TSTP Solution File: SWW474+6 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW474+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:11 EDT 2022
% Result : Unknown 201.15s 201.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW474+6 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 4 15:12:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.49/1.87 ============================== Prover9 ===============================
% 1.49/1.87 Prover9 (32) version 2009-11A, November 2009.
% 1.49/1.87 Process 24199 was started by sandbox on n027.cluster.edu,
% 1.49/1.87 Sat Jun 4 15:12:23 2022
% 1.49/1.87 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24045_n027.cluster.edu".
% 1.49/1.87 ============================== end of head ===========================
% 1.49/1.87
% 1.49/1.87 ============================== INPUT =================================
% 1.49/1.87
% 1.49/1.87 % Reading from file /tmp/Prover9_24045_n027.cluster.edu
% 1.49/1.87
% 1.49/1.87 set(prolog_style_variables).
% 1.49/1.87 set(auto2).
% 1.49/1.87 % set(auto2) -> set(auto).
% 1.49/1.87 % set(auto) -> set(auto_inference).
% 1.49/1.87 % set(auto) -> set(auto_setup).
% 1.49/1.87 % set(auto_setup) -> set(predicate_elim).
% 1.49/1.87 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.49/1.87 % set(auto) -> set(auto_limits).
% 1.49/1.87 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.49/1.87 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.49/1.87 % set(auto) -> set(auto_denials).
% 1.49/1.87 % set(auto) -> set(auto_process).
% 1.49/1.87 % set(auto2) -> assign(new_constants, 1).
% 1.49/1.87 % set(auto2) -> assign(fold_denial_max, 3).
% 1.49/1.87 % set(auto2) -> assign(max_weight, "200.000").
% 1.49/1.87 % set(auto2) -> assign(max_hours, 1).
% 1.49/1.87 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.49/1.87 % set(auto2) -> assign(max_seconds, 0).
% 1.49/1.87 % set(auto2) -> assign(max_minutes, 5).
% 1.49/1.87 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.49/1.87 % set(auto2) -> set(sort_initial_sos).
% 1.49/1.87 % set(auto2) -> assign(sos_limit, -1).
% 1.49/1.87 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.49/1.87 % set(auto2) -> assign(max_megs, 400).
% 1.49/1.87 % set(auto2) -> assign(stats, some).
% 1.49/1.87 % set(auto2) -> clear(echo_input).
% 1.49/1.87 % set(auto2) -> set(quiet).
% 1.49/1.87 % set(auto2) -> clear(print_initial_clauses).
% 1.49/1.87 % set(auto2) -> clear(print_given).
% 1.49/1.87 assign(lrs_ticks,-1).
% 1.49/1.87 assign(sos_limit,10000).
% 1.49/1.87 assign(order,kbo).
% 1.49/1.87 set(lex_order_vars).
% 1.49/1.87 clear(print_given).
% 1.49/1.87
% 1.49/1.87 % formulas(sos). % not echoed (622 formulas)
% 1.49/1.87
% 1.49/1.87 ============================== end of input ==========================
% 1.49/1.87
% 1.49/1.87 % From the command line: assign(max_seconds, 300).
% 1.49/1.87
% 1.49/1.87 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.49/1.87
% 1.49/1.87 % Formulas that are not ordinary clauses:
% 1.49/1.87 1 (all X_b all X_c all X_a ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 2 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 3 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 4 (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].
% 1.49/1.87 5 (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].
% 1.49/1.87 6 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),bool),finite_comp_fun_idem(X_a,X_b)) = finite_comp_fun_idem(X_a,X_b)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 7 (all X_a ti(fun(fun(X_a,bool),bool),finite_finite(X_a)) = finite_finite(X_a)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 8 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite1357897459simple(X_a,X_b)) = finite1357897459simple(X_a,X_b)) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 9 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite908156982e_idem(X_a,X_b)) = finite908156982e_idem(X_a,X_b)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 10 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite_folding_one(X_a)) = finite_folding_one(X_a)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 11 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite2073411215e_idem(X_a)) = finite2073411215e_idem(X_a)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 12 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b)))),fun_upd(X_a,X_b)) = fun_upd(X_a,X_b)) # label(tsy_c_Fun_Ofun__upd_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 13 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),inj_on(X_a,X_b)) = inj_on(X_a,X_b)) # label(tsy_c_Fun_Oinj__on_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 14 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)))),override_on(X_a,X_b)) = override_on(X_a,X_b)) # label(tsy_c_Fun_Ooverride__on_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 15 (all X_b (minus(X_b) -> ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)) = minus_minus(X_b))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 16 (all X_a ti(fun(fun(X_a,bool),X_a),the_1(X_a)) = the_1(X_a)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 17 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 18 (all X_a ti(fun(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool)),hoare_279057269derivs(X_a)) = hoare_279057269derivs(X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 19 (all X_a ti(fun(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool)),hoare_2027193591valids(X_a)) = hoare_2027193591valids(X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 20 (all X_a ti(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hoare_246368825triple(X_a)) = hoare_246368825triple(X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 21 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a)),hoare_1312322281e_case(X_b,X_a)) = hoare_1312322281e_case(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 22 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a)),hoare_1632998903le_rec(X_b,X_a)) = hoare_1632998903le_rec(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 23 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 24 (all X_a (semilattice_inf(X_a) -> ti(fun(X_a,fun(X_a,X_a)),semilattice_inf_inf(X_a)) = semilattice_inf_inf(X_a))) # label(tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 25 (all X_a (semilattice_sup(X_a) -> ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a)) = semilattice_sup_sup(X_a))) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 26 (all X_b all X_a ti(fun(fun(X_b,option(X_a)),fun(X_b,bool)),dom(X_b,X_a)) = dom(X_b,X_a)) # label(tsy_c_Map_Odom_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 27 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool)))),fold_graph(X_a,X_b)) = fold_graph(X_a,X_b)) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 28 (all X_b ti(option(X_b),none(X_b)) = none(X_b)) # label(tsy_c_Option_Ooption_ONone_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 29 (all X_a ti(fun(X_a,option(X_a)),some(X_a)) = some(X_a)) # label(tsy_c_Option_Ooption_OSome_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 30 (all X_a all X_b ti(fun(X_a,fun(fun(X_b,X_a),fun(option(X_b),X_a))),option_rec(X_a,X_b)) = option_rec(X_a,X_b)) # label(tsy_c_Option_Ooption_Ooption__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 31 (all X_a ti(fun(option(X_a),fun(X_a,bool)),set(X_a)) = set(X_a)) # label(tsy_c_Option_Oset_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 32 (all X_a ti(fun(option(X_a),X_a),the(X_a)) = the(X_a)) # label(tsy_c_Option_Othe_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 33 (all X_a (bot(X_a) -> ti(X_a,bot_bot(X_a)) = bot_bot(X_a))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 34 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)) = ord_less_eq(X_a))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 35 (all X_a ti(fun(X_a,fun(fun(X_a,bool),X_a)),partial_flat_lub(X_a)) = partial_flat_lub(X_a)) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 36 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 37 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool))),image(X_a,X_b)) = image(X_a,X_b)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 38 (all X_a ti(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),insert(X_a)) = insert(X_a)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 39 (all X_a ti(fun(fun(X_a,bool),X_a),the_elem(X_a)) = the_elem(X_a)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 40 (all X_a ti(fun(fun(X_a,bool),bool),fAll(X_a)) = fAll(X_a)) # label(tsy_c_fAll_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 41 (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].
% 1.49/1.87 42 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 43 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 44 (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].
% 1.49/1.87 45 (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].
% 1.49/1.87 46 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 47 (all X_a all G_1 hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 48 (all X_a all Ts all G_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_a),bool)),Ts),G_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts)))) # label(fact_1_asm) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 49 (all X_a all Ts all G_1 all Ts_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts_1)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_a),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts))))) # label(fact_2_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 50 (all X_a all G_1 all G_2 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),ord_less_eq(fun(hoare_1656922687triple(X_a),bool)),G_2),G_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 51 (all X_a all G_1 all G_2 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_2),Ts)) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),G_2)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 52 (all X_a all Ts all G_1 all T_3 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),Ts)))))) # label(fact_5_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 53 (all X_a all G_1 all T_3 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),Ts))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),T_3),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) & hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts)))) # label(fact_6_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 54 (all Pn_1 all G_1 (hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),G_1)),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1)))),bot_bot(fun(hoare_1656922687triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),bot_bot(fun(hoare_1656922687triple(state),bool))))))) # label(fact_7_MGT__BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 55 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 56 (all X_b all X_a all H all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),Fa))))) # label(fact_9_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 57 (all X_a all A_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)),bot_bot(fun(X_a,bool))),A_1))) # label(fact_10_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 58 (all X_a all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),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_3),A_1))))) # label(fact_11_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 59 (all X_a hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),bot_bot(fun(X_a,bool))))) # label(fact_12_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 60 (all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)))))) # label(fact_13_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 61 (all X_b all X_a all C_1 all A_1 ((ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1) = bot_bot(fun(X_b,bool))) & (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),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),C_1),bot_bot(fun(X_b,bool)))))) # label(fact_14_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 62 (all X_b all X_a all C_1 all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),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),C_1),bot_bot(fun(X_b,bool))))) # label(fact_15_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 63 (all X_b all X_a all F all X_2 all Y_2 (hAPP(X_b,option(X_a),F,X_2) = hAPP(X_a,option(X_a),some(X_a),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,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F)) = hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F))) # label(fact_16_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 64 (all X_b all X_a all B all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),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_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))))) # label(fact_17_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 65 (all X_a all A_1 all X_2 (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)),A_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),X_2),bot_bot(fun(X_a,bool))))) -> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) | ti(fun(X_a,bool),A_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),X_2),bot_bot(fun(X_a,bool))))) # label(fact_18_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 66 (all C_1 (hBOOL(hoare_1924220188gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP(com,bool,wt,C_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),bot_bot(fun(hoare_1656922687triple(state),bool))),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_1656922687triple(state),bool))))))))) # label(fact_19_MGF) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 67 (all X_a all A_3 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),bot_bot(fun(X_a,bool))))) # label(fact_20_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 68 (all X_a all B_1 all A_3 all B ((-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),B)) -> ti(X_a,A_3) = ti(X_a,B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B))))) # label(fact_21_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 69 (all X_a all A_3 all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_1))) -> (ti(X_a,A_3) != ti(X_a,B_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))))) # label(fact_22_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 70 (all X_a all A_1 all B (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)),A_1),B)) -> (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)),B),A_1)) -> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)))) # label(fact_23_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 71 (all X_a all C_1 all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))))) # label(fact_24_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 72 (all X_a all X_b all A_1 all B_1 all F all X_2 (ti(X_a,B_1) = hAPP(X_b,X_a,F,X_2) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))))) # label(fact_25_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 73 (all X_a all A_3 all A_1 (ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)))) # label(fact_26_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 74 (all X_a all P_1 (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = bot_bot(fun(X_a,bool)) <-> (all X_1 -hBOOL(hAPP(X_a,bool,P_1,X_1))))) # label(fact_27_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 75 (all X_a all C_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),bot_bot(fun(X_a,bool))))) # label(fact_28_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 76 (all X_a all P_1 (bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) <-> (all X_1 -hBOOL(hAPP(X_a,bool,P_1,X_1))))) # label(fact_29_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 77 (all X_a all A_1 ((exists X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))) <-> ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)))) # label(fact_30_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 78 (all X_a all A_1 ((all X_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_31_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 79 (all X_a bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fFalse))) # label(fact_32_empty__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 80 (all X_a (finite_finite_1(X_a) -> (all A_1 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_33_finite__code) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 81 (all X_a (finite_finite_1(X_a) -> (all A_1 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_34_finite) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 82 (all X_a all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_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),A_3),A_1) = ti(fun(X_a,bool),A_1))) # label(fact_35_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 83 (all X_a all B_1 all A_3 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B))))) # label(fact_36_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 84 (all X_a all B all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_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),X_2),B) <-> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B))))) # label(fact_37_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 85 (all X_a all Y_2 all A_1 all X_2 (hBOOL(hAPP(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),Y_2),A_1),X_2)) <-> ti(X_a,Y_2) = ti(X_a,X_2) | hBOOL(hAPP(X_a,bool,A_1,X_2)))) # label(fact_38_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 86 (all X_a all A_3 all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_1))) <-> ti(X_a,A_3) = ti(X_a,B_1) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)))) # label(fact_39_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 87 (all X_a all X_2 all Y_2 all A_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),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),A_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),Y_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1))) # label(fact_40_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 88 (all X_a all X_2 all A_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),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_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),X_2),A_1)) # label(fact_41_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 89 (all X_a all A_3 all P_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),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fimplies),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3)))),P_1))) # label(fact_42_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 90 (all X_a all A_3 all B 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_3),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B)))) # label(fact_43_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 91 (all X_a all A_3 all B hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3),B)))) # label(fact_44_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 92 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> -(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)),A_1),B)) -> -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)),B),A_1))))) # label(fact_45_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 93 (all X_a all C all A_1 all B (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)),A_1),B)) -> (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)),B),C)) -> 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)),A_1),C))))) # label(fact_46_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 94 (all X_a all X_2 all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))))) # label(fact_47_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 95 (all X_a all B all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))))) # label(fact_48_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 96 (all X_a all X_2 all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))))) # label(fact_49_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 97 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> 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)),B),A_1)))) # label(fact_50_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 98 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> 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)),A_1),B)))) # label(fact_51_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 99 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) <-> 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)),A_1),B)) & 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)),B),A_1)))) # label(fact_52_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 100 (all X_a all A_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)),A_1),A_1))) # label(fact_53_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 101 (all X_b all X_a all B_1 all F all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(X_b,B_1) = hAPP(X_a,X_b,F,X_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))))) # label(fact_54_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 102 (all X_b all X_a all F all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))))) # label(fact_55_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.87 103 (all X_a all X_b all Z all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),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)) & ti(X_a,Z) = hAPP(X_b,X_a,F,X_1))))) # label(fact_56_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 104 (all X_a all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))))) # label(fact_57_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 105 (all X_a all X_1 all Xa hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),Xa) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),Xa)))) # label(fact_58_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 106 (all X_a all Y_3 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3)) # label(fact_59_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 107 (all X_b all X_a all X_c all F all G all A_1 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),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),G),A_1)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_1)) # label(fact_60_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 108 (all X_a all A_3 all B_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),A_3),bot_bot(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),B_1),bot_bot(fun(X_a,bool))) -> ti(X_a,A_3) = ti(X_a,B_1))) # label(fact_61_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 109 (all X_a all B_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_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),A_3),bot_bot(fun(X_a,bool))))) -> ti(X_a,B_1) = ti(X_a,A_3))) # label(fact_62_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 110 (all X_a all A_3 all B_1 all C_1 all D (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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(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),C_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),D),bot_bot(fun(X_a,bool)))) <-> ti(X_a,A_3) = ti(X_a,C_1) & ti(X_a,B_1) = ti(X_a,D) | ti(X_a,A_3) = ti(X_a,D) & ti(X_a,B_1) = ti(X_a,C_1))) # label(fact_63_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 111 (all X_a all B_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_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),A_3),bot_bot(fun(X_a,bool))))) <-> ti(X_a,B_1) = ti(X_a,A_3))) # label(fact_64_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 112 (all X_a all A_3 all A_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),A_3),A_1) != bot_bot(fun(X_a,bool))) # label(fact_65_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 113 (all X_a all A_3 all A_1 bot_bot(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_3),A_1)) # label(fact_66_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 114 (all X_a all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),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_3),A_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)))) # label(fact_67_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 115 (all X_a all A_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)),A_1),bot_bot(fun(X_a,bool)))) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_68_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 116 (all X_b all X_a all F all A_1 (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = bot_bot(fun(X_a,bool)) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_69_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 117 (all X_b all X_a all F hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_a,bool))) # label(fact_70_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 118 (all X_a all X_b all F all A_1 (bot_bot(fun(X_a,bool)) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_71_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 119 (all X_a all A_1 all B (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)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_72_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 120 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> (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)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_73_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 121 (all X_a all A_3 all C all D_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)),C),D_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)),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_3),C)),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_3),D_1))))) # label(fact_74_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 122 (all X_a all X_b all F all G ((all X_1 hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 123 (all X_a all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) <-> hBOOL(hAPP(X_a,bool,A_1,X_2)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 124 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 125 (all X_a all B_1 all A_1 all B (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)),A_1),B)) -> 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)),A_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),B_1),B))))) # label(fact_78_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 126 (all X_a all B all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_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),X_2),B))) <-> 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)),A_1),B))))) # label(fact_79_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 127 (all X_a all X_2 all A_1 all B (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),X_2),A_1)),B)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) & 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)),A_1),B)))) # label(fact_80_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 128 (all X_a all B all A_3 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)),B),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_3),B)))) # label(fact_81_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 129 (all X_b all X_a all F all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),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),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) # label(fact_82_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 130 (all X_b all X_a all F all A_3 all B hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)) = 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(X_b,X_a,F,A_3)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B))) # label(fact_83_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 131 (all X_b all X_a all F all A_1 all B (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)),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)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))))) # label(fact_84_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 132 (all X_a all X_b all B all F all A_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)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) <-> (exists AA (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)),AA),A_1)) & ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA))))) # label(fact_85_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 133 (all X_b all X_a all M all A_3 all B_1 (hAPP(X_b,option(X_a),M,A_3) = hAPP(X_a,option(X_a),some(X_a),B_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),M))))) # label(fact_86_domI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 134 (all X_a all P_1 all A_3 ((hBOOL(hAPP(X_a,bool,P_1,A_3)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),P_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),A_3),bot_bot(fun(X_a,bool)))) & (-hBOOL(hAPP(X_a,bool,P_1,A_3)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),P_1)) = bot_bot(fun(X_a,bool))))) # label(fact_87_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 135 (all X_a all P_1 all A_3 ((hBOOL(hAPP(X_a,bool,P_1,A_3)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3))),P_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),A_3),bot_bot(fun(X_a,bool)))) & (-hBOOL(hAPP(X_a,bool,P_1,A_3)) -> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3))),P_1)) = bot_bot(fun(X_a,bool))))) # label(fact_88_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 136 (all X_a all A_3 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3)) = 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_3),bot_bot(fun(X_a,bool)))) # label(fact_89_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 137 (all X_a all A_3 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3)) = 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_3),bot_bot(fun(X_a,bool)))) # label(fact_90_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 138 (all C_1 all G_1 (hBOOL(hoare_1924220188gleton) -> ((all X_1 (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_1),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,X_1))),bot_bot(fun(hoare_1656922687triple(state),bool))))))) -> (hBOOL(hAPP(com,bool,wt,C_1)) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_1656922687triple(state),bool))))))))) # label(fact_91_MGF__lemma1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 139 (all Pn all B_2 (hBOOL(wT_bodies) -> (hAPP(pname,option(com),body,Pn) = hAPP(com,option(com),some(com),B_2) -> hBOOL(hAPP(com,bool,wt,B_2))))) # label(fact_92_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 140 (all X_a all X_b all B_1 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) -> -(all X_1 (ti(X_a,B_1) = hAPP(X_b,X_a,F,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)))))) # label(fact_93_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 141 (all X_a all P_1 all A_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (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)),Fa),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool)))) -> ((all A_5 all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_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),A_5),F_1)))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa))))))) # label(fact_94_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 142 (all P (hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,P))) -> -(all Y_1 hAPP(pname,option(com),body,P) != hAPP(com,option(com),some(com),Y_1)))) # label(fact_95_WTs__elim__cases_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 143 (all X_a all B all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)))) -> 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)),A_1),B)))) # label(fact_96_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 144 (all X_b all X_a all F all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> (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)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) -> (exists C_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)),C_3),A_1)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),C_3)) & ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_3)))))) # label(fact_97_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 145 (all X_a all P_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool)))) -> ((all X_1 all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_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),X_1),F_1))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa)))))) # label(fact_99_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 146 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_3)) <-> ti(fun(X_a,bool),A_3) = bot_bot(fun(X_a,bool)) | (exists A_4 exists A_5 (ti(fun(X_a,bool),A_3) = 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_5),A_4) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_4)))))) # label(fact_100_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 147 (all X_b all X_a all F all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) & -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_1))))))))))) # label(fact_101_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 148 (all Pname_2 all Pname_1 (hAPP(pname,com,body_1,Pname_2) = hAPP(pname,com,body_1,Pname_1) <-> ti(pname,Pname_2) = ti(pname,Pname_1))) # label(fact_102_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 149 (all G_1 all Procs (hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),semilattice_sup_sup(fun(hoare_1656922687triple(state),bool)),G_1),hAPP(fun(pname,bool),fun(hoare_1656922687triple(state),bool),hAPP(fun(pname,hoare_1656922687triple(state)),fun(fun(pname,bool),fun(hoare_1656922687triple(state),bool)),image(pname,hoare_1656922687triple(state)),hAPP(fun(pname,com),fun(pname,hoare_1656922687triple(state)),hAPP(fun(com,hoare_1656922687triple(state)),fun(fun(pname,com),fun(pname,hoare_1656922687triple(state))),combb(com,hoare_1656922687triple(state),pname),hoare_Mirabelle_MGT),body_1)),Procs))),hAPP(fun(pname,bool),fun(hoare_1656922687triple(state),bool),hAPP(fun(pname,hoare_1656922687triple(state)),fun(fun(pname,bool),fun(hoare_1656922687triple(state),bool)),image(pname,hoare_1656922687triple(state)),hAPP(fun(pname,com),fun(pname,hoare_1656922687triple(state)),hAPP(fun(com,hoare_1656922687triple(state)),fun(fun(pname,com),fun(pname,hoare_1656922687triple(state))),combb(com,hoare_1656922687triple(state),pname),hoare_Mirabelle_MGT),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),Procs))) -> (hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),Procs)) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(pname,bool),fun(hoare_1656922687triple(state),bool),hAPP(fun(pname,hoare_1656922687triple(state)),fun(fun(pname,bool),fun(hoare_1656922687triple(state),bool)),image(pname,hoare_1656922687triple(state)),hAPP(fun(pname,com),fun(pname,hoare_1656922687triple(state)),hAPP(fun(com,hoare_1656922687triple(state)),fun(fun(pname,com),fun(pname,hoare_1656922687triple(state))),combb(com,hoare_1656922687triple(state),pname),hoare_Mirabelle_MGT),body_1)),Procs)))))) # label(fact_103_MGT__Body) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 