	629 -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_423_less__add__one) # label(axiom).  [clausify(319)].
1.72/2.01	630 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_452_zero__less__one) # label(axiom).  [clausify(427)].
1.72/2.01	631 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_453_not__one__less__zero) # label(axiom).  [clausify(444)].
1.72/2.01	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))).  [resolve(625,a,626,a)].
1.72/2.01	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))).  [resolve(625,a,627,a)].
1.72/2.01	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),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(625,a,628,a)].
1.72/2.01	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(625,a,629,a)].
1.72/2.01	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))).  [resolve(625,a,630,a)].
1.72/2.06	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))).  [resolve(625,a,631,a)].
1.72/2.06	632 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
1.72/2.06	633 -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_308_add__strict__right__mono) # label(axiom).  [clausify(84)].
1.72/2.06	634 -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_387_add__le__less__mono) # label(axiom).  [clausify(151)].
1.72/2.06	635 -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_388_add__less__le__mono) # label(axiom).  [clausify(164)].
1.72/2.06	636 -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_307_add__strict__left__mono) # label(axiom).  [clausify(308)].
1.72/2.06	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),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))).  [resolve(632,a,633,a)].
1.72/2.06	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(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(632,a,634,a)].
1.72/2.06	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(632,a,635,a)].
1.72/2.06	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(632,a,636,a)].
1.72/2.06	637 -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_306_add__strict__mono) # label(axiom).  [clausify(537)].
1.72/2.06	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(637,a,632,a)].
1.72/2.06	638 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom).  [assumption].
1.72/2.06	639 -zero_neq_one(A) | one_one(A) != zero_zero(A) # label(fact_458_zero__neq__one) # label(axiom).  [clausify(86)].
1.72/2.06	640 -zero_neq_one(A) | one_one(A) != zero_zero(A) # label(fact_457_one__neq__zero) # label(axiom).  [clausify(115)].
1.72/2.06	Derived: one_one(nat) != zero_zero(nat).  [resolve(638,a,639,a)].
1.72/2.06	641 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
4.19/4.46	642 -comm_monoid_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) # label(fact_496_add_Ocomm__neutral) # label(axiom).  [clausify(210)].
4.19/4.46	643 -comm_monoid_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) # label(fact_493_add__0) # label(axiom).  [clausify(354)].
4.19/4.46	644 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
4.19/4.46	645 -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_245_add__imp__eq) # label(axiom).  [clausify(221)].
4.19/4.46	646 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
4.19/4.46	647 -ab_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(274)].
4.19/4.46	648 -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_249_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom).  [clausify(404)].
4.19/4.46	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(646,a,648,a)].
4.19/4.46	
4.19/4.46	============================== end predicate elimination =============
4.19/4.46	
4.19/4.46	Auto_denials:  (non-Horn, no changes).
4.19/4.46	
4.19/4.46	Term ordering decisions:
4.19/4.46	Function symbol KB weights:  bool=1. nat=1. suc=1. x_a=1. pname=1. com=1. fconj=1. fdisj=1. fimplies=1. u=1. mgt_call=1. p=1. fNot=1. fFalse=1. mgt=1. wt=1. body=1. g=1. na=1. fTrue=1. pn=1. fun=1. ti=1. image=1. sum_sum=1. sum_Plus=1. finite1357897459simple=1. combk=1. finite_comp_fun_idem=1. f6=1. f7=1. f12=1. f13=1. f18=1. f24=1. f25=1. f27=1. f34=1. f53=1. f54=1. f56=1. f57=1. f58=1. f59=1. f64=1. f66=1. f67=1. f70=1. f73=1. f74=1. ord_less_eq=1. ord_less=1. insert=1. minus_minus=1. bot_bot=1. plus_plus=1. finite_finite=1. member=1. zero_zero=1. finite_card=1. collect=1. fequal=1. one_one=1. the=1. finite_folding_one=1. finite2073411215e_idem=1. nat_case=1. option=1. combi=1. partial_flat_lub=1. the_1=1. the_elem=1. undefined=1. f26=1. f55=1. combc=1. combb=1. combs=1. f3=1. f4=1. f5=1. f10=1. f20=1. f21=1. f22=1. f23=1. f32=1. f42=1. f49=1. f50=1. f51=1. f52=1. f71=1. f72=1. f78=1. f79=1. hAPP=1. f2=1. f15=1. f19=1. f28=1. f33=1. f40=1. f41=1. f45=1. f48=1. f60=1. f61=1. f63=1. f11=1. f29=1. f35=1. f65=1. f75=1. f76=1. f77=1. f8=1. f9=1. f16=1. f17=1. f30=1. f31=1. f36=1. f37=1. f38=1. f39=1. f43=1. f44=1. f46=1. f47=1. f68=1. f69=1. f14=1.
