0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n014.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1200
0.12/0.33	% DateTime   : Wed Jul 14 16:47:33 EDT 2021
0.12/0.33	% CPUTime    : 
0.88/1.16	============================== Prover9 ===============================
0.88/1.16	Prover9 (32) version 2009-11A, November 2009.
0.88/1.16	Process 19006 was started by sandbox on n014.cluster.edu,
0.88/1.16	Wed Jul 14 16:47:34 2021
0.88/1.16	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_18853_n014.cluster.edu".
0.88/1.16	============================== end of head ===========================
0.88/1.16	
0.88/1.16	============================== INPUT =================================
0.88/1.16	
0.88/1.16	% Reading from file /tmp/Prover9_18853_n014.cluster.edu
0.88/1.16	
0.88/1.16	set(prolog_style_variables).
0.88/1.16	set(auto2).
0.88/1.16	    % set(auto2) -> set(auto).
0.88/1.16	    % set(auto) -> set(auto_inference).
0.88/1.16	    % set(auto) -> set(auto_setup).
0.88/1.16	    % set(auto_setup) -> set(predicate_elim).
0.88/1.16	    % set(auto_setup) -> assign(eq_defs, unfold).
0.88/1.16	    % set(auto) -> set(auto_limits).
0.88/1.16	    % set(auto_limits) -> assign(max_weight, "100.000").
0.88/1.16	    % set(auto_limits) -> assign(sos_limit, 20000).
0.88/1.16	    % set(auto) -> set(auto_denials).
0.88/1.16	    % set(auto) -> set(auto_process).
0.88/1.16	    % set(auto2) -> assign(new_constants, 1).
0.88/1.16	    % set(auto2) -> assign(fold_denial_max, 3).
0.88/1.16	    % set(auto2) -> assign(max_weight, "200.000").
0.88/1.16	    % set(auto2) -> assign(max_hours, 1).
0.88/1.16	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.88/1.16	    % set(auto2) -> assign(max_seconds, 0).
0.88/1.16	    % set(auto2) -> assign(max_minutes, 5).
0.88/1.16	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.88/1.16	    % set(auto2) -> set(sort_initial_sos).
0.88/1.16	    % set(auto2) -> assign(sos_limit, -1).
0.88/1.16	    % set(auto2) -> assign(lrs_ticks, 3000).
0.88/1.16	    % set(auto2) -> assign(max_megs, 400).
0.88/1.16	    % set(auto2) -> assign(stats, some).
0.88/1.16	    % set(auto2) -> clear(echo_input).
0.88/1.16	    % set(auto2) -> set(quiet).
0.88/1.16	    % set(auto2) -> clear(print_initial_clauses).
0.88/1.16	    % set(auto2) -> clear(print_given).
0.88/1.16	assign(lrs_ticks,-1).
0.88/1.16	assign(sos_limit,10000).
0.88/1.16	assign(order,kbo).
0.88/1.16	set(lex_order_vars).
0.88/1.16	clear(print_given).
0.88/1.16	
0.88/1.16	% formulas(sos).  % not echoed (161 formulas)
0.88/1.16	
0.88/1.16	============================== end of input ==========================
0.88/1.16	
0.88/1.16	% From the command line: assign(max_seconds, 1200).
0.88/1.16	
0.88/1.16	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.88/1.16	
0.88/1.16	% Formulas that are not ordinary clauses:
0.88/1.16	1 (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].