150 (all X_a all X_b all A_3 all M (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M))) -> (exists B_4 hAPP(X_a,option(X_b),M,A_3) = hAPP(X_b,option(X_b),some(X_b),B_4)))) # label(fact_104_domD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 151 (all X_a all X_2 hAPP(fun(X_a,bool),X_a,the_elem(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2)) # label(fact_105_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 152 (all X_b all X_a all F all B all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,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)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),B)))) # label(fact_106_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 153 (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_107_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 154 (all X_a all A_1 (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) <-> (exists X_1 exists B_3 (ti(fun(X_a,bool),A_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),X_1),B_3) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_3)))))) # label(fact_108_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 155 (all X_a all X hAPP(option(X_a),X_a,the(X_a),hAPP(X_a,option(X_a),some(X_a),X)) = ti(X_a,X)) # label(fact_109_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 156 (all X_a all G_1 all P_1 all Pn_1 all Q_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1))),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),hAPP(pname,com,body_1,Pn_1)),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))))) # label(fact_110_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 157 (all X_a all A_1 all C_1 all B ((-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))))) # label(fact_111_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 158 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))))) # label(fact_112_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 159 (all X_a all P_1 all Q_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) # label(fact_113_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 160 (all X_a all Fun1_1 all Com_2 all Fun2_1 all Fun1_2 all Com_1 all Fun2_2 (hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Fun1_1),Com_2),Fun2_1) = hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Fun1_2),Com_1),Fun2_2) <-> Fun1_1 = Fun1_2 & Com_2 = Com_1 & Fun2_1 = Fun2_2)) # label(fact_114_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 161 (all X_a all A_1 all C_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))))) # label(fact_115_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 162 (all X_a all B all C_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))))) # label(fact_116_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 163 (all X_a all P_1 all A_1 all B ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))) & (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))))) # label(fact_117_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 164 (all X_a all P_1 all A_1 all B ((exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) & hBOOL(hAPP(X_a,bool,P_1,X_1)))) <-> (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) & hBOOL(hAPP(X_a,bool,P_1,X_1)))) | (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) & hBOOL(hAPP(X_a,bool,P_1,X_1)))))) # label(fact_118_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 165 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))) # label(fact_119_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 166 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))) # label(fact_120_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 167 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C))) # label(fact_121_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 168 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) # label(fact_122_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 169 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),A_1)) # label(fact_123_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 170 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B)))) # label(fact_124_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 171 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1)) # label(fact_125_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 172 (all X_a all A_1 all B (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = bot_bot(fun(X_a,bool)) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) & ti(fun(X_a,bool),B) = bot_bot(fun(X_a,bool)))) # label(fact_126_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 173 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))) = ti(fun(X_a,bool),A_1)) # label(fact_127_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 174 (all X_a all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),bot_bot(fun(X_a,bool))),B) = ti(fun(X_a,bool),B)) # label(fact_128_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 175 (all X_a all G_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),G_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_1)))))) # label(fact_129_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 176 (all X_a all Fa all G_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),Fa),G_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),G_1)))) # label(fact_130_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 177 (all X_a all A_3 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(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_3),B)),C) = 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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))) # label(fact_131_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 178 (all X_a all A_1 all A_3 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_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),A_3),B)) = 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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) # label(fact_132_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 179 (all X_a all B all D_1 all A_1 all C (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)),A_1),C)) -> (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)),B),D_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),D_1)))))) # label(fact_133_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 180 (all X_a all B all A_1 all C (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)),A_1),C)) -> (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)),B),C)) -> 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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),C))))) # label(fact_134_Un__least) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 181 (all X_a all B all A_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)),B),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),A_1))) # label(fact_135_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 182 (all X_a all A_1 all B (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)),A_1),B)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B))) # label(fact_136_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 183 (all X_a all A_1 all B (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)),A_1),B)) <-> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B))) # label(fact_137_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 184 (all X_a all B all A_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)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))) # label(fact_138_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 185 (all X_a all A_1 all B 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)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)))) # label(fact_139_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 186 (all X_b all X_a all F all A_1 all B hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B))) # label(fact_140_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 187 (all X_a all A_3 all B 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_3),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),B)) # label(fact_141_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 188 (all X_a all A_3 all A_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),A_3),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(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_3),bot_bot(fun(X_a,bool)))),A_1)) # label(fact_142_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 189 (all X_a all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),semilattice_sup_sup(fun(hoare_1656922687triple(X_a),bool)),G_1),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),body_1)),Q_1)),Procs))),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),Q_1)),Procs))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),body_1)),Q_1)),Procs))))) # label(fact_143_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 190 (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_144_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 191 (all X_a (order(X_a) -> (all Z_1 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_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))))))) # label(fact_145_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 192 (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_146_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 193 (all X_a (preorder(X_a) -> (all Z_1 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_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))))))) # label(fact_147_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 194 (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_148_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 195 (all X_a (order(X_a) -> (all C_2 all B_2 all A_6 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_6)) -> (ti(X_a,B_2) = ti(X_a,C_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),A_6))))))) # label(fact_149_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 196 (all X_a (ord(X_a) -> (all C_2 all A_6 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),B_2)) -> (B_2 = C_2 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),C_2))))))) # label(fact_150_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 197 (all X_a (order(X_a) -> (all C_2 all A_6 all B_2 (ti(X_a,A_6) = ti(X_a,B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_2),A_6))))))) # label(fact_151_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 198 (all X_a (ord(X_a) -> (all C_2 all A_6 all B_2 (A_6 = B_2 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),C_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),C_2))))))) # label(fact_152_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 199 (all X_a (order(X_a) -> (all Y_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_153_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 200 (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_154_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 201 (all X_a (order(X_a) -> (all X_2 all Y_2 (ti(X_a,X_2) = ti(X_a,Y_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)))))) # label(fact_155_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 202 (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_156_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 203 (all X_a all A_3 all A_7 (hAPP(X_a,option(X_a),some(X_a),A_3) = hAPP(X_a,option(X_a),some(X_a),A_7) <-> ti(X_a,A_3) = ti(X_a,A_7))) # label(fact_157_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.88 204 (all X_a all G_1 all P_1 all C_1 all Q_1 all C ((hBOOL(C) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),hAPP(bool,fun(X_a,fun(state,bool)),hAPP(fun(X_a,fun(bool,fun(state,bool))),fun(bool,fun(X_a,fun(state,bool))),combc(X_a,bool,fun(state,bool)),hAPP(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_a),combc(state,bool,bool)),hAPP(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),P_1))),C)),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))))) # label(fact_158_constant) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 205 (all X_a all Pn_1 all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),semilattice_sup_sup(fun(hoare_1656922687triple(X_a),bool)),G_1),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),body_1)),Q_1)),Procs))),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),Q_1)),Procs))) -> (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn_1),Procs)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),hAPP(pname,fun(X_a,fun(state,bool)),P_1,Pn_1)),hAPP(pname,com,body_1,Pn_1)),hAPP(pname,fun(X_a,fun(state,bool)),Q_1,Pn_1))),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_159_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 206 (all X_a (bot(X_a) -> (all A_6 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),bot_bot(X_a))) -> ti(X_a,A_6) = bot_bot(X_a))))) # label(fact_160_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 207 (all X_a (bot(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),bot_bot(X_a))) <-> ti(X_a,A_3) = bot_bot(X_a))))) # label(fact_161_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 208 (all X_a (bot(X_a) -> (all A_6 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_6))))) # label(fact_162_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 209 (all X_a all X_b (ord(X_b) -> (all X_2 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))))) # label(fact_163_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 210 (all X_a all X_b (ord(X_b) -> (all X_2 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))))) # label(fact_164_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 211 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))))))) # label(fact_165_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 212 (all X_b all X_a (bot(X_a) -> (all X_2 hAPP(X_b,X_a,bot_bot(fun(X_b,X_a)),X_2) = bot_bot(X_a)))) # label(fact_166_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 213 (all X_a all X_b (bot(X_b) -> (all X_1 hAPP(X_a,X_b,bot_bot(fun(X_a,X_b)),X_1) = bot_bot(X_b)))) # label(fact_167_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 214 (all X_a all P_1 all Pn_1 all Q_1 all G_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),hAPP(pname,com,body_1,Pn_1)),Q_1)),G_1)),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1))),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),hAPP(pname,com,body_1,Pn_1)),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))))) # label(fact_168_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 215 (all X_b all X_a all P_1 all Q_1 all G_1 all P_2 all C0_1 all Q_2 all U_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),U_1)) -> ((all P_3 (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),G_1),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),hAPP(X_a,fun(X_b,fun(state,bool)),P_2,P_3)),hAPP(X_a,com,C0_1,P_3)),hAPP(X_a,fun(X_b,fun(state,bool)),Q_2,P_3))),bot_bot(fun(hoare_1656922687triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),G_1),hAPP(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool),hAPP(hoare_1656922687triple(X_b),fun(fun(hoare_1656922687triple(X_b),bool),fun(hoare_1656922687triple(X_b),bool)),insert(hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),hAPP(X_a,fun(X_b,fun(state,bool)),P_1,P_3)),hAPP(X_a,com,C0_1,P_3)),hAPP(X_a,fun(X_b,fun(state,bool)),Q_1,P_3))),bot_bot(fun(hoare_1656922687triple(X_b),bool))))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),G_1),hAPP(fun(X_a,bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(X_a,hoare_1656922687triple(X_b)),fun(fun(X_a,bool),fun(hoare_1656922687triple(X_b),bool)),image(X_a,hoare_1656922687triple(X_b)),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_1656922687triple(X_b)),hAPP(fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),fun(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_1656922687triple(X_b))),combs(X_a,fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),combs(X_a,com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),X_a),hoare_246368825triple(X_b)),P_2)),C0_1)),Q_2)),U_1))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_b),bool),bool,hAPP(fun(hoare_1656922687triple(X_b),bool),fun(fun(hoare_1656922687triple(X_b),bool),bool),hoare_279057269derivs(X_b),G_1),hAPP(fun(X_a,bool),fun(hoare_1656922687triple(X_b),bool),hAPP(fun(X_a,hoare_1656922687triple(X_b)),fun(fun(X_a,bool),fun(hoare_1656922687triple(X_b),bool)),image(X_a,hoare_1656922687triple(X_b)),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_1656922687triple(X_b)),hAPP(fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),fun(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,hoare_1656922687triple(X_b))),combs(X_a,fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(X_a,com),fun(X_a,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),combs(X_a,com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hAPP(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)))),fun(fun(X_a,fun(X_b,fun(state,bool))),fun(X_a,fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),X_a),hoare_246368825triple(X_b)),P_1)),C0_1)),Q_1)),U_1))))))) # label(fact_169_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 