4.19/4.46	
4.19/4.46	============================== end of process initial clauses ========
4.19/4.46	
4.19/4.46	============================== CLAUSES FOR SEARCH ====================
4.19/4.46	
4.19/4.46	============================== end of clauses for search =============
4.19/4.46	
4.19/4.46	============================== SEARCH ================================
4.19/4.46	
4.19/4.46	% Starting search at 0.74 seconds.
4.19/4.46	
4.19/4.46	Low Water (keep): wt=148.000, iters=3403
4.19/4.46	
4.19/4.46	Low Water (keep): wt=139.000, iters=3374
4.19/4.46	
4.19/4.46	Low Water (keep): wt=136.000, iters=3374
4.19/4.46	
4.19/4.46	Low Water (keep): wt=135.000, iters=3390
4.19/4.46	
4.19/4.46	Low Water (keep): wt=133.000, iters=3558
4.19/4.46	
4.19/4.46	Low Water (keep): wt=132.000, iters=3548
4.19/4.46	
4.19/4.46	Low Water (keep): wt=122.000, iters=3381
4.19/4.46	
4.19/4.46	Low Water (keep): wt=115.000, iters=3368
4.19/4.46	
4.19/4.46	Low Water (keep): wt=110.000, iters=3389
4.19/4.46	
4.19/4.46	Low Water (keep): wt=109.000, iters=3365
4.19/4.46	
4.19/4.46	Low Water (keep): wt=108.000, iters=3520
4.19/4.46	
4.19/4.46	Low Water (keep): wt=102.000, iters=3352
4.19/4.46	
4.19/4.46	Low Water (keep): wt=100.000, iters=3373
4.19/4.46	
4.19/4.46	Low Water (keep): wt=99.000, iters=3353
4.19/4.46	
4.19/4.46	Low Water (keep): wt=98.000, iters=3387
4.19/4.46	
4.19/4.46	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 61 (0.00 of 2.79 sec).
4.19/4.46	
4.19/4.46	Low Water (keep): wt=96.000, iters=3378
4.19/4.46	
4.19/4.46	Low Water (keep): wt=95.000, iters=3382
4.19/4.46	
4.19/4.46	Low Water (keep): wt=92.000, iters=3341
4.19/4.46	
4.19/4.46	Low Water (keep): wt=91.000, iters=3357
4.19/4.46	
4.19/4.46	Low Water (keep): wt=90.000, iters=3373
4.19/4.46	
4.19/4.46	Low Water (keep): wt=89.000, iters=3345
81.22/81.58	
81.22/81.58	Low Water (keep): wt=88.000, iters=3335
81.22/81.58	
81.22/81.58	Low Water (keep): wt=87.000, iters=3440
81.22/81.58	
81.22/81.58	Low Water (keep): wt=86.000, iters=3387
81.22/81.58	
81.22/81.58	Low Water (keep): wt=85.000, iters=3356
81.22/81.58	
81.22/81.58	Low Water (keep): wt=83.000, iters=3339
81.22/81.58	
81.22/81.58	Low Water (keep): wt=81.000, iters=3358
81.22/81.58	
81.22/81.58	Low Water (keep): wt=79.000, iters=3448
81.22/81.58	
81.22/81.58	Low Water (keep): wt=76.000, iters=3379
81.22/81.58	
81.22/81.58	Low Water (keep): wt=75.000, iters=3346
81.22/81.58	
81.22/81.58	Low Water (keep): wt=74.000, iters=3402
81.22/81.58	
81.22/81.58	Low Water (keep): wt=72.000, iters=3375
81.22/81.58	
81.22/81.58	Low Water (keep): wt=71.000, iters=3405
81.22/81.58	
81.22/81.58	Low Water (keep): wt=70.000, iters=3424
81.22/81.58	
81.22/81.58	Low Water (keep): wt=65.000, iters=3339
81.22/81.58	
81.22/81.58	Low Water (keep): wt=64.000, iters=3348
81.22/81.58	
81.22/81.58	Low Water (keep): wt=62.000, iters=3441
81.22/81.58	
81.22/81.58	Low Water (keep): wt=57.000, iters=3381
81.22/81.58	
81.22/81.58	Low Water (keep): wt=55.000, iters=3335
81.22/81.58	
81.22/81.58	Low Water (keep): wt=53.000, iters=3336
81.22/81.58	
81.22/81.58	Low Water (keep): wt=51.000, iters=3394
81.22/81.58	
81.22/81.58	Low Water (keep): wt=50.000, iters=3508
81.22/81.58	
81.22/81.58	Low Water (keep): wt=49.000, iters=3405
81.22/81.58	
81.22/81.58	Low Water (keep): wt=46.000, iters=3341
81.22/81.58	
81.22/81.58	Low Water (keep): wt=39.000, iters=3348
81.22/81.58	
81.22/81.58	Low Water (keep): wt=38.000, iters=3447
81.22/81.58	
81.22/81.58	Low Water (keep): wt=37.000, iters=3548
81.22/81.58	
81.22/81.58	Low Water (keep): wt=32.000, iters=3448
81.22/81.58	
81.22/81.58	Low Water (keep): wt=24.000, iters=3345
81.22/81.58	
81.22/81.58	Low Water (keep): wt=20.000, iters=3384
81.22/81.58	
81.22/81.58	Low Water (keep): wt=16.000, iters=3360
81.22/81.58	
81.22/81.58	Low Water (keep): wt=14.000, iters=3334
81.22/81.58	
81.22/81.58	Low Water (displace): id=2663, wt=200.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=5346, wt=196.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=12204, wt=190.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13099, wt=183.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13078, wt=182.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13079, wt=181.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=10948, wt=173.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13311, wt=169.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13206, wt=167.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13007, wt=166.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13018, wt=164.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=8194, wt=162.