0.88/1.16	2 (all X_c finite_card(X_c) = ti(fun(fun(X_c,bool),nat),finite_card(X_c))) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	3 (all X_b all X_c all B_1 all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_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_1))) -> -(all X_1 (ti(X_b,B_1) = hAPP(X_c,X_b,F,X_1) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)))))) # label(fact_92_imageE) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	4 (all X_b all A_2 all B hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B)))) # label(fact_55_insertI1) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	5 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	6 (all X_b all B_1 all A_2 all B ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B)) -> ti(X_b,A_2) = ti(X_b,B_1)) -> 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_1),B))))) # label(fact_53_insertCI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	7 (all X_c all X_a all B_1_1 all B_2 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	8 (all L all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L))))) # label(fact_43_diff__le__mono) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	9 (all X_b all A_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1)) -> ti(fun(X_b,bool),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_1))) # label(fact_64_insert__absorb) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	10 (all X_b all Pa ti(fun(X_b,bool),Pa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) # label(fact_76_Collect__def) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	11 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,Y) = ti(X_a,X))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	12 (all X_b all X_1 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_1),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_1))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))) # label(fact_80_insert__compr__raw) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	13 (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].
0.88/1.16	14 (all X_b all C all A_1 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_1),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)),B),C)) -> 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_1),C))))) # label(fact_72_subset__trans) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	15 (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].
0.88/1.16	16 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	17 (all X_b all B all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_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_1),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))))) # label(fact_70_set__rev__mp) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	18 (all Na all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_3)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_3))))) # label(fact_33_Suc__le__mono) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	19 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1))) # label(fact_36_Suc__n__not__le__n) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	20 (all X_b (finite_finite_1(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_14_finite__code) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	21 (all X_b all B_1 all A_2 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B_1),B))))) # label(fact_63_insertI2) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	22 (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].
0.88/1.16	23 (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].
0.88/1.16	24 (all K_1 all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_1))))) # label(fact_21_le__trans) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	25 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	26 (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_57_insert__Collect) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	27 (all M_2 all N_1 all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)),K_1) = 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_2)),N_1)),hAPP(nat,nat,suc,K_1))) # label(fact_37_Suc__diff__diff) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	28 (all X_b all B 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),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)))) # label(fact_83_subset__insertI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	29 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),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)),B),A_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_1),B)))) # label(fact_66_set__eq__subset) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	30 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | hBOOL(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	31 (all I all Pa all K (hBOOL(hAPP(nat,bool,Pa,K)) -> ((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),I)))))) # label(fact_94_zero__induct__lemma) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	32 (all X_b all X_2 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1))) # label(fact_58_insert__absorb2) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	33 (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].
0.88/1.16	34 (all X_b (finite_finite_1(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_15_finite) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	35 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	36 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	37 (all I_1 all J all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_1)),J) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K_1)) # label(fact_25_diff__commute) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	38 (all X_a all X_c all B_1_1 all B_2 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2) = hAPP(X_a,X_c,B_1_1,B_2)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	39 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> Y = X)) # label(fact_16_Suc__inject) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	40 (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].
0.88/1.16	41 (all X_b all A_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_1),A_1))) # label(fact_65_subset__refl) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	42 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(Q))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	43 (all N_1 N_1 != hAPP(nat,nat,suc,N_1)) # label(fact_19_n__not__Suc__n) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	44 (all X_b all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> 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_1)))))) # label(fact_1_finite__Collect__subsets) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	45 (all N_1 all K_1 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)))) # label(fact_40_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	46 (all N (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N)) <-> (exists M all X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M)))))) # label(fact_98_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	47 (all X_b all X_c all X_a ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	48 (all X_b all A_2 all B_1 all A_1 (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_1),A_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1)) | ti(X_b,B_1) = ti(X_b,A_2))) # label(fact_60_insert__iff) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	49 (all X_b all A_1 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_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_28_finite__subset) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	50 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1) = 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_2),A_1))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)) = 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_2),A_1))))) # label(fact_8_card__insert__if) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	51 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	52 (all X_b all A_1 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_1),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)),B),A_1)) -> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)))) # label(fact_51_equalityI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	53 (all X_b all X_c all B all F all A_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)),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_1))) <-> (exists AA (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) & 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_1)))))) # label(fact_90_subset__image__iff) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	54 (all M_3 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_3)) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)))) # label(fact_35_not__less__eq__eq) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	55 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(Q))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	56 (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].