216 (all X_a all G_1 all C_1 all Q_1 all P_1 ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_3),S_3)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),hAPP(fun(state,bool),fun(X_a,fun(state,bool)),combk(fun(state,bool),X_a),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),S_3))),C_1),hAPP(fun(state,bool),fun(X_a,fun(state,bool)),combk(fun(state,bool),X_a),hAPP(X_a,fun(state,bool),Q_1,Z_3)))),bot_bot(fun(hoare_1656922687triple(X_a),bool))))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))))) # label(fact_170_escape) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 217 (all X_a all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_2027193591valids(X_a),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),semilattice_sup_sup(fun(hoare_1656922687triple(X_a),bool)),G_1),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),body_1)),Q_1)),Procs))),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),Q_1)),Procs))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_2027193591valids(X_a),G_1),hAPP(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool),hAPP(fun(pname,hoare_1656922687triple(X_a)),fun(fun(pname,bool),fun(hoare_1656922687triple(X_a),bool)),image(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a)),hAPP(fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,hoare_1656922687triple(X_a))),combs(pname,fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,com),fun(pname,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),combs(pname,com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hAPP(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),hAPP(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)))),fun(fun(pname,fun(X_a,fun(state,bool))),fun(pname,fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))))),combb(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),pname),hoare_246368825triple(X_a)),P_1)),body_1)),Q_1)),Procs))))) # label(fact_171_Body__sound__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 218 (all X_a all P_1 all G_1 all P_2 all C_1 all Q_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_2),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_3),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_2,Z_3),S_3)))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_172_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 219 (all X_a all Q_1 all G_1 all P_1 all C_1 all Q_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),C_1),Q_2)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_3),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_1,Z_3),S_3)))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_173_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 220 (all P_1 all Q_1 all C_1 (hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),bot_bot(fun(hoare_1656922687triple(state),bool))),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_1656922687triple(state),bool))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_2027193591valids(state),bot_bot(fun(hoare_1656922687triple(state),bool))),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),hoare_1656922687triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state))),hoare_246368825triple(state),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),bot_bot(fun(hoare_1656922687triple(state),bool))),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),hoare_1656922687triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state))),hoare_246368825triple(state),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(state),bool)))))))) # label(fact_174_MGF__complete) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 221 (all X_a all A_1 all B all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)) -> (-hBOOL(hAPP(X_a,bool,A_1,X_2)) -> hBOOL(hAPP(X_a,bool,B,X_2))))) # label(fact_175_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 222 (all X_a all A_1 all B all X_2 ((-hBOOL(hAPP(X_a,bool,B,X_2)) -> hBOOL(hAPP(X_a,bool,A_1,X_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)))) # label(fact_176_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 223 (all X_a all G_1 all Ts (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),Ts)) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_2027193591valids(X_a),G_1),Ts)))) # label(fact_177_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 224 (all X_a all X_1 (hBOOL(hAPP(X_a,bool,bot_bot(fun(X_a,bool)),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),bot_bot(fun(X_a,bool)))))) # label(fact_178_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 225 (all X_a all Q_1 all P_1 all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> (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)),P_1),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2))))) # label(fact_179_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 226 (all X_a all X_2 all P_1 all Q_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)),P_1),Q_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2))))) # label(fact_180_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 227 (all X_a all A_1 all B all X_2 (hBOOL(hAPP(X_a,bool,B,X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)))) # label(fact_181_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 228 (all X_a all B all A_1 all X_2 (hBOOL(hAPP(X_a,bool,A_1,X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B),X_2)))) # label(fact_182_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 229 (all X_a all R_1 all S (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(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))) <-> 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)),R_1),S)))) # label(fact_183_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 230 (all X_a all R_1 all S all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),R_1),S))))) # label(fact_184_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 231 (all X_a all Q_1 all P_1 all G_1 all P_2 all C_1 all Q_2 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_2),C_1),Q_2)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> ((all Z_3 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_3),S_3)) -> (all S_4 ((all Z_4 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_2,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_4),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_1,Z_3),S_4)))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_185_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 232 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_186_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 233 (all X_b all X_a all F1 all Fun1_1 all Com_2 all Fun2_1 hAPP(hoare_1656922687triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a),hoare_1312322281e_case(X_b,X_a),F1),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Fun1_1),Com_2),Fun2_1)) = hAPP(fun(X_b,fun(state,bool)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_2),Fun2_1)) # label(fact_187_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 234 (all X_b all X_a all F1 all Fun1_1 all Com_2 all Fun2_1 hAPP(hoare_1656922687triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_1656922687triple(X_b),X_a),hoare_1632998903le_rec(X_b,X_a),F1),hAPP(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_1656922687triple(X_b))),hoare_246368825triple(X_b),Fun1_1),Com_2),Fun2_1)) = hAPP(fun(X_b,fun(state,bool)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_2),Fun2_1)) # label(fact_188_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 235 (all X_a all X_2 hAPP(option(X_a),fun(X_a,bool),set(X_a),hAPP(X_a,option(X_a),some(X_a),X_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) # label(fact_189_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 236 (all X_a all X_2 all Xo (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(option(X_a),fun(X_a,bool),set(X_a),Xo))) <-> ti(option(X_a),Xo) = hAPP(X_a,option(X_a),some(X_a),X_2))) # label(fact_190_elem__set) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 237 (all X_a all X_2 all P_1 all A_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(option(X_a),fun(X_a,bool),set(X_a),A_1))) -> hBOOL(hAPP(X_a,bool,P_1,X_1)))) -> (ti(option(X_a),A_1) = hAPP(X_a,option(X_a),some(X_a),X_2) -> hBOOL(hAPP(X_a,bool,P_1,X_2))))) # label(fact_191_ospec) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 238 (all X_a all X_b (lattice(X_b) -> (all F all G all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_sup_sup(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))) # label(fact_192_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 239 (all X_b all X_a (lattice(X_a) -> (all F all G all X_2 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_sup_sup(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2))))) # label(fact_193_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 240 hBOOL(hoare_1924220188gleton) -> (all T_5 -(all S_3 S_3 = T_5)) # label(fact_194_single__stateE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 241 hBOOL(hoare_1924220188gleton) <-> (exists S_3 exists T_5 S_3 != T_5) # label(fact_195_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 242 (all X_a (semilattice_sup(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1))))) # label(fact_196_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 243 (all X_a (lattice(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1))))) # label(fact_197_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 244 (all X_a (semilattice_sup(X_a) -> (all A_6 all B_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2)),C_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),C_2))))) # label(fact_198_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 245 (all X_a (semilattice_sup(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z_1))))) # label(fact_199_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 246 (all X_a (lattice(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z_1))))) # label(fact_200_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 247 (all X_a (semilattice_sup(X_a) -> (all B_2 all A_6 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),C_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),C_2))))) # label(fact_201_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 248 (all X_a (semilattice_sup(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))) # label(fact_202_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 249 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))) # label(fact_203_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 250 (all X_a (semilattice_sup(X_a) -> (all A_6 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2)))) # label(fact_204_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 251 (all X_a (semilattice_sup(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)))) # label(fact_205_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 252 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)))) # label(fact_206_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 253 (all X_a (semilattice_sup(X_a) -> (all A_6 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),A_6)))) # label(fact_207_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 254 (all X_a (semilattice_sup(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X) = ti(X_a,X)))) # label(fact_208_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 255 (all X_a (semilattice_sup(X_a) -> (all A_6 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),A_6) = ti(X_a,A_6)))) # label(fact_209_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 256 (all X_a (semilattice_sup(X_a) -> (all A_6 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X))))))) # label(fact_210_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 257 (all X_a (semilattice_sup(X_a) -> (all B_2 all D_2 all A_6 all C_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),C_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_2)) -> 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),semilattice_sup_sup(X_a),A_6),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),C_2),D_2)))))))) # label(fact_211_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 258 (all X_a (semilattice_sup(X_a) -> (all Z_1 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_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)),X))))))) # label(fact_212_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 259 (all X_a (semilattice_sup(X_a) -> (all B_2 all A_6 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2)),X))))))) # label(fact_213_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 260 (all X_a (semilattice_sup(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,X))))) # label(fact_214_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 261 (all X_a (semilattice_sup(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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y) = ti(X_a,Y))))) # label(fact_215_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 262 (all X_a (semilattice_sup(X_a) -> (all A_6 all X all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2))))))) # label(fact_216_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 263 (all X_a (semilattice_sup(X_a) -> (all B_2 all X all A_6 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_6)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),B_2))))))) # label(fact_217_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 264 (all X_a (semilattice_sup(X_a) -> (all X_2 all Y_2 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2)),Z)) <-> 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_2),Z)))))) # label(fact_218_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 265 (all X_a (semilattice_sup(X_a) -> (all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2) = ti(X_a,Y_2))))) # label(fact_219_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 266 (all X_a (semilattice_sup(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_220_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 267 (all X_a (lattice(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_221_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 268 (all X_a (semilattice_sup(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_222_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 269 (all X_a (lattice(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))))) # label(fact_223_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 270 (all X_a (bounded_lattice_bot(X_a) -> (all X_2 all Y_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2) = bot_bot(X_a) <-> ti(X_a,X_2) = bot_bot(X_a) & ti(X_a,Y_2) = bot_bot(X_a))))) # label(fact_224_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 271 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),bot_bot(X_a)) = ti(X_a,X)))) # label(fact_225_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 272 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),bot_bot(X_a)),X) = ti(X_a,X)))) # label(fact_226_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 273 (all X_a all B all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> (ti(fun(X_a,bool),B) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,A_1)),hAPP(fun(X_a,bool),X_a,Fa,B)))))))) # label(fact_227_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 274 (all X_a all B all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),B) != bot_bot(fun(X_a,bool)) -> (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)),B),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,B)),hAPP(fun(X_a,bool),X_a,Fa,A_1)) = hAPP(fun(X_a,bool),X_a,Fa,A_1)))))) # label(fact_228_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 275 (all X_a all G_1 all P_1 hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),skip),P_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))) # label(fact_229_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 276 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,A_1)))))) # label(fact_230_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 277 (all X_a all P_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) -> (ti(fun(X_a,bool),Fa) != bot_bot(fun(X_a,bool)) -> ((all X_1 hBOOL(hAPP(fun(X_a,bool),bool,P_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),X_1),bot_bot(fun(X_a,bool)))))) -> ((all X_1 all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_1)) -> (ti(fun(X_a,bool),F_1) != bot_bot(fun(X_a,bool)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_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),X_1),F_1)))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa))))))) # label(fact_231_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 278 (all X_a all X_2 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2))) # label(fact_232_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 279 (all Pname hAPP(pname,com,body_1,Pname) != skip) # label(fact_233_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 280 (all Pname skip != hAPP(pname,com,body_1,Pname)) # label(fact_234_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 281 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,A_1)) = hAPP(fun(X_a,bool),X_a,Fa,A_1))))) # label(fact_236_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 282 (all X_a all N_1 all H