0.00/0.10	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.11	% Command  : tptp2X_and_run_prover9 %d %s
0.10/0.30	% Computer : n008.cluster.edu
0.10/0.30	% Model    : x86_64 x86_64
0.10/0.30	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.30	% Memory   : 8042.1875MB
0.10/0.30	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.30	% CPULimit : 960
0.10/0.30	% WCLimit  : 120
0.10/0.30	% DateTime : Tue Aug  9 05:10:08 EDT 2022
0.10/0.30	% CPUTime  : 
1.33/1.68	============================== Prover9 ===============================
1.33/1.68	Prover9 (32) version 2009-11A, November 2009.
1.33/1.68	Process 25589 was started by sandbox2 on n008.cluster.edu,
1.33/1.68	Tue Aug  9 05:10:10 2022
1.33/1.68	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_25434_n008.cluster.edu".
1.33/1.68	============================== end of head ===========================
1.33/1.68	
1.33/1.68	============================== INPUT =================================
1.33/1.68	
1.33/1.68	% Reading from file /tmp/Prover9_25434_n008.cluster.edu
1.33/1.68	
1.33/1.68	set(prolog_style_variables).
1.33/1.68	set(auto2).
1.33/1.68	    % set(auto2) -> set(auto).
1.33/1.68	    % set(auto) -> set(auto_inference).
1.33/1.68	    % set(auto) -> set(auto_setup).
1.33/1.68	    % set(auto_setup) -> set(predicate_elim).
1.33/1.68	    % set(auto_setup) -> assign(eq_defs, unfold).
1.33/1.68	    % set(auto) -> set(auto_limits).
1.33/1.68	    % set(auto_limits) -> assign(max_weight, "100.000").
1.33/1.68	    % set(auto_limits) -> assign(sos_limit, 20000).
1.33/1.68	    % set(auto) -> set(auto_denials).
1.33/1.68	    % set(auto) -> set(auto_process).
1.33/1.68	    % set(auto2) -> assign(new_constants, 1).
1.33/1.68	    % set(auto2) -> assign(fold_denial_max, 3).
1.33/1.68	    % set(auto2) -> assign(max_weight, "200.000").
1.33/1.68	    % set(auto2) -> assign(max_hours, 1).
1.33/1.68	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
1.33/1.68	    % set(auto2) -> assign(max_seconds, 0).
1.33/1.68	    % set(auto2) -> assign(max_minutes, 5).
1.33/1.68	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
1.33/1.68	    % set(auto2) -> set(sort_initial_sos).
1.33/1.68	    % set(auto2) -> assign(sos_limit, -1).
1.33/1.68	    % set(auto2) -> assign(lrs_ticks, 3000).
1.33/1.68	    % set(auto2) -> assign(max_megs, 400).
1.33/1.68	    % set(auto2) -> assign(stats, some).
1.33/1.68	    % set(auto2) -> clear(echo_input).
1.33/1.68	    % set(auto2) -> set(quiet).
1.33/1.68	    % set(auto2) -> clear(print_initial_clauses).
1.33/1.68	    % set(auto2) -> clear(print_given).
1.33/1.68	assign(lrs_ticks,-1).
1.33/1.68	assign(sos_limit,10000).
1.33/1.68	assign(order,kbo).
1.33/1.68	set(lex_order_vars).
1.33/1.68	clear(print_given).
1.33/1.68	
1.33/1.68	% formulas(sos).  % not echoed (609 formulas)
1.33/1.68	
1.33/1.68	============================== end of input ==========================
1.33/1.68	
1.33/1.68	% From the command line: assign(max_seconds, 960).
1.33/1.68	
1.33/1.68	============================== PROCESS NON-CLAUSAL FORMULAS ==========
1.33/1.68	
1.33/1.68	% Formulas that are not ordinary clauses:
1.33/1.68	1 (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].
1.33/1.68	2 (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].
1.33/1.68	3 (all X_b (zero(X_b) -> ti(X_b,zero_zero(X_b)) = zero_zero(X_b))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause).  [assumption].
1.33/1.68	4 (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].
1.33/1.68	5 (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].
1.33/1.68	6 (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].
1.33/1.68	7 (all X_b (zero(X_b) -> (all X_1 (ti(X_b,X_1) = zero_zero(X_b) <-> zero_zero(X_b) = ti(X_b,X_1))))) # label(fact_487_zero__reorient) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	8 (all X_a (monoid_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	9 (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 (hAPP(X_c,X_b,F,X_2) = ti(X_b,B) -> -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].
1.44/1.68	10 (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].
1.44/1.68	11 (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].
1.44/1.68	12 (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].
1.44/1.68	13 (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].
1.44/1.68	14 (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].
1.44/1.68	15 (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].
1.44/1.68	16 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_458_zero__neq__one) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	17 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(Q) | -hBOOL(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	18 (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].
1.44/1.68	19 (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].
1.44/1.68	20 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_23_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	21 (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].
1.44/1.68	22 (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].
1.44/1.68	23 (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].
1.44/1.68	24 (all X_c ti(fun(fun(X_c,bool),nat),finite_card(X_c)) = finite_card(X_c)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	25 (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].
1.44/1.68	26 (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].
1.44/1.68	27 (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].
1.44/1.68	28 (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)) -> (zero_zero(X_b) = ti(X_b,X_1) & zero_zero(X_b) = ti(X_b,Y_1) <-> zero_zero(X_b) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_1))))))) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	29 (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].
1.44/1.68	30 (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].
1.44/1.68	31 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,A_2) = ti(X_b,X_2))) -> 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].
1.44/1.68	32 (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].
1.44/1.68	33 (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].
1.44/1.68	34 (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].
1.44/1.68	35 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	36 (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].
1.44/1.68	37 (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].
1.44/1.68	38 (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].
1.44/1.68	39 (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].
1.44/1.68	40 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_481_Suc__neq__Zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	41 (all X_b collect(X_b) = ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b))) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	42 (all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)) # label(fact_474_diff__self__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	43 (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_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].
1.44/1.68	44 (all X_a (comm_monoid_add(X_a) -> (all 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) = ti(X_a,A_1)))) # label(fact_493_add__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	45 (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].
1.44/1.68	46 (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].
1.44/1.68	47 (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_109_empty__Collect__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	48 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_76_Collect__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	49 (all M_1 all Na (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),ord_less(nat),M_1),Na)))) # label(fact_354_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	50 (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].
1.44/1.68	51 (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].
1.44/1.68	52 (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].
1.44/1.68	53 (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].
1.44/1.68	54 (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 (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,F,X_2))))) # label(fact_79_image__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	55 (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].
1.44/1.68	56 (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),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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)))))) # label(fact_403_less__diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	57 (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),A_2),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))))))) # label(fact_310_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	58 (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].
1.44/1.68	59 (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,B) = ti(X_b,A_2)))))) # label(fact_186_diff__eq__diff__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.68	60 (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].
1.44/1.68	61 (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].
1.44/1.68	62 (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].
1.44/1.68	63 (all X_b all X_c (order(X_c) & order(X_b) -> (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].
1.44/1.68	64 (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].