0.88/1.16	57 (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].
0.88/1.16	58 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_18_Suc__n__not__n) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	59 (all K 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))))) # label(fact_12_finite__Collect__le__nat) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	60 (all M_2 all N_1 (M_2 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)))) # label(fact_22_eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	61 (all X_b all X_c all A_1 all B_1 all F all X_2 (ti(X_b,B_1) = hAPP(X_c,X_b,F,X_2) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_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_1)))))) # label(fact_50_image__eqI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	62 (all X_b all X_2 all A_1 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_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))))) # label(fact_69_in__mono) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	63 (all P (hBOOL(hAPP(bool,bool,fNot,P)) | hBOOL(P))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	64 (all X_b all B all X_2 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_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_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),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_1),B))))) # label(fact_85_subset__insert) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	65 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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_1),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_29_rev__finite__subset) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	66 (all X_c all X_b all F all A_2 all 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),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)) = 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))) # label(fact_88_image__insert) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	67 (all X_c all X_b all F all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> 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_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_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_1))) # label(fact_89_insert__image) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	68 (all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I_1)) = I_1)) # label(fact_42_diff__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	69 (all X_b all A_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> 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_1))))) # label(fact_3_finite_OinsertI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	70 (all X_b all Pa all Q_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1)))))) # label(fact_26_finite__Collect__disjI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	71 (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].
0.88/1.17	72 (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].
0.88/1.17	73 (all X_b all Y_2 all A_1 all X_2 (ti(X_b,Y_2) = ti(X_b,X_2) | hBOOL(hAPP(X_b,bool,A_1,X_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_1),X_2)))) # label(fact_61_insert__code) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	74 (all X_b member(X_b) = ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))) # label(tsy_c_member_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	75 (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].
0.88/1.17	76 (all X_b all X_2 all A_1 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_1),B)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1)),B)))) # label(fact_84_insert__subset) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	77 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1)) -> (exists M hAPP(nat,nat,suc,M) = M_1))) # label(fact_95_Suc__le__D) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	78 (all X_a fequal(X_a) = ti(fun(X_a,fun(X_a,bool)),fequal(X_a))) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	79 (all X_c all X_b all H all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) -> 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_1))))) # label(fact_2_finite__imageI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	80 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> N_1 = M_2))) # label(fact_20_le__antisym) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	81 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1))))) # label(fact_32_le__SucI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	82 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)))))) # label(fact_5_card__mono) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	83 (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].
0.88/1.17	84 (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),A_2),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),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)))) # label(fact_56_insert__compr) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	85 (all X_a all X_c all B_1_1 all B_2 hAPP(X_a,X_c,B_1_1,B_2) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	86 (all X_b all A_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) <-> 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_1))))) # label(fact_27_finite__insert) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	87 (all T_2 all T_1 (finite_finite_1(T_1) & finite_finite_1(T_2) -> finite_finite_1(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	88 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause).  [assumption].