all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F),Fa)) -> ((all X_1 all Y_1 hAPP(X_a,X_a,H,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_a,X_a,H,X_1)),hAPP(X_a,X_a,H,Y_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),N_1)) -> (ti(fun(X_a,bool),N_1) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,Fa,N_1)) = hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),H),N_1))))))) # label(fact_237_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 283 (all X_a all G_1 all P_1 all B_1 all C_1 hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),hAPP(fun(state,bool),fun(X_a,fun(state,bool)),hAPP(fun(X_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(X_a,fun(state,bool))),combc(X_a,fun(state,bool),fun(state,bool)),hAPP(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X_a,fun(state,fun(bool,bool))),fun(X_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X_a),combs(state,bool,bool)),hAPP(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_a,fun(state,bool)),fun(X_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),P_1))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),B_1))),hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),P_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))) # label(fact_238_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 284 (all X_a all D all R_1 all G_1 all P_1 all C_1 all Q_1 (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),C_1),Q_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Q_1),D),R_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(X_a),bool),bool,hAPP(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool),hoare_279057269derivs(X_a),G_1),hAPP(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool),hAPP(hoare_1656922687triple(X_a),fun(fun(hoare_1656922687triple(X_a),bool),fun(hoare_1656922687triple(X_a),bool)),insert(hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),P_1),hAPP(com,com,hAPP(com,fun(com,com),semi,C_1),D)),R_1)),bot_bot(fun(hoare_1656922687triple(X_a),bool)))))))) # label(fact_239_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 285 (all X_a all X_3 hAPP(fun(X_a,bool),X_a,the_elem(X_a),X_3) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),fequal(fun(X_a,bool)),X_3)),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),insert(X_a)),bot_bot(fun(X_a,bool)))))) # label(fact_240_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 286 (all B_1 all C_1 (hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1))) -> hBOOL(hAPP(com,bool,wt,C_1)))) # label(fact_241_WTs__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 287 (all C1 all C2 (hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(com,fun(com,com),semi,C1),C2))) -> -(hBOOL(hAPP(com,bool,wt,C1)) -> -hBOOL(hAPP(com,bool,wt,C2))))) # label(fact_242_WTs__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 288 (all Com1_3 all Com2_3 all Fun all Com_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1)) # label(fact_243_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 289 (all Fun all Com_1 all Com1_3 all Com2_3 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3)) # label(fact_244_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 290 (all Com1_3 all Com2_3 all Com1_2 all Com2_2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) <-> Com1_3 = Com1_2 & Com2_3 = Com2_2)) # label(fact_245_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 291 (all Fun_1 all Com_2 all Fun all Com_1 (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2) = hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1) <-> Fun_1 = Fun & Com_2 = Com_1)) # label(fact_246_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 292 (all Pname_1 all Fun_1 all Com_2 hAPP(pname,com,body_1,Pname_1) != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2)) # label(fact_247_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 293 (all Fun_1 all Com_2 all Pname_1 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2) != hAPP(pname,com,body_1,Pname_1)) # label(fact_248_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 294 (all B_1 all C_1 (hBOOL(hAPP(com,bool,wt,C_1)) -> hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1))))) # label(fact_249_While) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 295 (all Fun all Com_1 skip != hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1)) # label(fact_250_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 296 (all Fun all Com_1 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1) != skip) # label(fact_251_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 297 (all Pname all Com1_1 all Com2_1 hAPP(pname,com,body_1,Pname) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1)) # label(fact_252_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 298 (all Com1_1 all Com2_1 all Pname hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) != hAPP(pname,com,body_1,Pname)) # label(fact_253_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 299 (all C1 all C0 (hBOOL(hAPP(com,bool,wt,C0)) -> (hBOOL(hAPP(com,bool,wt,C1)) -> hBOOL(hAPP(com,bool,wt,hAPP(com,com,hAPP(com,fun(com,com),semi,C0),C1)))))) # label(fact_254_WT_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.89 300 (all Com1 all Com2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_255_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 301 (all Com1 all Com2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != skip) # label(fact_256_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 302 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,A_1))))))) # label(fact_257_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 303 (all X_a all X_2 all Y_2 all P_1 ((hBOOL(P_1) -> ti(X_a,X_2) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,P_1)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_2)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,P_1))),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Y_2))))) & (-hBOOL(P_1) -> ti(X_a,Y_2) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,P_1)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_2)))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,P_1))),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),Y_2))))))) # label(fact_258_If__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 304 (all X_a all A_3 hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3)) = ti(X_a,A_3)) # label(fact_259_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 305 (all X_a all X_2 hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_2)) = ti(X_a,X_2)) # label(fact_260_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 306 (all X_a all X_2 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))) = ti(X_a,X_2))) # label(fact_261_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 307 (all X_a all P_1 all A_3 (hBOOL(hAPP(X_a,bool,P_1,A_3)) -> ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> ti(X_a,X_1) = ti(X_a,A_3))) -> hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1) = ti(X_a,A_3)))) # label(fact_262_the__equality) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 308 (all X_a all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> ((all X_1 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_1),Y_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),X_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),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,Fa,A_1)),A_1))))))) # label(fact_263_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 309 (all X_a all P_1 ((exists X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) & (all Y_1 (hBOOL(hAPP(X_a,bool,P_1,Y_1)) -> ti(X_a,Y_1) = ti(X_a,X_1))))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1))))) # label(fact_264_theI_H) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 310 (all X_a all A_3 all P_1 ((exists X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) & (all Y_1 (hBOOL(hAPP(X_a,bool,P_1,Y_1)) -> ti(X_a,Y_1) = ti(X_a,X_1))))) -> (hBOOL(hAPP(X_a,bool,P_1,A_3)) -> hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1) = ti(X_a,A_3)))) # label(fact_265_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 311 (all X_a all P_1 all A_3 (hBOOL(hAPP(X_a,bool,P_1,A_3)) -> ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> ti(X_a,X_1) = ti(X_a,A_3))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1)))))) # label(fact_266_theI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 312 (all X_a all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hAPP(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_1656922687triple(X_a))),hoare_246368825triple(X_a),Fun1),Com),Fun2))) # label(fact_267_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 313 (all X_b all X_a all B all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B)))))) # label(fact_268_folding__image__simple__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 314 (all X_b all X_a all B all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_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)),B),A_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,B)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1))))) # label(fact_269_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 315 (all X_b all X_a all X_2 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),X_2) = ti(X_a,X_2))) # label(fact_270_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 316 (all X_b all X_a all X_2 all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa)) -> (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(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1)) = hAPP(fun(X_b,bool),X_a,Fa,A_1))))) # label(fact_271_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 317 (all X_b all X_a all X_2 all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(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(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1))))) # label(fact_272_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 318 (all X_b all X_a all F1 all F2 all A_3 hAPP(option(X_b),X_a,hAPP(fun(X_b,X_a),fun(option(X_b),X_a),hAPP(X_a,fun(fun(X_b,X_a),fun(option(X_b),X_a)),option_rec(X_a,X_b),F1),F2),hAPP(X_b,option(X_b),some(X_b),A_3)) = hAPP(X_b,X_a,F2,A_3)) # label(fact_273_option_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 319 (all X_b all X_a all F all G all M_1 all N_1 (ti(fun(X_a,bool),M_1) = ti(fun(X_a,bool),N_1) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),N_1)) -> hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1))) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),M_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),G),N_1)))) # label(fact_274_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 320 (all X_a all Q_1 all P_1 ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_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)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))))) # label(fact_275_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 321 (all X_a all Q_1 all P_1 ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_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)),P_1),Q_1)))) # label(fact_276_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 322 (all X_a all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) -> (exists B_3 (ti(fun(X_a,bool),A_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),A_3),B_3) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),B_3)))))) # label(fact_277_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 323 (all X_a all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> -(all B_3 (ti(fun(X_a,bool),A_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),X_2),B_3) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_3)))))) # label(fact_278_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 324 (all X_a all A_1 ((all Y_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))) -> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)))) # label(fact_279_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 325 (all G_1 all C_1 (hBOOL(hoare_1924220188gleton) -> (hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),hoare_1656922687triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state))),hoare_246368825triple(state),hAPP(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool)),hAPP(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),state),hAPP(fun(fun(state,bool),bool),fun(fun(state,fun(state,bool)),fun(state,bool)),combb(fun(state,bool),bool,state),fAll(state))),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool))),hAPP(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool)))),combb(fun(state,bool),fun(state,fun(state,bool)),state),hAPP(fun(state,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(state,fun(state,bool))),combc(state,fun(state,bool),fun(state,bool)),hAPP(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),state),combs(state,bool,bool)),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),state),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fimplies)),hAPP(com,fun(state,fun(state,bool)),evalc,C_1))))),fequal(state)))),C_1),fequal(state))),bot_bot(fun(hoare_1656922687triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_1656922687triple(state),bool)))))))) # label(fact_280_MGT__alternD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 326 (all G_1 all C_1 (hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_1656922687triple(state),bool))))) -> hBOOL(hAPP(fun(hoare_1656922687triple(state),bool),bool,hAPP(fun(hoare_1656922687triple(state),bool),fun(fun(hoare_1656922687triple(state),bool),bool),hoare_279057269derivs(state),G_1),hAPP(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool),hAPP(hoare_1656922687triple(state),fun(fun(hoare_1656922687triple(state),bool),fun(hoare_1656922687triple(state),bool)),insert(hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),hoare_1656922687triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state))),hoare_246368825triple(state),hAPP(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool)),hAPP(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(state,fun(state,fun(state,bool))),fun(state,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),state),hAPP(fun(fun(state,bool),bool),fun(fun(state,fun(state,bool)),fun(state,bool)),combb(fun(state,bool),bool,state),fAll(state))),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool))),hAPP(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(state,bool)))),combb(fun(state,bool),fun(state,fun(state,bool)),state),hAPP(fun(state,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(state,fun(state,bool))),combc(state,fun(state,bool),fun(state,bool)),hAPP(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(state,fun(state,fun(bool,bool))),fun(state,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),state),combs(state,bool,bool)),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(state,fun(state,bool)),fun(state,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),state),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fimplies)),hAPP(com,fun(state,fun(state,bool)),evalc,C_1))))),fequal(state)))),C_1),fequal(state))),bot_bot(fun(hoare_1656922687triple(state),bool))))))) # label(fact_281_MGT__alternI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 327 (all C_1 hAPP(com,hoare_1656922687triple(state),hoare_Mirabelle_MGT,C_1) = hAPP(fun(state,fun(state,bool)),hoare_1656922687triple(state),hAPP(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state)),hAPP(fun(state,fun(state,bool)),fun(com,fun(fun(state,fun(state,bool)),hoare_1656922687triple(state))),hoare_246368825triple(state),fequal(state)),C_1),hAPP(com,fun(state,fun(state,bool)),evalc,C_1))) # label(fact_282_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 328 (all Pn all S0 all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn))),S0),S1_1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body_1,Pn)),S0),S1_1)))) # label(fact_283_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 329 (all P all S_2 all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body_1,P)),S_2),S1_1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,P))),S_2),S1_1)))) # label(fact_284_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 330 (all S_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_2),T_4)) -> T_4 = S_2)) # label(fact_285_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 331 (all C_1 all B_1 all S_1 (-hBOOL(hAPP(state,bool,B_1,S_1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_1),S_1)))) # label(fact_286_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 332 (all S2_1 all C_1 all S1_2 all B_1 all S0_1 (hBOOL(hAPP(state,bool,B_1,S0_1)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S0_1),S1_2)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1_2),S2_1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S0_1),S2_1)))))) # label(fact_287_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 333 (all C1 all S2 all C0 all S0 all S1_1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C0),S0),S1_1)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S1_1),S2)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C0),C1)),S0),S2))))) # label(fact_288_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 334 (all S_2 hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,skip),S_2),S_2))) # label(fact_289_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 