1.44/1.68	65 (all X_b all X_1 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))) # label(fact_60_insert__absorb2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	66 (all X_b all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) # label(fact_58_insert__compr) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	67 (all 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))) = Na) # label(fact_385_card__Collect__less__nat) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	68 (all X_b hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool))) = zero_zero(nat)) # label(fact_451_card_Oempty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	69 (all X_b all X_2 all Xa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))) # label(fact_82_insert__compr__raw) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	70 (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(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,A_3))))) # label(fact_183_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	71 (all X_b all X_c (order(X_b) & order(X_c) -> (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].
1.44/1.69	72 (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(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)) & (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_219_card__Diff__singleton__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	73 (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].
1.44/1.69	74 (all M all N M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)) # label(fact_250_diff__add__inverse2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	75 (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].
1.44/1.69	76 (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_121_singleton__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	77 (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))) -> hAPP(fun(X_c,bool),X_b,F_2,A_3) = ti(X_b,Z_1))))) # label(fact_211_folding__image__simple_Oneutral) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	78 (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].
1.44/1.69	79 (all I all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N)) -> 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)) = I)) # label(fact_42_diff__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	80 (all P (hBOOL(hAPP(bool,bool,fNot,P)) | hBOOL(P))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	81 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	82 (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].
1.44/1.69	83 (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].
1.44/1.69	84 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	85 (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)),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))))) # label(fact_249_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	86 (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].
1.44/1.69	87 (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].
1.44/1.69	88 (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].
1.44/1.69	89 (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].
1.44/1.69	90 (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(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)) = 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))) & (-(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))) -> zero_zero(nat) = 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))))) # label(fact_446_card__Plus__conv__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	91 (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].
1.44/1.69	92 (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].
1.44/1.69	93 (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].
1.44/1.69	94 (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].
1.44/1.69	95 (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].
1.44/1.69	96 (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].
1.44/1.69	97 (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].
1.44/1.69	98 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) # label(fact_205_set__diff__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	99 (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].
1.44/1.69	100 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)) # label(fact_476_diff__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	101 (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].
1.44/1.69	102 (all X_b all X_c finite_comp_fun_idem(X_b,X_c) = ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c))) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	103 (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].
1.44/1.69	104 (all X_b all A_3 (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),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))))) # label(fact_110_ex__in__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	105 (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].
1.44/1.69	106 (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].
1.44/1.69	107 (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].
1.44/1.69	108 (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),M),hAPP(nat,nat,suc,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),M),K)),hAPP(nat,nat,suc,J_2)))) # label(fact_284_diff__Suc__diff__eq1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	109 (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].
1.44/1.69	110 (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,suc,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))) & (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(fun(X_b,bool),nat,finite_card(X_b),A_3)))) # label(fact_8_card__insert__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	111 (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].
1.44/1.69	112 (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].
1.44/1.69	113 (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].
1.44/1.69	114 (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(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].
1.44/1.69	115 (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)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)))))) # label(fact_363_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	116 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	117 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat))) # label(fact_470_diff__is__0__eq_H) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	118 (all X_b all Pa ((all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))) <-> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool)))) # label(fact_107_Collect__empty__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	119 (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].
1.44/1.69	120 (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].
1.44/1.69	121 (all X_b all X_c all F all G ((all X_2 hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,F,X_2)) -> ti(fun(X_b,X_c),G) = ti(fun(X_b,X_c),F))) # label(fact_74_ext) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	122 (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].
1.44/1.69	123 (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),A_2),zero_zero(X_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),A_2)),zero_zero(X_b))))))) # label(fact_460_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	124 (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].
1.44/1.69	125 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	126 (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,X) = ti(X_a,Y)))))) # label(fact_139_order__antisym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	127 (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].
1.44/1.69	128 (all X_b all X_1 all Y_1 all Pa ((-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))))) & (hBOOL(Pa) -> ti(X_b,X_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].
1.44/1.69	129 (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].
1.44/1.69	130 (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].
1.44/1.69	131 (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].
1.44/1.69	132 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	133 (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].
1.44/1.69	134 (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),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(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_181_finite__Diff__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	135 (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].
1.44/1.69	136 (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].
1.44/1.69	137 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_457_one__neq__zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	138 (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].
1.44/1.69	139 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) # label(fact_91_insert__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	140 (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].
1.44/1.69	141 (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].
1.44/1.69	142 (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].
1.44/1.69	143 (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].
1.44/1.69	144 (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)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_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)))))) # label(fact_47_finite__subset__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	145 (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].
1.44/1.69	146 (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].
1.44/1.69	147 (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].
1.44/1.69	148 (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].
1.44/1.69	149 (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].
1.44/1.69	150 (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].
1.44/1.69	151 (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(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_196_folding__image__simple_Oremove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	152 (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].
1.44/1.69	153 (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].
1.44/1.69	154 (all X_b (linorder(X_b) -> (all X_1 all 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),Y_1),X_1)) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)))))) # label(fact_332_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	155 (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_eq(nat),M_1),Na)))) # label(fact_326_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	156 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_198_the__sym__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	157 (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),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].
1.44/1.69	158 (all K_2 all M_1 all Na (M_1 = Na <-> 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].
1.44/1.69	159 (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].
1.44/1.69	160 (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),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_276_le__add__diff__inverse) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	161 (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].
1.44/1.69	162 (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].
1.44/1.69	163 (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].
1.44/1.69	164 (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].
1.44/1.69	165 (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].
1.44/1.69	166 (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].
1.44/1.69	167 (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].
1.44/1.69	168 (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].
1.44/1.69	169 (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].
1.44/1.69	170 (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].
1.44/1.69	171 (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].
1.44/1.69	172 (all I_1 all J_1 all K_2 (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))) <-> 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)))) # label(fact_401_less__diff__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	173 (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].
1.44/1.69	174 (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,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),A_3))))) # label(fact_54_insertE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	175 (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].
1.44/1.69	176 (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].
1.44/1.69	177 (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].
1.44/1.69	178 (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].
1.44/1.69	179 (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].
1.44/1.69	180 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,suc,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,suc,M)),N))) # label(fact_11_Suc__diff__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	181 (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].
1.44/1.69	182 (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].
1.44/1.69	183 (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 hAPP(nat,nat,suc,M_2) = M_3))) # label(fact_56_Suc__le__D) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	184 (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].
1.44/1.69	185 (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].
1.44/1.69	186 (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].
1.44/1.69	187 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_2)) # label(fact_177_Diff__insert2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	188 (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].
1.44/1.69	189 (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].
1.44/1.69	190 (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].
1.44/1.69	191 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_335_linorder__neqE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	192 (all X_a (group_add(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1)))) # label(fact_478_diff__self) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	193 (all K_2 all M_1 all 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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)))) # label(fact_301_nat__add__left__cancel__less) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	194 (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].
1.44/1.69	195 (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(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_162_folding__one_Oinsert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	196 (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,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),A_3)))) # label(fact_62_insert__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.69	197 (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].
1.44/1.69	198 (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].
1.44/1.69	199 (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].
1.44/1.69	200 (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].
1.44/1.69	201 (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].
1.44/1.69	202 (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].
1.44/1.70	203 (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].
1.44/1.70	204 (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,A_1) != ti(X_a,B_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].
1.44/1.70	205 (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].