0.88/1.17	89 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	90 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_24_le__refl) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	91 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	92 (all X_c all X_b all F all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),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_1))) -> (exists C_2 (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_2)) & hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_2) = ti(fun(X_b,bool),B) & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_1))))))) # label(fact_47_finite__subset__image) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	93 (all X_c all X_b all X_d all F all G all A_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),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_1)) = 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_1)) # label(fact_81_image__image) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	94 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)))) # label(fact_23_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	95 (all X_b all Y_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_1) = ti(fun(X_b,bool),Y_1)) # label(fact_82_image__ident) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	96 (all X_a undefined(X_a) = ti(X_a,undefined(X_a))) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	97 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)),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_2),A_1)))))) # label(fact_7_card__insert__le) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	98 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))) -> ti(fun(X_b,bool),B) = ti(fun(X_b,bool),A_1))))) # label(fact_6_card__seteq) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	99 (all X_c all X_b all B_1 all F all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> (hAPP(X_b,X_c,F,X_2) = ti(X_c,B_1) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B_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_1)))))) # label(fact_79_rev__image__eqI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	100 (all M_2 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)) # label(fact_38_diff__Suc__Suc) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	101 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> 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_2),A_1)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))))) # label(fact_9_card__insert__disjoint) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	102 (all X_b all X_c all Z all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z),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_1))) <-> (exists X_1 (ti(X_b,Z) = hAPP(X_c,X_b,F,X_1) & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)))))) # label(fact_77_image__iff) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	103 (all L all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M_2))))) # label(fact_44_diff__le__mono2) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	104 (all X_b all X_2 all Y_2 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1))) # label(fact_59_insert__commute) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	105 (all M_2 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)),M_2))) # label(fact_45_diff__le__self) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	106 (all X_a all X_b all 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)) = combs(X_a,X_b,X_c)) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	107 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) <-> hBOOL(hAPP(X_b,bool,A_1,X_2)))) # label(fact_75_mem__def) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	108 (all X_b all B_1 all A_1 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_1),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_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),B_1),B))))) # label(fact_86_subset__insertI2) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	109 (all X_b all X_c all F all G ((all X_1 hAPP(X_b,X_c,G,X_1) = hAPP(X_b,X_c,F,X_1)) -> ti(fun(X_b,X_c),G) = ti(fun(X_b,X_c),F))) # label(fact_74_ext) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	110 (all X_b all X_2 all A_1 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_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))))) # label(fact_71_set__mp) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	111 (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].
0.88/1.17	112 (all X_b all A_2 all C all D (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),D)) -> 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)),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))))) # label(fact_87_insert__mono) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	113 (all X_b all A_1 all B (ti(fun(X_b,bool),B) = ti(fun(X_b,bool),A_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_1),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)),B),A_1))))) # label(fact_73_equalityE) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	114 (all X_b all A_2 all B_1 all A_1 (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_1),A_1))) -> (ti(X_b,B_1) != ti(X_b,A_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1))))) # label(fact_54_insertE) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	115 (all X_b all C_1 all A_1 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_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B))))) # label(fact_52_subsetD) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	116 (all X_c all X_b all F all A_1 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_1),B)) -> 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_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),B))))) # label(fact_91_image__mono) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	117 (all X_c all X_b all F all B all A_1 ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> 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)),B)))) -> 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_1)),B)))) # label(fact_96_image__subsetI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	118 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),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_1),B)))) # label(fact_67_equalityD1) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	119 (all N_1 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),N_1))) # label(fact_11_Suc__diff__le) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	120 (all Nat_1 all Nat (hAPP(nat,nat,suc,Nat) = hAPP(nat,nat,suc,Nat_1) <-> Nat = Nat_1)) # label(fact_17_nat_Oinject) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	121 (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].
0.88/1.17	122 (all M_3 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)) | M_3 = hAPP(nat,nat,suc,Na))) # label(fact_34_le__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	123 (all X_b ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	124 (all Na all K all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Na)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_3),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K) <-> Na = M_3)))) # label(fact_41_eq__diff__iff) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	125 (all X_b all B all A_1 ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),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_1),B)))) # label(fact_93_subsetI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	126 (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].
0.88/1.17	127 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> M_2 = hAPP(nat,nat,suc,N_1)))) # label(fact_31_le__SucE) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	128 (all X_a (preorder(X_a) -> ord_less_eq(X_a) = ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	129 (all X_c all X_b all F all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> 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)),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_1))))) # label(fact_78_imageI) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	130 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)) = hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R)) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	131 (all X_c all X_b all B all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (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),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_1))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B))))) # label(fact_46_finite__surj) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	132 (all Na all K all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),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_3),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K))))))) # label(fact_39_le__diff__iff) # label(axiom) # label(non_clause).  [assumption].