335 (all U all C_2 all S_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_2),S_2),T_4)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_2),S_2),U)) -> U = T_4))) # label(fact_290_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 336 (all C1 all C2 all S_2 all T_4 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(com,fun(com,com),semi,C1),C2)),S_2),T_4)) -> -(all S1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C1),S_2),S1)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C2),S1),T_4)))))) # label(fact_291_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 337 (all B_1 all C_1 all S_1 all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S_1),T_3)) -> ((T_3 = S_1 -> hBOOL(hAPP(state,bool,B_1,S_1))) -> -(hBOOL(hAPP(state,bool,B_1,S_1)) -> (all S1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S_1),S1)) -> -hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,B_1),C_1)),S1),T_3)))))))) # label(fact_292_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 338 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all B_1 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_3)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,B_1))) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,A_3))))))))) # label(fact_293_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 339 (all X_b all X_a (order(X_a) & ord(X_b) -> (all C_1 all F all B_1 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B_1)),A_3)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),B_1)) -> ((all X_1 all Y_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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,C_1)),A_3)))))))) # label(fact_294_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 340 (all X_a (order(X_a) -> (all C_1 all A_3 all F all B_1 (ti(X_a,A_3) = hAPP(X_a,X_a,F,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_1)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,Y_1)),hAPP(X_a,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,C_1)),A_3)))))))) # label(fact_295_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 341 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all A_3 all F all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_b,X_a,F,B_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_1),C_1)) -> ((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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_296_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 342 (all X_a (order(X_a) -> (all F all C_1 all B_1 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_3)) -> (hAPP(X_a,X_a,F,B_1) = ti(X_a,C_1) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,F,Y_1)),hAPP(X_a,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),hAPP(X_a,X_a,F,A_3))))))))) # label(fact_297_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 343 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all F all C_1 all A_3 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_1)) -> (hAPP(X_a,X_b,F,B_1) = C_1 -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,A_3)),C_1)))))))) # label(fact_298_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 344 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all A_3 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,B_1)),C_1)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,A_3)),C_1)))))))) # label(fact_299_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 345 (all X_a all X_b (ord(X_b) & ord(X_a) -> (all C_1 all A_3 all F all B_1 (A_3 = hAPP(X_b,X_a,F,B_1) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_1),C_1)) -> ((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_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_300_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 346 (all X_a all B all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) != bot_bot(fun(X_a,bool)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,A_1)),hAPP(fun(X_a,bool),X_a,Fa,B))))))) # label(fact_301_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 347 (all X_a all B all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> (ti(fun(X_a,bool),B) != bot_bot(fun(X_a,bool)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_a,bool),X_a,Fa,A_1)),hAPP(fun(X_a,bool),X_a,Fa,B))))))))) # label(fact_302_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 348 (all X_a all B all C_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))))) # label(fact_303_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 349 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))))) # label(fact_304_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 350 (all X_a all B all A_1 all X_2 (hBOOL(hAPP(X_a,bool,A_1,X_2)) -> (hBOOL(hAPP(X_a,bool,B,X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2))))) # label(fact_305_inf1I) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 351 (all X_a all A_1 all B all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2)) -> -(hBOOL(hAPP(X_a,bool,A_1,X_2)) -> -hBOOL(hAPP(X_a,bool,B,X_2))))) # label(fact_306_inf1E) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 352 (all X_a all G_1 all Fa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),G_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),Fa),G_1))))) # label(fact_307_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 353 (all X_a all A_1 all B (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = bot_bot(fun(X_a,bool)) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),B)) -> ti(X_a,X_1) != ti(X_a,Xa))))))) # label(fact_308_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 354 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))) = bot_bot(fun(X_a,bool))) # label(fact_309_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 355 (all X_a all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),bot_bot(fun(X_a,bool))),B) = bot_bot(fun(X_a,bool))) # label(fact_310_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 356 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),A_1) = ti(fun(X_a,bool),A_1)) # label(fact_311_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 357 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B)))) # label(fact_312_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 358 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),A_1)) # label(fact_313_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 359 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) # label(fact_314_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 360 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C))) # label(fact_315_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 361 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))) # label(fact_316_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 362 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C))) # label(fact_317_Int__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 363 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)))) # label(fact_318_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 364 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))) # label(fact_319_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 365 (all X_a all P_1 all Q_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) # label(fact_320_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 366 (all X_a all X_2 all A_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) # label(fact_321_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 367 (all X_a all R_1 all S all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)),X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),R_1),S))))) # label(fact_322_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 368 (all X_a all A_1 all B all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2)) -> hBOOL(hAPP(X_a,bool,A_1,X_2)))) # label(fact_323_inf1D1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 369 (all X_a all A_1 all B all X_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B),X_2)) -> hBOOL(hAPP(X_a,bool,B,X_2)))) # label(fact_324_inf1D2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 370 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),A_1))) # label(fact_325_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 371 (all X_a all B all C all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),C),A_1))) # label(fact_326_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 372 (all X_a all B all C all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),A_1))) # label(fact_327_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 373 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),C))) # label(fact_328_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 374 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C))) # label(fact_329_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 375 (all X_a all B all D_1 all A_1 all C (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)),A_1),C)) -> (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)),B),D_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),D_1)))))) # label(fact_330_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 376 (all X_a all B all C all A_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)),C),A_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)),C),B)) -> 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)),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))))) # label(fact_331_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 377 (all X_a all B all A_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)),B),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),B))) # label(fact_332_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 378 (all X_a all A_1 all B (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)),A_1),B)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),A_1))) # label(fact_333_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 379 (all X_a all A_1 all B 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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),B))) # label(fact_334_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 380 (all X_a all A_1 all B 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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),A_1))) # label(fact_335_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 381 (all X_a all B all A_3 all C (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),C)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(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_3),B)),C) = 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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)))) # label(fact_336_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 382 (all X_a all B all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_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),A_3),B)) = 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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))) # label(fact_337_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 383 (all X_a all B all A_3 all C (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),C)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(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_3),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C))) # label(fact_338_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 384 (all X_a all B all A_3 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_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),A_3),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) # label(fact_339_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 385 (all X_a all A_3 all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(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_3),A_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),A_3),B)) = 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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) # label(fact_340_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 386 (all X_a all B all A_3 all C ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),C)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(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_3),B)),C) = 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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),C)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(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_3),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)))) # label(fact_341_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 387 (all X_a all B all A_3 all A_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_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),A_3),B)) = 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_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_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),A_3),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))) # label(fact_342_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 388 (all X_a (lattice(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X))))) # label(fact_343_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 389 (all X_a (semilattice_inf(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),X))))) # label(fact_344_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 390 (all X_a (lattice(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y))))) # label(fact_345_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 391 (all X_a (semilattice_inf(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Y))))) # label(fact_346_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 392 (all X_a (semilattice_inf(X_a) -> (all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_2) = ti(X_a,X_2))))) # label(fact_347_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 393 (all X_a (semilattice_inf(X_a) -> (all X_2 all Y_2 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_2),Z))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z)))))) # label(fact_348_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 394 (all X_a (semilattice_inf(X_a) -> (all B_2 all A_6 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2)),X)))))) # label(fact_349_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 395 (all X_a (semilattice_inf(X_a) -> (all A_6 all B_2 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2)),X)))))) # label(fact_350_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 396 (all X_a (semilattice_inf(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)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,X))))) # label(fact_351_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 397 (all X_a (semilattice_inf(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = ti(X_a,Y))))) # label(fact_352_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 398 (all X_a (semilattice_inf(X_a) -> (all B_2 all X all A_6 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_6)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2)))))))) # label(fact_353_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 399 (all X_a (semilattice_inf(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1)))))))) # label(fact_354_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 400 (all X_a (semilattice_inf(X_a) -> (all B_2 all D_2 all A_6 all C_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_6),C_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_2)) -> 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),semilattice_inf_inf(X_a),A_6),B_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),C_2),D_2)))))))) # label(fact_355_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 401 (all X_a (semilattice_inf(X_a) -> (all X all A_6 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_6)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B_2))))))) # label(fact_356_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 402 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)) = ti(X_a,X)))) # label(fact_357_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 403 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = ti(X_a,X)))) # label(fact_358_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 404 (all X_a (distrib_lattice(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z_1))))) # label(fact_359_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 405 (all X_a (distrib_lattice(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z_1))))) # label(fact_360_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 406 (all X_a (distrib_lattice(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Z_1),X))))) # label(fact_361_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 407 (all X_a (distrib_lattice(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Z_1),X))))) # label(fact_362_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 408 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),bot_bot(X_a)) = bot_bot(X_a)))) # label(fact_363_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 409 (all X_a (bounded_lattice_bot(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),bot_bot(X_a)),X) = bot_bot(X_a)))) # label(fact_364_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 410 (all X_a (semilattice_inf(X_a) -> (all A_6 