1.44/1.70	206 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),F_2) -> ((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)) -> (ti(fun(X_b,bool),F_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),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].
1.44/1.70	207 (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].
1.44/1.70	208 (all M all K 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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_254_diff__cancel2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	209 (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].
1.44/1.70	210 (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].
1.44/1.70	211 (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].
1.44/1.70	212 (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)) -> (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_141_ord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	213 (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].
1.44/1.70	214 (all X_b 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))) <-> bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3))) # label(fact_111_all__not__in__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	215 (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].
1.44/1.70	216 (all X_b all Y_1 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,A_3,X_1)) | ti(X_b,Y_1) = ti(X_b,X_1) <-> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3),X_1)))) # label(fact_63_insert__code) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	217 (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))) -> ti(X_a,A_1) = bot_bot(X_a))))) # label(fact_115_le__bot) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	218 (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].
1.44/1.70	219 (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].
1.44/1.70	220 (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	221 (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].
1.44/1.70	222 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (M != N -> 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].
1.44/1.70	223 (all X_b all X_c 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_127_empty__is__image) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	224 (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,Y_2) = ti(X_b,X_2))) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) -> (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_216_the1__equality) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	225 (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].
1.44/1.70	226 (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].
1.44/1.70	227 (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].
1.44/1.70	228 (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].
1.44/1.70	229 (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].
1.44/1.70	230 (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].
1.44/1.70	231 (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].
1.44/1.70	232 (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].
1.44/1.70	233 (all Nat hAPP(nat,nat,suc,Nat) != zero_zero(nat)) # label(fact_485_nat_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	234 (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].
1.44/1.70	235 (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].
1.44/1.70	236 (all X_b all A_2 all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) # label(fact_59_insert__Collect) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	237 (all X_a (group_add(X_a) -> (all A_1 all B_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) = ti(X_a,A_1)))) # label(fact_266_diff__add__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	238 (all X_c all X_b (order(X_b) & ord(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),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].
1.44/1.70	239 (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].
1.44/1.70	240 (all X_b all X_c all B_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) <-> (exists AA (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))))) # label(fact_92_subset__image__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	241 (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(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))) & (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = ti(X_b,X_1)))))) # label(fact_174_folding__one_Oremove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	242 (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_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) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	243 (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(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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))))))) # label(fact_422_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	244 (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].
1.44/1.70	245 (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),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B)),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)))))) # label(fact_466_le__iff__diff__le__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	246 (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].
1.44/1.70	247 (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,X_1) = ti(X_b,Y_1)))))) # label(fact_370_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	248 (all X_b (order(X_b) -> (all X_1 all 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)) <-> 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].
1.44/1.70	249 (all X_b (ab_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_479_eq__iff__diff__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	250 (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].
1.44/1.70	251 (all X_b (linord219039673up_add(X_b) -> (all 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) <-> ti(X_b,A_2) = zero_zero(X_b))))) # label(fact_494_double__zero__sym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	252 (all X_b all 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)) = ti(X_b,A_2)) # label(fact_209_the__eq__trivial) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	253 (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].
1.44/1.70	254 (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].
1.44/1.70	255 (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].
1.44/1.70	256 (all X_c all X_b (minus(X_b) -> (all A_3 all B_2 all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_2),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_2,X_1))))) # label(fact_213_minus__apply) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	257 (all X_a all X_b ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b)) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	258 (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_327_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	259 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) | ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) # label(fact_411_subset__iff__psubset__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	260 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat))) <-> zero_zero(nat) = Na)) # label(fact_489_le__0__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	261 (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].
1.44/1.70	262 (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].
1.44/1.70	263 (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].
1.44/1.70	264 (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)) -> 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)) = ti(fun(X_b,bool),A_3)))) # label(fact_171_double__diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	265 (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].
1.44/1.70	266 (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].
1.44/1.70	267 (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].
1.44/1.70	268 (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].
1.44/1.70	269 (all X_b (cancel_semigroup_add(X_b) -> (all B all A_2 all 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) <-> ti(X_b,C_1) = ti(X_b,B))))) # label(fact_247_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	270 (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)) -> M = hAPP(nat,nat,suc,N)))) # label(fact_31_le__SucE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	271 (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].
1.44/1.70	272 (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].
1.44/1.70	273 (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].
1.44/1.70	274 (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].
1.44/1.70	275 (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,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))))) # label(fact_225_card_Oremove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	276 (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)) -> (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_334_linorder__antisym__conv3) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	277 (all X_b all A_3 all F all Na (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))) = ti(fun(X_b,bool),A_3) -> 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].
1.44/1.70	278 (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].
1.44/1.70	279 (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].
1.44/1.70	280 (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].
1.44/1.70	281 (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].
1.44/1.70	282 (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].
1.44/1.70	283 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> T_3 != S)) # label(fact_358_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	284 (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].
1.44/1.70	285 (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].
1.44/1.70	286 (all X all Y (hAPP(nat,nat,suc,Y) = hAPP(nat,nat,suc,X) -> Y = X)) # label(fact_16_Suc__inject) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	287 (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))))) -> 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)))))) = 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))))) -> 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)))) # label(fact_217_flat__lub__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	288 (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].
1.44/1.70	289 (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))) <-> bot_bot(X_b) = ti(X_b,A_2))))) # label(fact_116_bot__unique) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	290 (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].
1.44/1.70	291 (all M_1 all Na (hAPP(nat,nat,suc,zero_zero(nat)) = M_1 & Na = zero_zero(nat) | Na = hAPP(nat,nat,suc,zero_zero(nat)) & M_1 = zero_zero(nat) <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na))) # label(fact_467_add__is__1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	292 (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),A_2),B)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),D_1))))))) # label(fact_157_diff__eq__diff__less__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	293 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	294 (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,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),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].
1.44/1.70	295 (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(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))),one_one(nat)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))))))) # label(fact_223_card__Diff__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	296 (all X_b all 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(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_130_singleton__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	297 (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].
1.44/1.70	298 (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),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),J_2)),K))) # label(fact_275_add__diff__assoc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	299 (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].
1.44/1.70	300 (all M all N (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) -> (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) -> M = N))) # label(fact_473_diffs0__imp__equal) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	301 (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	302 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	303 (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].
1.44/1.70	304 (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,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),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))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_1)) -> (ti(fun(X_b,bool),N_1) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_2,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))))))) # label(fact_193_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	305 (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].
1.44/1.70	306 (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].
1.44/1.70	307 (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].
1.44/1.70	308 (all X_b all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) -> zero_zero(nat) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) # label(fact_450_card__infinite) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	309 (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].
1.44/1.70	310 (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)) & ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2))) # label(fact_412_psubset__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	311 (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].
1.44/1.70	312 (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].
1.44/1.70	313 (all X_b all 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)))) = ti(X_b,X_1)) # label(fact_153_the__elem__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	314 (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].
1.44/1.70	315 (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].
1.44/1.70	316 (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].
1.44/1.70	317 (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].
1.44/1.70	318 (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].
1.44/1.70	319 (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,B_1) = ti(X_a,C))))) # label(fact_245_add__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	320 (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].
1.44/1.70	321 (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].
1.44/1.70	322 (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].
1.44/1.70	323 (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].
1.44/1.70	324 (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].