0.88/1.17	133 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)))) # label(fact_30_Suc__leD) # label(axiom) # label(non_clause).  [assumption].
1.93/2.20	134 (all X_c all X_b all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> 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_1))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))))) # label(fact_4_card__image__le) # label(axiom) # label(non_clause).  [assumption].
1.93/2.20	135 (all X_c all X_b all F all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (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_1))) -> (exists X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_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),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_1))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),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_1))))))))))) # label(fact_49_pigeonhole__infinite) # label(axiom) # label(non_clause).  [assumption].
1.93/2.20	136 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),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)),B),A_1)))) # label(fact_68_equalityD2) # label(axiom) # label(non_clause).  [assumption].
1.93/2.20	137 (all X_b all B all X_2 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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_2),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_2),A_1) <-> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B))))) # label(fact_62_insert__ident) # label(axiom) # label(non_clause).  [assumption].
1.93/2.20	
1.93/2.20	============================== end of process non-clausal formulas ===
1.93/2.20	
1.93/2.20	============================== PROCESS INITIAL CLAUSES ===============
1.93/2.20	
1.93/2.20	============================== PREDICATE ELIMINATION =================
1.93/2.20	
1.93/2.20	============================== end predicate elimination =============
1.93/2.20	
1.93/2.20	Auto_denials:  (non-Horn, no changes).
1.93/2.20	
1.93/2.20	Term ordering decisions:
1.93/2.20	Function symbol KB weights:  bool=1. nat=1. suc=1. x_a=1. pname=1. fdisj=1. fconj=1. u=1. fimplies=1. mgt_call=1. fNot=1. g=1. na=1. p=1. pn=1. fun=1. ti=1. image=1. f5=1. f7=1. ord_less_eq=1. member=1. finite_finite=1. insert=1. minus_minus=1. collect=1. finite_card=1. fequal=1. combi=1. undefined=1. f4=1. combb=1. combc=1. combs=1. f3=1. f12=1. hAPP=1. f2=1. f10=1. f13=1. f1=1. f6=1. f8=1. f9=1. f11=1.
1.93/2.20	
1.93/2.20	============================== end of process initial clauses ========
1.93/2.20	
1.93/2.20	============================== CLAUSES FOR SEARCH ====================
1.93/2.20	
1.93/2.20	============================== end of clauses for search =============
1.93/2.20	
1.93/2.20	============================== SEARCH ================================
1.93/2.20	
1.93/2.20	% Starting search at 0.10 seconds.
1.93/2.20	
1.93/2.20	Low Water (keep): wt=193.000, iters=3380
1.93/2.20	
1.93/2.20	Low Water (keep): wt=189.000, iters=3345
1.93/2.20	
1.93/2.20	Low Water (keep): wt=171.000, iters=3346
1.93/2.20	
1.93/2.20	Low Water (keep): wt=166.000, iters=3552
1.93/2.20	
1.93/2.20	Low Water (keep): wt=165.000, iters=3539
1.93/2.20	
1.93/2.20	Low Water (keep): wt=151.000, iters=3355
1.93/2.20	
1.93/2.20	Low Water (keep): wt=150.000, iters=3342
5.38/5.69	
5.38/5.69	Low Water (keep): wt=145.000, iters=3490
5.38/5.69	
5.38/5.69	Low Water (keep): wt=144.000, iters=3469
5.38/5.69	
5.38/5.69	Low Water (keep): wt=143.000, iters=3472
5.38/5.69	
5.38/5.69	Low Water (keep): wt=138.000, iters=3368
5.38/5.69	
5.38/5.69	Low Water (keep): wt=130.000, iters=3370
5.38/5.69	
5.38/5.69	Low Water (keep): wt=126.000, iters=3443
5.38/5.69	
5.38/5.69	Low Water (keep): wt=124.000, iters=3396
5.38/5.69	
5.38/5.69	Low Water (keep): wt=120.000, iters=3432
5.38/5.69	
5.38/5.69	Low Water (keep): wt=118.000, iters=3389
5.38/5.69	
5.38/5.69	Low Water (keep): wt=117.000, iters=3465
5.38/5.69	
5.38/5.69	Low Water (keep): wt=115.000, iters=3431
5.38/5.69	
5.38/5.69	Low Water (keep): wt=105.000, iters=3364
5.38/5.69	
5.38/5.69	Low Water (keep): wt=104.000, iters=3335
5.38/5.69	
5.38/5.69	Low Water (keep): wt=103.000, iters=3557
5.38/5.69	
5.38/5.69	Low Water (keep): wt=99.000, iters=3476
5.38/5.69	
5.38/5.69	Low Water (keep): wt=85.000, iters=3407
5.38/5.69	
5.38/5.69	Low Water (keep): wt=82.000, iters=3375
5.38/5.69	
5.38/5.69	Low Water (keep): wt=75.000, iters=3450
5.38/5.69	
5.38/5.69	Low Water (keep): wt=72.000, iters=3366
5.38/5.69	
5.38/5.69	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 33 (0.00 of 1.83 sec).