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13101, wt=161.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13055, wt=159.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=10963, wt=156.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=11324, wt=155.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13160, wt=153.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13313, wt=147.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13204, wt=145.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=11325, wt=143.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=11766, wt=142.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13006, wt=141.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13100, wt=139.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13030, wt=138.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13068, wt=133.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13692, wt=129.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13371, wt=128.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=12999, wt=127.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13518, wt=126.000
81.22/81.58	
81.22/81.58	Low Water (displace): id=13811, wt=12.000
81.22/81.58	
81.22/81.58	============================== PROOF =================================
81.22/81.58	% SZS status Theorem
81.22/81.58	% SZS output start Refutation
81.22/81.58	
81.22/81.58	% Proof 1 at 78.65 (+ 1.32) seconds.
81.22/81.58	% Length of proof is 10.
81.22/81.58	% Level of proof is 3.
81.22/81.58	% Maximum clause weight is 87.000.
81.22/81.58	% Given clauses 10392.
81.22/81.58	
81.22/81.58	302 (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_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_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)))) # label(fact_91_insert__image) # label(axiom) # label(non_clause).  [assumption].
81.22/81.58	342 (all X_b all A_2 all C_2 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_2),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_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),D_2))))) # label(fact_89_insert__mono) # label(axiom) # label(non_clause).  [assumption].
81.22/81.58	979 hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) # label(conj_1) # label(hypothesis).  [assumption].
81.22/81.58	1121 -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hAPP(fun(D,bool),fun(D,bool),hAPP(D,fun(fun(D,bool),fun(D,bool)),insert(D),hAPP(A,D,E,B)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C)) = hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C) # label(fact_91_insert__image) # label(axiom).  [clausify(302)].
81.22/81.58	1186 hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)) # label(conj_4) # label(hypothesis).  [assumption].
81.22/81.58	1200 -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,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),C))) # label(fact_89_insert__mono) # label(axiom).  [clausify(342)].
81.22/81.58	1526 -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) # label(conj_6) # label(negated_conjecture).  [assumption].
81.22/81.58	3468 hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),hAPP(pname,A,B,pn)),hAPP(fun(pname,bool),fun(A,bool),hAPP(fun(pname,A),fun(fun(pname,bool),fun(A,bool)),image(pname,A),B),u)) = hAPP(fun(pname,bool),fun(A,bool),hAPP(fun(pname,A),fun(fun(pname,bool),fun(A,bool)),image(pname,A),B),u).  [resolve(1186,a,1121,a)].
81.22/81.58	3541 hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),A),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),A),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))).  [resolve(1200,a,979,a)].
81.22/81.58	128436 $F.  [para(3468(a,1),3541(a,1,4)),unit_del(a,1526)].
81.22/81.58	
81.22/81.58	% SZS output end Refutation
81.22/81.58	============================== end of proof ==========================
81.22/81.58	
81.22/81.58	============================== STATISTICS ============================
81.22/81.58	
81.22/81.58	Given=10392. Generated=2144790. Kept=127485. proofs=1.
81.22/81.58	Usable=10261. Sos=9996. Demods=438. Limbo=0, Disabled=108093. Hints=0.
81.22/81.58	Megabytes=361.37.
81.22/81.58	User_CPU=78.65, System_CPU=1.32, Wall_clock=80.
81.22/81.58	
81.22/81.58	============================== end of statistics =====================
81.22/81.58	
81.22/81.58	============================== end of search =========================
81.22/81.58	
81.22/81.58	THEOREM PROVED
81.22/81.58	% SZS status Theorem
81.22/81.58	
81.22/81.58	Exiting with 1 proof.
81.22/81.58	
81.22/81.58	Process 10263 exit (max_proofs) Thu Jul  2 07:54:17 2020
81.22/81.58	Prover9 interrupted
81.22/81.58	EOF