1.44/1.70	325 (all X_c all X_b all F 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))) = bot_bot(fun(X_b,bool))) # label(fact_126_image__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	326 (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].
1.44/1.70	327 (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),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(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))))) # label(fact_87_subset__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	328 (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].
1.44/1.70	329 (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].
1.44/1.70	330 (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].
1.44/1.70	331 (all X_a all P ti(X_a,P) = hAPP(X_a,X_a,combi(X_a),P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	332 (all X_b (one(X_b) -> ti(X_b,one_one(X_b)) = one_one(X_b))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	333 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	334 (all X_b (one(X_b) -> (all X_1 (ti(X_b,X_1) = one_one(X_b) <-> one_one(X_b) = ti(X_b,X_1))))) # label(fact_220_one__reorient) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	335 (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].
1.44/1.70	336 (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].
1.44/1.70	337 (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].
1.44/1.70	338 (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].
1.44/1.70	339 (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].
1.44/1.70	340 (all Nat_2 all Nat_3 (Nat_2 = Nat_3 <-> hAPP(nat,nat,suc,Nat_3) = hAPP(nat,nat,suc,Nat_2))) # label(fact_17_nat_Oinject) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	341 (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].
1.44/1.70	342 (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].
1.44/1.70	343 (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].
1.44/1.70	344 (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].
1.44/1.70	345 (all X_b ti(fun(fun(X_b,bool),X_b),the(X_b)) = the(X_b)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	346 (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(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(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))))) # label(fact_218_card__Diff__singleton) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	347 (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(nat),X_2),M_2)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1)))) # label(fact_383_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	348 (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].
1.44/1.70	349 (all Q all P (hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	350 (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].
1.44/1.70	351 (all X_a combi(X_a) = ti(fun(X_a,X_a),combi(X_a))) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	352 (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].
1.44/1.70	353 (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].
1.44/1.70	354 (all X_a all X all Y (ti(X_a,Y) != ti(X_a,X) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	355 (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].
1.44/1.70	356 (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].
1.44/1.70	357 (all X_b all X_c all X_a combb(X_b,X_c,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))) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	358 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) | 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].
1.44/1.70	359 (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].
1.44/1.70	360 (all X_b all A_3 all X_1 all B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2)))) # label(fact_170_insert__Diff__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.70	361 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool))) # label(fact_122_insert__not__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	362 (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	363 (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].
1.44/1.71	364 (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].
1.44/1.71	365 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_482_Zero__neq__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	366 (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].
1.44/1.71	367 (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].
1.44/1.71	368 (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	369 (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].
1.44/1.71	370 (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].
1.44/1.71	371 (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	372 (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].
1.44/1.71	373 (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	374 (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)) -> (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_144_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	375 (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].
1.44/1.71	376 (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].
1.44/1.71	377 (all X_b (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,A_2) = ti(X_b,B))))) # label(fact_480_right__minus__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	378 (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)) & (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,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_175_folding__one_Oinsert__remove) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	379 (all X_a all X_b all X_c combc(X_a,X_b,X_c) = ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c))) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	380 (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),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),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B))))))) # label(fact_229_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	381 (all M_1 all Na ((exists K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) = Na) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)))) # label(fact_257_le__iff__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	382 (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].
1.44/1.71	383 (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].
1.44/1.71	384 (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	385 (all X_c (ord(X_c) -> ord_less_eq(X_c) = ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	386 (all X_b all 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)) = sum_Plus(X_b,X_c)) # label(tsy_c_Sum__Type_OPlus_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	387 (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].
1.44/1.71	388 (all X_c all X_b all F all A_3 (ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)) <-> bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) # label(fact_125_image__is__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	389 (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	390 (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].
1.44/1.71	391 (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	392 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = ti(fun(X_b,bool),A_3))) # label(fact_66_insert__absorb) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	393 (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)) -> (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) <-> Na = M_1)))) # label(fact_41_eq__diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	394 (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].
1.44/1.71	395 (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	396 (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(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(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))))) # label(fact_416_psubset__insert__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	397 (all P (fFalse = ti(bool,P) | fTrue = ti(bool,P))) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	398 (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].
1.44/1.71	399 (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].
1.44/1.71	400 (all K all M 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),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N))) # label(fact_253_diff__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	401 (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,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))),M) = 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)))) # label(fact_283_diff__Suc__diff__eq2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	402 (all X_b all X_c (order(X_c) & order(X_b) -> (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].
1.44/1.71	403 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,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)) # label(fact_221_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	404 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),Na) = zero_zero(nat))) # label(fact_471_diff__is__0__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	405 (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].
1.44/1.71	406 (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].
1.44/1.71	407 (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].
1.44/1.71	408 (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	409 (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].
1.44/1.71	410 (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].
1.44/1.71	411 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | N = M -> 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].
1.44/1.71	412 (all X_b ti(fun(fun(X_b,bool),bool),finite_finite(X_b)) = finite_finite(X_b)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	413 (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)) -> (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_159_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	414 (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].
1.44/1.71	415 (all X_b ti(fun(fun(X_b,bool),X_b),the_elem(X_b)) = the_elem(X_b)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	416 (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].
1.44/1.71	417 (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),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_eq(X_b),A_2),B)))))) # label(fact_228_add__le__cancel__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	418 (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].
1.44/1.71	419 (all X_a (group_add(X_a) -> (all A_1 ti(X_a,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))))) # label(fact_477_diff__0__right) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	420 (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].
1.44/1.71	421 (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,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_376_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	422 (all X_b (linorder(X_b) -> (all X_1 all 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),Y_1),X_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)))))) # label(fact_331_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	423 (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].
1.44/1.71	424 (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	425 (all X_c all X_b all A_3 all B_2 (bot_bot(fun(sum_sum(X_b,X_c),bool)) = 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) <-> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) & ti(fun(X_c,bool),B_2) = bot_bot(fun(X_c,bool)))) # label(fact_445_Plus__eq__empty__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	426 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) <-> (exists K_1 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)) = Na))) # label(fact_391_less__iff__Suc__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	427 (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),Q) = 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)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	428 (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)))) <-> bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3))) # label(fact_154_nonempty__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	429 (all N N != hAPP(nat,nat,suc,N)) # label(fact_18_Suc__n__not__n) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	430 (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_eq(nat),hAPP(nat,nat,suc,Na)),M_1)))) # label(fact_392_less__eq__Suc__le) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	431 (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].
1.44/1.71	432 (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].
1.44/1.71	433 (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].
1.44/1.71	434 (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].
1.44/1.71	435 (all X_c all X_b all C_1 all A_3 ((ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = bot_bot(fun(X_c,bool))) & (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),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_134_image__constant__conv) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	436 (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),J_2),I)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)),I))) # label(fact_270_add__diff__assoc2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	437 (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].
1.44/1.71	438 (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),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,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)) # label(fact_37_Suc__diff__diff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	439 (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	440 (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),M),L) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N) -> 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].
1.44/1.71	441 (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].
1.44/1.71	442 (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].
1.44/1.71	443 (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	444 (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),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_146_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	445 (all X_b all 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) = ti(fun(X_b,bool),Y_3)) # label(fact_84_image__ident) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	446 (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	447 (all X_b all B_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> (ti(fun(X_b,bool),A_3) = ti(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),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),B_2))))) # label(fact_64_insert__ident) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	448 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (exists K_1 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)) = N))) # label(fact_407_less__imp__Suc__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	449 (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].