5.38/5.69	
5.38/5.69	Low Water (keep): wt=61.000, iters=3406
5.38/5.69	
5.38/5.69	Low Water (keep): wt=54.000, iters=3547
5.38/5.69	
5.38/5.69	Low Water (keep): wt=43.000, iters=3368
5.38/5.69	
5.38/5.69	Low Water (keep): wt=33.000, iters=3489
5.38/5.69	
5.38/5.69	Low Water (keep): wt=28.000, iters=3350
5.38/5.69	
5.38/5.69	Low Water (keep): wt=24.000, iters=3421
5.38/5.69	
5.38/5.69	Low Water (keep): wt=22.000, iters=3340
5.38/5.69	
5.38/5.69	Low Water (displace): id=4159, wt=200.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3921, wt=199.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3936, wt=198.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3929, wt=197.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3863, wt=196.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3919, wt=195.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3768, wt=194.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3910, wt=193.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3906, wt=192.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3901, wt=191.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3802, wt=190.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3932, wt=189.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3832, wt=188.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=4367, wt=187.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=4390, wt=186.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=4382, wt=185.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=3799, wt=184.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=4368, wt=183.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=4162, wt=182.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=4398, wt=181.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=4339, wt=180.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=5115, wt=179.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=5964, wt=178.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=9336, wt=177.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=7482, wt=176.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=7259, wt=175.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10053, wt=174.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=8678, wt=173.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=7480, wt=172.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10191, wt=171.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10042, wt=170.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=9966, wt=169.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=9854, wt=168.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=6998, wt=167.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=9934, wt=166.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10362, wt=165.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10760, wt=164.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10190, wt=163.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=9964, wt=162.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10758, wt=161.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=9617, wt=160.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10173, wt=159.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=9949, wt=158.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10642, wt=157.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10852, wt=156.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10587, wt=155.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10050, wt=154.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10791, wt=153.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10575, wt=152.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10565, wt=151.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10511, wt=150.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10624, wt=149.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11488, wt=148.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11481, wt=147.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11431, wt=146.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10622, wt=145.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11471, wt=144.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11415, wt=143.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11406, wt=142.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=10872, wt=141.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11469, wt=140.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11769, wt=139.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11888, wt=138.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11103, wt=137.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11467, wt=136.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=12110, wt=135.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=11388, wt=134.000
5.38/5.69	
5.38/5.69	Low Water (displace): id=12339, wt=133.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12384, wt=132.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12480, wt=131.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12510, wt=130.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12517, wt=129.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12735, wt=128.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12799, wt=127.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12932, wt=126.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12093, wt=125.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=12921, wt=124.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=13202, wt=123.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=13332, wt=122.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=13505, wt=121.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=13438, wt=120.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=13684, wt=119.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=13794, wt=118.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=14035, wt=117.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=14172, wt=116.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=14407, wt=115.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=14776, wt=114.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=15542, wt=113.000
26.53/26.81	
26.53/26.81	Low Water (displace): id=15875, wt=20.000
26.53/26.81	
26.53/26.81	Low Water (keep): wt=20.000, iters=3333
26.53/26.81	
26.53/26.81	============================== PROOF =================================
26.53/26.81	% SZS status Theorem
26.53/26.81	% SZS output start Refutation
26.53/26.81	
26.53/26.81	% Proof 1 at 25.36 (+ 0.33) seconds.