1.44/1.71	450 (all N all M zero_zero(nat) = 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))) # label(fact_469_diff__add__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	451 (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].
1.44/1.71	452 (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].
1.44/1.71	453 (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].
1.44/1.71	454 (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].
1.44/1.71	455 (all X_b all A_3 all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3) | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)))) # label(fact_132_subset__singletonD) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	456 (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	457 (all X_b (cancel_semigroup_add(X_b) -> (all A_2 all B all C_1 (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),A_2),B) <-> ti(X_b,C_1) = ti(X_b,B))))) # label(fact_248_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	458 (all X_b all A_2 all B all C_1 all D_1 (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) <-> 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)))) = 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)))))) # label(fact_120_doubleton__eq__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	459 (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].
1.44/1.71	460 (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,suc,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_9_card__insert__disjoint) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	461 (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	462 (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].
1.44/1.71	463 (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].
1.44/1.71	464 (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].
1.44/1.71	465 (all M_1 all K_2 all Na (M_1 = 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))) # label(fact_239_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	466 (all X_b all X_c ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c)) = image(X_b,X_c)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	467 (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].
1.44/1.71	468 (all M_1 all Na (hAPP(nat,nat,suc,zero_zero(nat)) = M_1 & zero_zero(nat) = Na | zero_zero(nat) = M_1 & hAPP(nat,nat,suc,zero_zero(nat)) = Na <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na))) # label(fact_468_one__is__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	469 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_475_minus__nat_Odiff__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	470 (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].
1.44/1.71	471 (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].
1.44/1.71	472 (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	473 (all X_b all A_2 (ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)) | (exists A_4 exists A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_4)) & hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) = ti(fun(X_b,bool),A_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2)))) # label(fact_151_finite_Osimps) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	474 (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)) -> N = M))) # label(fact_314_less__SucE) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	475 (all X_b all X_1 all A_3 (hBOOL(hAPP(X_b,bool,A_3,X_1)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)))) # label(fact_75_mem__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	476 (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].
1.44/1.71	477 (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(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)) = 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))))) # label(fact_440_card__Plus) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	478 (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].
1.44/1.71	479 (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)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) # label(fact_187_folding__one_Osingleton) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	480 (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].
1.44/1.71	481 (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].
1.44/1.71	482 (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].
1.44/1.71	483 (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),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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)))))) # label(fact_39_le__diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	484 (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].
1.44/1.71	485 (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)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) = K_2 <-> J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),I_1)))) # label(fact_272_le__imp__diff__is__add) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	486 (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].
1.44/1.71	487 (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	488 (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	489 (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].
1.44/1.71	490 (all M 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,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_38_diff__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	491 (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))) -> M = N))) # label(fact_318_less__antisym) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	492 (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),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_204_Diff__iff) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	493 (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].
1.44/1.71	494 (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	495 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,ti(fun(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	496 (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,B_1) = ti(X_a,C) -> 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].
1.44/1.71	497 (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),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	498 (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].
1.44/1.71	499 (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].
1.44/1.71	500 (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].
1.44/1.71	501 (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))) -> ((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),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	502 (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),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),K)),J_2)) # label(fact_25_diff__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	503 (all X_b all X_c finite1357897459simple(X_b,X_c) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c))) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	504 (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	505 (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].
1.44/1.71	506 (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].
1.44/1.71	507 (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	508 (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),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)))) <-> 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))))) # label(fact_26_finite__Collect__disjI) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	509 (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),bot_bot(fun(X_b,bool)))) <-> bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3))) # label(fact_124_subset__empty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	510 (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].
1.44/1.71	511 (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),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))) # label(fact_128_Collect__conv__if) # label(axiom) # label(non_clause).  [assumption].
1.44/1.71	512 (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	513 (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].
1.44/1.72	514 (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	515 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_486_Zero__not__Suc) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	516 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),B_2)) # label(fact_203_Diff__idemp) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	517 (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].
1.44/1.72	518 (all X all Y all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z))) # label(fact_242_nat__add__left__commute) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	519 (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].
1.44/1.72	520 (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].
1.44/1.72	521 (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].
1.44/1.72	522 (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)),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)) <-> ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3))) # label(fact_68_set__eq__subset) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	523 (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].
1.44/1.72	524 (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].
1.44/1.72	525 (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	526 (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].
1.44/1.72	527 (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	528 (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),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)))) = 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_176_Diff__insert) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	529 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_484_Suc__not__Zero) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	530 (all M_1 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) | hAPP(nat,nat,suc,Na) = M_1 <-> 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].
1.44/1.72	531 (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].
1.44/1.72	532 (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].
1.44/1.72	533 (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].
1.44/1.72	534 (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	535 (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].
1.44/1.72	536 (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	537 (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].
1.44/1.72	538 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	539 (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].
1.44/1.72	540 (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].
1.44/1.72	541 (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)) = 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)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa))))) # label(fact_129_Collect__conv__if2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	542 (all X_b 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,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	543 (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	544 (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].
1.44/1.72	545 (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)) -> hAPP(fun(X_c,bool),X_b,F_2,bot_bot(fun(X_c,bool))) = ti(X_b,Z_1))) # label(fact_206_folding__image__simple_Oempty) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	546 (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].
1.44/1.72	547 (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].
1.44/1.72	548 (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),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	549 (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].
1.44/1.72	550 (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].
1.44/1.72	551 (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].
1.44/1.72	552 (all X_b all F1 all F2 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)) = ti(X_b,F1)) # label(fact_491_nat__case__0) # label(axiom) # label(non_clause).  [assumption].
1.44/1.72	553 (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	554 (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].
1.44/1.74	555 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat))) # label(fact_222_diff__Suc__1) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	556 (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)) -> (-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)))))) # label(fact_375_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	557 (all X_b all X_c (minus(X_c) -> (all A_3 all B_2 all 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) = 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))))) # label(fact_212_fun__diff__def) # label(axiom) # label(non_clause).  [assumption].
1.44/1.74	
1.44/1.74	============================== end of process non-clausal formulas ===
1.44/1.74	
1.44/1.74	============================== PROCESS INITIAL CLAUSES ===============
1.44/1.74	
1.44/1.74	============================== PREDICATE ELIMINATION =================
1.44/1.74	558 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
1.44/1.74	559 -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(1)].
1.44/1.74	560 -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(50)].
1.44/1.74	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(558,a,560,a)].
1.44/1.74	561 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_310_add__less__cancel__right) # label(axiom).  [clausify(57)].
1.44/1.74	562 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_310_add__less__cancel__right) # label(axiom).  [clausify(57)].
1.44/1.74	563 -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(129)].
1.44/1.74	564 -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(359)].
1.44/1.74	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)).  [resolve(564,a,558,a)].
1.44/1.74	565 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_229_add__le__cancel__left) # label(axiom).  [clausify(380)].
1.58/1.85	566 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_229_add__le__cancel__left) # label(axiom).  [clausify(380)].
1.58/1.85	567 -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(414)].
1.58/1.85	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),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(567,a,558,a)].
1.58/1.85	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(414)].
1.58/1.85	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),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(568,a,558,a)].
1.58/1.85	569 -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_228_add__le__cancel__right) # label(axiom).  [clausify(417)].
1.58/1.85	570 -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_228_add__le__cancel__right) # label(axiom).  [clausify(417)].
1.58/1.85	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)).  [resolve(570,a,558,a)].
1.58/1.85	571 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom).  [assumption].
1.58/1.85	572 -zero(A) | ti(A,zero_zero(A)) = zero_zero(A) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom).  [clausify(3)].
1.58/1.85	Derived: ti(nat,zero_zero(nat)) = zero_zero(nat).  [resolve(571,a,572,a)].
1.58/1.85	573 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom).  [assumption].
1.58/1.85	574 -monoid_add(A) | ti(fun(A,fun(A,A)),plus_plus(A)) = plus_plus(A) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom).  [clausify(8)].
1.58/1.85	Derived: ti(fun(nat,fun(nat,nat)),plus_plus(nat)) = plus_plus(nat).  [resolve(573,a,574,a)].
1.58/1.85	575 -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(355)].
1.58/1.85	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)).  [resolve(575,a,573,a)].
1.58/1.85	576 -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(398)].
1.58/1.85	Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A).  [resolve(576,a,573,a)].
1.58/1.85	577 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom).  [assumption].
1.58/1.85	578 -zero_neq_one(A) | one_one(A) != zero_zero(A) # label(fact_458_zero__neq__one) # label(axiom).  [clausify(16)].
1.58/1.85	579 -zero_neq_one(A) | one_one(A) != zero_zero(A) # label(fact_457_one__neq__zero) # label(axiom).  [clausify(137)].
1.58/1.85	Derived: one_one(nat) != zero_zero(nat).  [resolve(577,a,578,a)].
1.58/1.85	580 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
1.58/1.88	581 -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(18)].
1.58/1.88	582 -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(19)].
1.58/1.88	583 -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(133)].
1.58/1.88	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(583,a,580,a)].
1.58/1.88	584 -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(280)].
1.58/1.88	585 -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(488)].
1.58/1.88	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(585,a,580,a)].
1.58/1.88	586 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.58/1.88	587 -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)) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom).  [clausify(28)].
1.58/1.88	588 -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)) | ti(A,B) = zero_zero(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom).  [clausify(28)].
1.58/1.88	589 -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)) | ti(A,C) = zero_zero(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_462_add__nonneg__eq__0__iff) # label(axiom).  [clausify(28)].
1.58/1.88	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)) | ti(nat,A) != zero_zero(nat) | ti(nat,B) != zero_zero(nat) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B).  [resolve(586,a,587,a)].
1.58/1.88	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)) | ti(nat,A) = zero_zero(nat) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B).  [resolve(586,a,588,a)].
1.67/1.93	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)) | ti(nat,B) = zero_zero(nat) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B).  [resolve(586,a,589,a)].
1.67/1.93	590 -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(263)].
1.67/1.93	591 -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(321)].
1.67/1.93	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(591,a,586,a)].
1.67/1.93	592 -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(329)].
1.67/1.93	593 -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(344)].
1.67/1.93	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),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A))).  [resolve(593,a,586,a)].
1.67/1.93	594 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
1.67/1.93	595 -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(30)].
1.67/1.93	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C).  [resolve(594,a,595,a)].
1.67/1.93	596 -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_247_add__right__cancel) # label(axiom).  [clausify(269)].
1.67/1.93	597 -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_247_add__right__cancel) # label(axiom).  [clausify(269)].
1.67/1.93	Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) != ti(nat,C).  [resolve(597,a,594,a)].
1.67/1.93	598 -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_248_add__left__cancel) # label(axiom).  [clausify(457)].
1.67/1.93	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(598,a,594,a)].
1.67/1.93	599 -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_248_add__left__cancel) # label(axiom).  [clausify(457)].
1.67/1.96	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(599,a,594,a)].
1.67/1.96	600 -cancel_semigroup_add(A) | ti(fun(A,fun(A,A)),plus_plus(A)) = plus_plus(A) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom).  [clausify(521)].
1.67/1.96	601 -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(526)].
1.67/1.96	602 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom).  [assumption].
1.67/1.96	603 -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(38)].
1.67/1.96	604 -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(93)].
1.67/1.96	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(93)].
1.67/1.96	606 -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_363_linorder__not__le) # label(axiom).  [clausify(115)].
1.67/1.96	607 -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_363_linorder__not__le) # label(axiom).  [clausify(115)].
1.67/1.96	608 -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(122)].
1.67/1.96	609 -linorder(A) | ti(A,B) != ti(A,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(154)].
1.67/1.96	610 -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(154)].
1.67/1.96	611 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_332_not__less__iff__gr__or__eq) # label(axiom).  [clausify(154)].
1.67/1.96	612 -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(191)].
1.67/1.96	613 -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(205)].
1.67/1.96	614 -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(244)].
1.67/1.96	615 -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(247)].
1.67/1.96	616 -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(247)].
1.67/1.96	617 -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(271)].
1.67/1.96	618 -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_334_linorder__antisym__conv3) # label(axiom).  [clausify(276)].
1.82/2.06	619 -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_334_linorder__antisym__conv3) # label(axiom).  [clausify(276)].
1.82/2.06	620 -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(297)].
1.82/2.06	621 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_331_linorder__neq__iff) # label(axiom).  [clausify(422)].
1.82/2.06	622 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_331_linorder__neq__iff) # label(axiom).  [clausify(422)].
1.82/2.06	623 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_331_linorder__neq__iff) # label(axiom).  [clausify(422)].
1.82/2.06	624 -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(493)].
1.82/2.06	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),B),A)).  [resolve(602,a,603,a)].
1.82/2.06	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),B),A)).  [resolve(602,a,604,a)].
1.82/2.06	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_eq(nat),B),A)).  [resolve(602,a,608,a)].
1.82/2.06	Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).  [resolve(602,a,609,a)].
1.82/2.06	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),B),A)).  [resolve(602,a,610,a)].
1.82/2.06	Derived: ti(nat,A) = ti(nat,B) | 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(602,a,611,a)].
1.82/2.06	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),A),B)) | ti(nat,B) = ti(nat,A).  [resolve(602,a,615,a)].
1.82/2.06	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),A),B)) | ti(nat,B) != ti(nat,A).  [resolve(602,a,616,a)].
1.82/2.06	Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(602,a,622,a)].
1.82/2.06	625 -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(547)].
1.82/2.06	626 -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),B),C)) | ti(A,C) = ti(A,B) # label(fact_375_linorder__antisym__conv2) # label(axiom).  [clausify(556)].
1.82/2.06	627 -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),B),C)) | ti(A,C) != ti(A,B) # label(fact_375_linorder__antisym__conv2) # label(axiom).  [clausify(556)].
1.82/2.06	628 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
1.82/2.06	629 -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(44)].
1.82/2.06	630 -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(230)].
1.82/2.06	631 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
1.82/2.06	632 -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(85)].
1.87/2.11	633 -ab_semigroup_add(A) | ti(fun(A,fun(A,A)),plus_plus(A)) = plus_plus(A) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(437)].
1.87/2.11	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(631,a,632,a)].