26.53/26.81	% Length of proof is 11.
26.53/26.81	% Level of proof is 4.
26.53/26.81	% Maximum clause weight is 87.000.
26.53/26.81	% Given clauses 3528.
26.53/26.81	
26.53/26.81	67 (all X_c all X_b all F all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> 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_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_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_1))) # label(fact_89_insert__image) # label(axiom) # label(non_clause).  [assumption].
26.53/26.81	112 (all X_b all A_2 all C all D (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),D)) -> 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)),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))))) # label(fact_87_insert__mono) # label(axiom) # label(non_clause).  [assumption].
26.53/26.81	205 hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)) # label(conj_4) # label(hypothesis).  [assumption].
26.53/26.81	240 -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C) = hAPP(fun(D,bool),fun(D,bool),hAPP(D,fun(fun(D,bool),fun(D,bool)),insert(D),hAPP(A,D,E,B)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C)) # label(fact_89_insert__image) # label(axiom).  [clausify(67)].
26.53/26.81	241 -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hAPP(fun(D,bool),fun(D,bool),hAPP(D,fun(fun(D,bool),fun(D,bool)),insert(D),hAPP(A,D,E,B)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C)) = hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C).  [copy(240),flip(b)].
26.53/26.81	284 hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) # label(conj_1) # label(hypothesis).  [assumption].
26.53/26.81	314 -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),C))) # label(fact_87_insert__mono) # label(axiom).  [clausify(112)].
26.53/26.81	364 -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) # label(conj_6) # label(negated_conjecture).  [assumption].
26.53/26.81	614 hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),hAPP(pname,A,B,pn)),hAPP(fun(pname,bool),fun(A,bool),hAPP(fun(pname,A),fun(fun(pname,bool),fun(A,bool)),image(pname,A),B),u)) = hAPP(fun(pname,bool),fun(A,bool),hAPP(fun(pname,A),fun(fun(pname,bool),fun(A,bool)),image(pname,A),B),u).  [resolve(241,a,205,a)].
26.53/26.81	827 hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),A),g)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),A),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))).  [resolve(314,a,284,a)].
26.53/26.81	42691 $F.  [para(614(a,1),827(a,1,4)),unit_del(a,364)].
26.53/26.81	
26.53/26.81	% SZS output end Refutation
26.53/26.81	============================== end of proof ==========================
26.53/26.81	
26.53/26.81	============================== STATISTICS ============================
26.53/26.81	
26.53/26.81	Given=3528. Generated=499406. Kept=42504. proofs=1.
26.53/26.81	Usable=3513. Sos=9995. Demods=221. Limbo=0, Disabled=29196. Hints=0.
26.53/26.81	Megabytes=140.49.
26.53/26.81	User_CPU=25.36, System_CPU=0.33, Wall_clock=26.
26.53/26.81	
26.53/26.81	============================== end of statistics =====================
26.53/26.81	
26.53/26.81	============================== end of search =========================
26.53/26.81	
26.53/26.81	THEOREM PROVED
26.53/26.81	% SZS status Theorem
26.53/26.81	
26.53/26.81	Exiting with 1 proof.
26.53/26.81	
26.53/26.81	Process 19006 exit (max_proofs) Wed Jul 14 16:48:00 2021
26.53/26.82	Prover9 interrupted
26.53/26.82	EOF