1.87/2.11	634 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
1.87/2.11	635 -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(88)].
1.87/2.11	636 -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(342)].
1.87/2.11	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(634,a,635,a)].
1.87/2.11	637 -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(513)].
1.87/2.11	638 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.87/2.11	639 -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(96)].
1.87/2.11	640 -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(147)].
1.87/2.11	641 -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(231)].
1.87/2.11	642 -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(255)].
1.87/2.11	643 -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(350)].
1.87/2.11	644 -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(405)].
1.87/2.11	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(638,a,639,a)].
1.87/2.11	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))).  [resolve(638,a,640,a)].
1.87/2.11	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(638,a,641,a)].
1.87/2.11	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))).  [resolve(638,a,642,a)].
4.04/4.34	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))).  [resolve(638,a,643,a)].
4.04/4.34	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))).  [resolve(638,a,644,a)].
4.04/4.34	645 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom).  [clausify(332)].
4.04/4.34	646 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom).  [assumption].
4.04/4.34	Derived: one_one(nat) = ti(nat,one_one(nat)).  [resolve(645,a,646,a)].
4.04/4.34	647 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
4.04/4.34	648 -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(319)].
4.04/4.34	
4.04/4.34	============================== end predicate elimination =============
4.04/4.34	
4.04/4.34	Auto_denials:  (non-Horn, no changes).
4.04/4.34	
4.04/4.34	Term ordering decisions:
4.04/4.34	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. f1=1. f6=1. f12=1. f16=1. f19=1. f22=1. f32=1. f41=1. f51=1. f56=1. f60=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f72=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. f17=1. f57=1. combc=1. combb=1. combs=1. f3=1. f25=1. f26=1. f27=1. f28=1. f29=1. f33=1. f36=1. f37=1. f38=1. f39=1. f40=1. f54=1. f55=1. f58=1. f75=1. f76=1. f79=1. hAPP=1. f21=1. f23=1. f30=1. f31=1. f34=1. f35=1. f42=1. f43=1. f44=1. f48=1. f49=1. f50=1. f2=1. f7=1. f24=1. f47=1. f52=1. f53=1. f59=1. f4=1. f5=1. f8=1. f9=1. f10=1. f11=1. f13=1. f14=1. f45=1. f46=1. f61=1. f62=1. f73=1. f74=1. f77=1. f78=1. f15=1.
4.04/4.34	
4.04/4.34	============================== end of process initial clauses ========
4.04/4.34	
4.04/4.34	============================== CLAUSES FOR SEARCH ====================
4.04/4.34	
4.04/4.34	============================== end of clauses for search =============
4.04/4.34	
4.04/4.34	============================== SEARCH ================================
4.04/4.34	
4.04/4.34	% Starting search at 0.88 seconds.
4.04/4.34	
4.04/4.34	Low Water (keep): wt=153.000, iters=3542
4.04/4.34	
4.04/4.34	Low Water (keep): wt=137.000, iters=3373
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4.04/4.34	Low Water (keep): wt=136.000, iters=3382
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4.04/4.34	Low Water (keep): wt=131.000, iters=3356
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4.04/4.34	Low Water (keep): wt=128.000, iters=3374
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4.04/4.34	Low Water (keep): wt=121.000, iters=3342
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4.04/4.34	Low Water (keep): wt=115.000, iters=3345
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4.04/4.34	Low Water (keep): wt=113.000, iters=3417
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4.04/4.34	Low Water (keep): wt=110.000, iters=3391
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4.04/4.34	Low Water (keep): wt=108.000, iters=3359
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4.04/4.34	Low Water (keep): wt=106.000, iters=3369
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4.04/4.34	Low Water (keep): wt=105.000, iters=3377
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4.04/4.34	Low Water (keep): wt=104.000, iters=3367
4.04/4.34	
4.04/4.34	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 79 (0.00 of 2.18 sec).
4.04/4.34	
4.04/4.34	Low Water (keep): wt=103.000, iters=3398
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4.04/4.34	Low Water (keep): wt=101.000, iters=3373
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4.04/4.34	Low Water (keep): wt=99.000, iters=3336
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4.04/4.34	Low Water (keep): wt=95.000, iters=3334
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4.04/4.34	Low Water (keep): wt=94.000, iters=3338
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4.04/4.34	Low Water (keep): wt=93.000, iters=3378
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4.04/4.34	Low Water (keep): wt=92.000, iters=3381
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4.04/4.34	Low Water (keep): wt=91.000, iters=3362
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4.04/4.34	Low Water (keep): wt=90.000, iters=3514
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4.04/4.34	Low Water (keep): wt=88.000, iters=3434
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4.04/4.34	Low Water (keep): wt=87.000, iters=3400
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4.04/4.34	Low Water (keep): wt=86.000, iters=3345
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4.04/4.34	Low Water (keep): wt=84.000, iters=3448
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4.04/4.34	Low Water (keep): wt=78.000, iters=3417
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4.04/4.34	Low Water (keep): wt=77.000, iters=3375
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4.04/4.34	Low Water (keep): wt=76.000, iters=3379
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4.04/4.34	Low Water (keep): wt=75.000, iters=3363
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4.04/4.34	Low Water (keep): wt=74.000, iters=3362
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4.04/4.34	Low Water (keep): wt=72.000, iters=3512
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4.04/4.34	Low Water (keep): wt=70.000, iters=3512
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4.04/4.34	Low Water (keep): wt=69.000, iters=3407
112.48/113.22	
112.48/113.22	Low Water (keep): wt=67.000, iters=3547
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112.48/113.22	Low Water (keep): wt=47.000, iters=4006
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112.48/113.22	Low Water (keep): wt=39.000, iters=3348
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112.48/113.22	Low Water (keep): wt=37.000, iters=3573
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112.48/113.22	Low Water (keep): wt=32.000, iters=3483
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112.48/113.22	Low Water (keep): wt=25.000, iters=3373
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112.48/113.22	Low Water (keep): wt=16.000, iters=3358
112.48/113.22	
112.48/113.22	Low Water (keep): wt=14.000, iters=3349
112.48/113.22	
112.48/113.22	Low Water (displace): id=4286, wt=200.000
112.48/113.22	
112.48/113.22	Low Water (displace): id=4809, wt=198.000
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112.48/113.22	Low Water (displace): id=4375, wt=197.000
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112.48/113.22	Low Water (displace): id=4823, wt=196.000
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112.48/113.22	Low Water (displace): id=5140, wt=195.000
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112.48/113.22	Low Water (displace): id=4418, wt=194.000
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112.48/113.22	Low Water (displace): id=3815, wt=193.000
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112.48/113.22	Low Water (displace): id=4813, wt=191.000
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112.48/113.22	Low Water (displace): id=5124, wt=189.000
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112.48/113.22	Low Water (displace): id=5044, wt=188.000
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112.48/113.22	Low Water (displace): id=4815, wt=187.000
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112.48/113.22	Low Water (displace): id=4151, wt=186.000
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112.48/113.22	Low Water (displace): id=3653, wt=185.000
112.48/113.22	
112.48/113.22	Low Water (displace): id=4696, wt=182.000
112.48/113.22	
112.48/113.22	Low Water (displace): id=3811, wt=180.000
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112.48/113.22	Low Water (displace): id=4770, wt=179.000
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112.48/113.22	Low Water (displace): id=5117, wt=178.000
112.48/113.22	
112.48/113.22	Low Water (displace): id=13017, wt=12.000
112.48/113.22	
112.48/113.22	============================== STATISTICS ============================
112.48/113.22	
112.48/113.22	Given=7609. Generated=1233535. Kept=142557. proofs=0.
112.48/113.22	Usable=7580. Sos=10000. Demods=409. Limbo=6391, Disabled=119449. Hints=0.
112.48/113.22	Kept_by_rule=0, Deleted_by_rule=44000.
112.48/113.22	Forward_subsumed=178972. Back_subsumed=62.
112.48/113.22	Sos_limit_deleted=868006. Sos_displaced=117684. Sos_removed=0.
112.48/113.22	New_demodulators=509 (0 lex), Back_demodulated=553. Back_unit_deleted=287.
112.48/113.22	Demod_attempts=58300346. Demod_rewrites=178110.
112.48/113.22	Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
112.48/113.22	Nonunit_fsub_feature_tests=196082. Nonunit_bsub_feature_tests=12496.
112.48/113.22	Megabytes=419.43.
112.48/113.22	User_CPU=110.00, System_CPU=1.17, Wall_clock=111.
112.48/113.22	
112.48/113.22	Megs malloced by palloc(): 400.
112.48/113.22	  type (bytes each)        gets      frees     in use      bytes
112.48/113.22	chunk ( 104)              40403      40403          0      0.0 K
112.48/113.22	string_buf (   8)         36581      36581          0      0.0 K
112.48/113.22	token (  20)              92846      92846          0      0.0 K
112.48/113.22	pterm (  16)              64102      64102          0      0.0 K
112.48/113.22	hashtab (   8)              557        557          0      0.0 K
112.48/113.22	hashnode (   8)            2321       2321          0      0.0 K
112.48/113.22	term (  20)            80532052   69326978   11205074 218849.1 K
112.48/113.22	      term arg arrays:                                 50273.3 K
112.48/113.22	attribute (  12)           4213        140       4073     47.7 K
112.48/113.22	ilist (   8)          369772124  368891423     880701   6880.5 K
112.48/113.22	plist (   8)           10653226   10477804     175422   1370.5 K
112.48/113.22	i2list (  12)           3571925    3571925          0      0.0 K
112.48/113.22	just (  12)             1415324    1238239     177085   2075.2 K
112.48/113.22	parajust (  16)          401640     275024     126616   1978.4 K
112.48/113.22	instancejust (   8)           0          0          0      0.0 K
112.48/113.22	ivyjust (  24)                0          0          0      0.0 K
112.48/113.22	formula (  28)            24244      15936       8308    227.2 K
112.48/113.22	    formula arg arrays:                                   28.1 K
112.48/113.22	topform (  52)          1234993    1090978     144015   7313.3 K
112.48/113.22	clist_pos (  20)         407858     264029     143829   2809.2 K
112.48/113.22	clist (  16)                  8          1          7      0.1 K
112.48/113.22	context ( 808)          5705091    5705091          0      0.0 K
112.48/113.22	trail (  12)            9098757    9098757          0      0.0 K
112.48/113.22	ac_match_pos (70044)          0          0          0      0.0 K
112.48/113.22	ac_match_free_vars_pos (20020)
112.48/113.22	                              0          0          0      0.0 K
112.48/113.22	btm_state (  60)              0          0          0      0.0 K
112.48/113.22	btu_state (  60)              0          0          0      0.0 K
112.48/113.23	ac_position (285432)          0          0          0      0.0 K
112.48/113.23	fpa_trie (  20)         4244294    4028068     216226   4223.2 K
112.48/113.23	fpa_state (  28)       29168290   29168290          0      0.0 K
112.48/113.23	fpa_index (  12)             10          0         10      0.1 K
112.48/113.23	fpa_chunk (  20)        5896148    5744116     152032   2969.4 K
112.48/113.23	fpa_list (  16)         4094167          0    4094167  63971.4 K
112.48/113.23	      fpa_list chunks:                                 14300.2 K
112.48/113.23	discrim (  12)          4934236    4506187     428049   5016.2 K
112.48/113.23	discrim_pos (  16)       345362     345362          0      0.0 K
112.48/113.23	flat2 (  32)           38857574   38857574          0      0.0 K
112.48/113.23	flat (  48)                   0          0          0      0.0 K
112.48/113.23	flatterm (  32)        71268519   71268519          0      0.0 K
112.48/113.23	mindex (  28)                13          0         13      0.4 K
112.48/113.23	mindex_pos (  56)       2657489    2657489          0      0.0 K
112.48/113.23	lindex (  12)                 5          0          5      0.1 K
112.48/113.23	clash (  40)                  0          0          0      0.0 K
112.48/113.23	di_tree (  12)          6242688    4026908    2215780  25966.2 K
112.48/113.23	avl_node (  20)          271451     251451      20000    390.6 K
112.48/113.23	
112.48/113.23	Memory report, 20 @ 20 = 400 megs (400.00 megs used).
112.48/113.23	List   1, length       7,      0.0 K
112.48/113.23	List   2, length     977,      7.6 K
112.48/113.23	List   3, length   38482,    451.0 K
112.48/113.23	List   5, length     784,     15.3 K
112.48/113.23	List   6, length      27,      0.6 K
112.48/113.23	List   7, length     579,     15.8 K
112.48/113.23	List   8, length     619,     19.3 K
112.48/113.23	List   9, length      45,      1.6 K
112.48/113.23	List  10, length       1,      0.0 K
112.48/113.23	List  11, length       2,      0.1 K
112.48/113.23	List  12, length       3,      0.1 K
112.48/113.23	List  13, length       1,      0.1 K
112.48/113.23	List  14, length       2,      0.1 K
112.48/113.23	List  16, length    1254,     78.4 K
112.48/113.23	List  26, length     389,     39.5 K
112.48/113.23	List  32, length      56,      7.0 K
112.48/113.23	List  64, length      24,      6.0 K
112.48/113.23	List 128, length      10,      5.0 K
112.48/113.23	List 202, length       4,      3.2 K
112.48/113.23	List 256, length       1,      1.0 K
112.48/113.23	
112.48/113.23	============================== SELECTOR REPORT =======================
112.48/113.23	Sos_deleted=868006, Sos_displaced=117684, Sos_size=10000
112.48/113.23	  SELECTOR       PART   PRIORITY      ORDER       SIZE   SELECTED
112.48/113.23	         I 2147483647       high        age          0        597
112.48/113.23	         H          1       high     weight          0          0
112.48/113.23	         A          1        low        age      10000        780
112.48/113.23	         F          4        low     weight       2403       3116
112.48/113.23	         T          4        low     weight       7597       3116
112.48/113.23	============================== end of selector report ================
112.48/113.23	
112.48/113.23	============================== end of statistics =====================
112.48/113.23	
112.48/113.23	Exiting with failure.
112.48/113.23	
112.48/113.23	Process 25589 exit (max_megs) Tue Aug  9 05:12:01 2022
112.48/113.23	Prover9 interrupted
112.48/113.23	EOF