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),A_6) = ti(X_a,A_6)))) # label(fact_365_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.90 411 (all X_a (semilattice_inf(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),X) = ti(X_a,X)))) # label(fact_366_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 412 (all X_a all X_b (lattice(X_b) -> (all F all G all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),semilattice_inf_inf(fun(X_a,X_b)),F),G),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_inf_inf(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))) # label(fact_367_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 413 (all X_a (semilattice_inf(X_a) -> (all A_6 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),A_6)))) # label(fact_368_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 414 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)))) # label(fact_369_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 415 (all X_a (semilattice_inf(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),X)))) # label(fact_370_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 416 (all X_a (semilattice_inf(X_a) -> (all A_6 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2)))) # label(fact_371_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 417 (all X_a (lattice(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)))) # label(fact_372_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 418 (all X_a (semilattice_inf(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)))) # label(fact_373_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 419 (all X_a (semilattice_inf(X_a) -> (all B_2 all A_6 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),C_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),C_2))))) # label(fact_374_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 420 (all X_a (lattice(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z_1))))) # label(fact_375_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 421 (all X_a (semilattice_inf(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z_1))))) # label(fact_376_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 422 (all X_a (semilattice_inf(X_a) -> (all A_6 all B_2 all C_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2)),C_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),B_2),C_2))))) # label(fact_377_inf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 423 (all X_a (lattice(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1))))) # label(fact_378_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 424 (all X_a (semilattice_inf(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1))))) # label(fact_379_inf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 425 (all X_b all X_a (lattice(X_a) -> (all F all G all X_2 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),semilattice_inf_inf(fun(X_b,X_a)),F),G),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,G,X_2))))) # label(fact_380_inf__apply) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 426 (all X_a (lattice(X_a) -> (all X all Y all Z_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),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z_1))))))) # label(fact_381_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 427 (all X_a (lattice(X_a) -> (all X all Y all Z_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),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1))))))) # label(fact_382_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 428 (all X_a all X_b all F all A_1 all B 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_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B))))) # label(fact_383_image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 429 (all X_a all A_1 all B all C (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) <-> 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)),C),A_1)))) # label(fact_384_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 430 (all X_b all X_a all P_1 all F all G all S hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_b,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combs(X_b,X_a,fun(X_a,X_a)),hAPP(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(X_b,bool),fun(X_b,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),X_b),if(X_a)),P_1)),F)),G)),S) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),P_1)))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),S),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),P_1)))))) # label(fact_385_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 431 (all X_a all X_b all P_1 all F all G hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),hAPP(fun(X_a,option(X_b)),fun(X_a,option(X_b)),hAPP(fun(X_a,fun(option(X_b),option(X_b))),fun(fun(X_a,option(X_b)),fun(X_a,option(X_b))),combs(X_a,option(X_b),option(X_b)),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),option(X_b))),hAPP(fun(X_a,fun(option(X_b),fun(option(X_b),option(X_b)))),fun(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),option(X_b)))),combs(X_a,option(X_b),fun(option(X_b),option(X_b))),hAPP(fun(X_a,bool),fun(X_a,fun(option(X_b),fun(option(X_b),option(X_b)))),hAPP(fun(bool,fun(option(X_b),fun(option(X_b),option(X_b)))),fun(fun(X_a,bool),fun(X_a,fun(option(X_b),fun(option(X_b),option(X_b))))),combb(bool,fun(option(X_b),fun(option(X_b),option(X_b))),X_a),if(option(X_b))),P_1)),F)),G)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),G)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1))))) # label(fact_386_dom__if) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 432 (all X_a all Q_1 all P_1 all A_1 all B (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)),A_1),B)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))))))) # label(fact_387_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 433 (all X_a (lattice(X_a) -> (all X all Y all Z_1 ((all X_1 all Y_1 all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y_1),Z_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_1),Z_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Z_1)))))) # label(fact_388_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 434 (all X_a (lattice(X_a) -> (all X all Y all Z_1 ((all X_1 all Y_1 all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),Y_1),Z_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Z_1)))))) # label(fact_389_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 435 (all X_b all X_a all B all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B))))))) # label(fact_390_folding__image__simple_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 436 (all X_b all X_a all B all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B))),hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B)))))) # label(fact_391_folding__image__simple_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 437 (all X_b all X_a all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> hAPP(fun(X_b,bool),X_a,Fa,bot_bot(fun(X_b,bool))) = ti(X_a,Z))) # label(fact_392_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 438 (all X_b all X_a all X_2 all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> (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),X_a,Fa,hAPP(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(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,A_1)))))) # label(fact_393_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 439 (all X_b all X_a all B all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(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)),semilattice_inf_inf(fun(X_b,bool)),A_1),B))) -> hAPP(X_b,X_a,G,X_1) = ti(X_a,Z))) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(fun(X_b,bool),X_a,Fa,A_1)),hAPP(fun(X_b,bool),X_a,Fa,B))))))) # label(fact_394_folding__image__simple_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 440 (all X_b all X_a all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)) -> hAPP(X_b,X_a,G,X_1) = ti(X_a,Z))) -> hAPP(fun(X_b,bool),X_a,Fa,A_1) = ti(X_a,Z))))) # label(fact_395_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 441 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,A_1) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool))))))))))) # label(fact_396_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 442 (all X_a all X_2 all A_1 all F all Fa (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F),Fa)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = ti(X_a,X_2)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,X_2),hAPP(fun(X_a,bool),X_a,Fa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool)))))))))) # label(fact_397_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 443 (all X_a all B all C_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))))) # label(fact_398_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 444 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))))) # label(fact_399_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 445 (all X_a all B all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))))) # label(fact_400_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 446 (all X_a all C all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),A_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),C),B))) # label(fact_401_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 447 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),C))) # label(fact_402_Int__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 448 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C))) # label(fact_403_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 449 (all X_a all A_1 all C all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),C)),B)) # label(fact_404_Diff__Int2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 450 (all X_a all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_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),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),A_3),bot_bot(fun(X_a,bool))))) = ti(fun(X_a,bool),A_1))) # label(fact_405_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 451 (all X_a all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(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),X_2),A_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),X_2),bot_bot(fun(X_a,bool)))) = ti(fun(X_a,bool),A_1))) # label(fact_406_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 452 (all X_a all A_3 all A_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),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),A_3),bot_bot(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_3),A_1)) # label(fact_407_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 453 (all X_a all A_1 all A_3 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),A_3),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),A_3),bot_bot(fun(X_a,bool))))),B)) # label(fact_408_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 454 (all X_a all A_1 all A_3 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),A_3),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),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_3),bot_bot(fun(X_a,bool))))) # label(fact_409_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 455 (all X_a all A_1 all A_3 all B (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),A_3),B)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))))) # label(fact_410_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 456 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),A_1)) = bot_bot(fun(X_a,bool))) # label(fact_411_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 457 (all X_a all A_1 all B (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B) = ti(fun(X_a,bool),A_1))) # label(fact_412_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 458 (all X_a all X_b all F all A_1 all B 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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_1),B))))) # label(fact_413_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 459 (all X_a all A_1 all B (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)),A_1),B)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),A_1)) = ti(fun(X_a,bool),B))) # label(fact_414_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 460 (all X_a all A_1 all B all C (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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),C)) <-> 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)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C))))) # label(fact_415_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 461 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),C))) # label(fact_416_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 462 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),C)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),C))) # label(fact_417_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 463 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = ti(fun(X_a,bool),A_1)) # label(fact_418_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 464 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),A_1) = bot_bot(fun(X_a,bool))) # label(fact_419_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 465 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))) = ti(fun(X_a,bool),A_1)) # label(fact_420_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 466 (all X_a all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1) = bot_bot(fun(X_a,bool))) # label(fact_421_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 467 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))))) # label(fact_422_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 468 (all X_a all A_1 all X_2 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(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),X_2),A_1)),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) # label(fact_423_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 469 (all X_a all A_1 all X_2 all B ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(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),X_2),A_1)),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(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),X_2),A_1)),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))))) # label(fact_424_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 470 (all X_a all C all A_1 all B (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)),A_1),B)) -> (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)),B),C)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C),A_1)) = ti(fun(X_a,bool),A_1)))) # label(fact_425_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 471 (all X_a all D_1 all B all A_1 all C (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)),A_1),C)) -> (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)),D_1),B)) -> 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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C),D_1)))))) # label(fact_426_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 472 (all X_a all A_1 all B 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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),A_1))) # label(fact_427_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 473 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))))) # label(fact_428_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 474 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))) # label(fact_429_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 475 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),B) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)) # label(fact_430_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 476 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)))) # label(fact_431_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 477 (all X_a all C_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))) # label(fact_432_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 478 (all X_a all A_1 all B all C hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)),C) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),C)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),C))) # label(fact_433_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 479 (all X_a all B all A_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),A_1)),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),B),A_1)) # label(fact_434_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 480 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B)) # label(fact_435_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 481 (all X_a all X_b (minus(X_b) -> (all A_1 all B all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_1),B),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_1,X_1)),hAPP(X_a,X_b,B,X_1))))) # label(fact_436_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 482 (all X_b all X_a (minus(X_a) -> (all A_1 all B all X_2 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_1),B),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_1,X_2)),hAPP(X_b,X_a,B,X_2))))) # label(fact_437_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 483 (all X_a all A_1 all X_2 all B (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)),A_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),X_2),B))) <-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool))))),B))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_1),B))))) # label(fact_438_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 484 (all X_a all A_1 all X_2 all B (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(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool))))),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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)),A_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),X_2),B)))))) # label(fact_439_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 485 (all X_b all X_a all X_2 all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> (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),X_a,Fa,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,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_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),bot_bot(fun(X_b,bool)))))))))) # label(fact_440_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 486 (all X_b all X_a all X_2 all A_1 all F all Z all G all Fa (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite1357897459simple(X_a,X_b),F),Z),G),Fa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hAPP(fun(X_b,bool),X_a,Fa,hAPP(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(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F,hAPP(X_b,X_a,G,X_2)),hAPP(fun(X_b,bool),X_a,Fa,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_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),bot_bot(fun(X_b,bool))))))))) # label(fact_441_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 487 (all X_a all P_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,A_1)) -> ((all A_5 all A_4 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_5),A_4)) -> (hBOOL(hAPP(fun(X_a,bool),bool,P_1,A_4)) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_4),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_5),bot_bot(fun(X_a,bool)))))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool)))))))) # label(fact_442_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 488 (all X_a all X_b all F all G all A_1 hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),hAPP(fun(X_a,bool),fun(X_a,option(X_b)),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(X_a,option(X_b)))),override_on(X_a,option(X_b)),F),G),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),G)))))),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),G)))))) # label(fact_443_dom__override__on) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 489 (all X_a all X_b all F all G hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),bot_bot(fun(X_a,bool))) = ti(fun(X_a,X_b),F)) # label(fact_444_override__on__emptyset) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 490 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_1 all C_1 all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D))))))) # label(fact_445_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 491 (all X_a (ab_group_add(X_a) -> (all A_3 all B_1 all C_1 all D (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D) -> (ti(X_a,A_3) = ti(X_a,B_1) <-> ti(X_a,C_1) = ti(X_a,D)))))) # label(fact_446_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 492 (all X_b all X_a all F all G all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),A_3) = hAPP(X_a,X_b,G,A_3))) # label(fact_447_override__on__apply__in) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 493 (all X_b all X_a all F all G all A_3 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),A_3) = hAPP(X_a,X_b,F,A_3))) # label(fact_448_override__on__apply__notin) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 494 (all X_b all X_a all F all G all A_1 all X_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),X_1) = hAPP(X_a,X_b,G,X_1)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hAPP(X_a,X_b,hAPP(fun(X_a,bool),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_a,X_b))),override_on(X_a,X_b),F),G),A_1),X_1) = hAPP(X_a,X_b,F,X_1)))) # label(fact_449_override__on__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 495 (all X_a all A_1 all B_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)),A_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),B_1),bot_bot(fun(X_a,bool))))) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),partial_flat_lub(X_a),B_1),A_1) = ti(X_a,B_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)),A_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),B_1),bot_bot(fun(X_a,bool))))) -> hAPP(fun(X_a,bool),X_a,hAPP(X_a,fun(fun(X_a,bool),X_a),partial_flat_lub(X_a),B_1),A_1) = hAPP(fun(X_a,bool),X_a,the_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),B_1),bot_bot(fun(X_a,bool))))))))) # label(fact_450_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 496 (all X_a hBOOL(hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),bool,finite_comp_fun_idem(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),X_a),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),combc(fun(X_a,bool),fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)))),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(X_a,bool),fun(X_a,bool)),insert(X_a)),bot_bot(fun(X_a,bool))))))) # label(fact_451_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 497 (all X_a all X_b all X_2 all Z all F (hBOOL(hAPP(fun(X_a,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_a,X_b),F)) -> hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z)) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Z))) # label(fact_452_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 498 (all X_a (semilattice_inf(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),semilattice_inf_inf(X_a))))) # label(fact_453_comp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 499 (all X_a (semilattice_sup(X_a) -> hBOOL(hAPP(fun(X_a,fun(X_a,X_a)),bool,finite_comp_fun_idem(X_a,X_a),semilattice_sup_sup(X_a))))) # label(fact_454_comp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 500 (all X_a hBOOL(hAPP(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),bool,finite_comp_fun_idem(X_a,fun(X_a,bool)),insert(X_a)))) # label(fact_455_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 501 (all X_b all X_a all F all Y_2 all X_2 all A_1 ((hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),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_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool))))))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2)),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))) # label(fact_456_fun__upd__image) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 502 (all X_b all X_a all F all Z all Y_2 all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_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),X_2),bot_bot(fun(X_a,bool))))),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z),A_1),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F,X_2),Y_2)))))) # label(fact_457_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 503 (all X_b all X_a all F all X_2 hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),hAPP(X_a,X_b,F,X_2)) = ti(fun(X_a,X_b),F)) # label(fact_458_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 504 (all X_b all X_a all M all Y_2 all X_2 all A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(fun(X_a,bool),fun(option(X_b),bool),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(option(X_b),bool)),image(X_a,option(X_b)),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),M),X_2),hAPP(X_b,option(X_b),some(X_b),Y_2))),A_1) = hAPP(fun(X_a,bool),fun(option(X_b),bool),hAPP(fun(X_a,option(X_b)),fun(fun(X_a,bool),fun(option(X_b),bool)),image(X_a,option(X_b)),M),A_1))) # label(fact_459_image__map__upd) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 505 (all X_b all X_a all M all A_3 all X_2 all N all Y_2 (hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),M),A_3),hAPP(X_b,option(X_b),some(X_b),X_2)) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),N),A_3),hAPP(X_b,option(X_b),some(X_b),Y_2)) -> ti(X_b,X_2) = ti(X_b,Y_2))) # label(fact_460_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 506 (all X_b all X_a all T_3 all K all X_2 (hAPP(X_b,option(X_a),T_3,K) = hAPP(X_a,option(X_a),some(X_a),X_2) -> hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),T_3),K),hAPP(X_a,option(X_a),some(X_a),X_2)) = ti(fun(X_b,option(X_a)),T_3))) # label(fact_461_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 507 (all X_b all X_a all M all A_3 all B_1 all X_2 all Y_2 (hAPP(X_b,option(X_a),hAPP(option(X_a),fun(X_b,option(X_a)),hAPP(X_b,fun(option(X_a),fun(X_b,option(X_a))),hAPP(fun(X_b,option(X_a)),fun(X_b,fun(option(X_a),fun(X_b,option(X_a)))),fun_upd(X_b,option(X_a)),M),A_3),hAPP(X_a,option(X_a),some(X_a),B_1)),X_2) = hAPP(X_a,option(X_a),some(X_a),Y_2) <-> ti(X_b,X_2) = ti(X_b,A_3) & ti(X_a,B_1) = ti(X_a,Y_2) | ti(X_b,X_2) != ti(X_b,A_3) & hAPP(X_b,option(X_a),M,X_2) = hAPP(X_a,option(X_a),some(X_a),Y_2))) # label(fact_462_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 508 (all X_b all X_a all F all Z hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),fold_graph(X_a,X_b),F),Z),bot_bot(fun(X_a,bool))),Z))) # label(fact_463_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 509 (all X_b all X_a all F all X_2 all Y_2 (hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2) = ti(fun(X_a,X_b),F) <-> hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_2))) # label(fact_464_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 510 (all X_b all X_a all F all X_2 all Y_2 all Z hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2)),X_2),Z) = hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Z)) # label(fact_465_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.91 511 (all X_b all X_a all F all X_2 all Y_2 hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),hAPP(X_b,fun(X_a,fun(X_b,X_a)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,fun(X_b,X_a))),fun_upd(X_b,X_a),F),X_2),Y_2),X_2) = ti(X_a,Y_2)) # label(fact_466_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 512 (all X_b all X_a all F all Y_2 all Z all X_2 ((ti(X_a,Z) = ti(X_a,X_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2),Z) = ti(X_b,Y_2)) & (ti(X_a,Z) != ti(X_a,X_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2),Z) = hAPP(X_a,X_b,F,Z)))) # label(fact_467_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 513 (all X_b all X_a all M all B_1 all D all A_3 all C_1 (ti(X_a,A_3) != ti(X_a,C_1) -> hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),M),A_3),B_1)),C_1),D) = hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),M),C_1),D)),A_3),B_1))) # label(fact_468_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 514 (all X_b all X_a all F all Y_2 all Z all X_2 (ti(X_a,Z) != ti(X_a,X_2) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2),Z) = hAPP(X_a,X_b,F,Z))) # label(fact_469_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 515 (all X_b all X_a all F all X_2 all Y_2 (hAPP(X_b,X_a,F,X_2) = ti(X_a,Y_2) -> hAPP(X_a,fun(X_b,X_a),hAPP(X_b,fun(X_a,fun(X_b,X_a)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,fun(X_b,X_a))),fun_upd(X_b,X_a),F),X_2),Y_2) = ti(fun(X_b,X_a),F))) # label(fact_470_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 516 (all X_b all X_a all F all B_1 all A_3 all X_1 ((ti(X_a,X_1) = ti(X_a,A_3) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),A_3),B_1),X_1) = ti(X_b,B_1)) & (ti(X_a,X_1) != ti(X_a,A_3) -> hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),A_3),B_1),X_1) = hAPP(X_a,X_b,F,X_1)))) # label(fact_471_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 517 (all X_a all X_b all F all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B)) & hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B),A_1))) = bot_bot(fun(X_b,bool)))) # label(fact_472_inj__on__Un) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 518 (all X_a all X_b all F all X_2 (hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))) <-> (exists V ti(fun(X_a,option(X_b)),F) = hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(option(X_b),fun(X_a,option(X_b)),combk(option(X_b),X_a),none(X_b))),X_2),hAPP(X_b,option(X_b),some(X_b),V))))) # label(fact_473_dom__eq__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 519 (all X_a all X_b all F hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),bot_bot(fun(X_a,bool))))) # label(fact_474_inj__on__empty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 520 (all X_a all X_b all X_2 all X_1 hAPP(X_a,option(X_b),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),hAPP(option(X_b),fun(X_a,option(X_b)),combk(option(X_b),X_a),none(X_b))),X_2),none(X_b)),X_1) = none(X_b)) # label(fact_475_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 521 (all X_a all X_b all T_3 all K all X_2 -(all X_1 hAPP(X_a,option(X_b),hAPP(option(X_b),fun(X_a,option(X_b)),hAPP(X_a,fun(option(X_b),fun(X_a,option(X_b))),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),fun(X_a,option(X_b)))),fun_upd(X_a,option(X_b)),T_3),K),hAPP(X_b,option(X_b),some(X_b),X_2)),X_1) = none(X_b))) # label(fact_476_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 522 (all X_a all X_b all X_2 all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(X_a,fun(X_b,fun(X_a,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,fun(X_a,X_b))),fun_upd(X_a,X_b),F),X_2),Y_2)),A_1))))) # label(fact_477_inj__on__fun__updI) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 523 (all X_a all X_b all B all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))))) # label(fact_478_inj__on__diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 524 (all X_a all X_b all B all A_1 all F all C (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),C)) -> (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)),A_1),C)) -> (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)),B),C)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),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_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))))) # label(fact_479_inj__on__image__set__diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 525 (all X_a all X_b all B all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)))))) # label(fact_480_inj__on__Int) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 526 (all X_a all X_b all B all A_1 all F all C (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),C)) -> (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)),A_1),C)) -> (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)),B),C)) -> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_inf_inf(fun(X_a,bool)),A_1),B)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_inf_inf(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))))) # label(fact_481_inj__on__image__Int) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 527 (all X_a all X_b all F all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),semilattice_sup_sup(fun(X_a,bool)),A_1),B))) -> (hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B) <-> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)))) # label(fact_482_inj__on__Un__image__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 528 (all X_a all X_b all X_2 all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_2) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1)) -> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_483_inj__onD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 529 (all X_a all X_b all Y_2 all X_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1)) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_2) <-> ti(X_a,X_2) = ti(X_a,Y_2)))))) # label(fact_484_inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 530 (all X_a all X_b all X_2 all Y_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (ti(X_a,X_2) != ti(X_a,Y_2) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_2),A_1)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_2)))))) # label(fact_485_inj__on__contraD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 531 (all X_a all X_b all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) <-> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) -> (hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Xa) -> ti(X_a,X_1) = ti(X_a,Xa)))))))) # label(fact_486_inj__on__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 532 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),combi(X_a)),A_1))) # label(fact_487_inj__on__id2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 533 (all X_a all X_b all A_1 all F all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),B)) -> (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)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1))))) # label(fact_488_subset__inj__on) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 534 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,option(X_a)),fun(fun(X_a,bool),bool),inj_on(X_a,option(X_a)),some(X_a)),A_1))) # label(fact_489_inj__Some) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 535 (all X_a all X_b all M hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(option(X_b),fun(X_a,bool),hAPP(fun(X_a,fun(option(X_b),bool)),fun(option(X_b),fun(X_a,bool)),combc(X_a,option(X_b),bool),hAPP(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),bool)),hAPP(fun(option(X_b),fun(option(X_b),bool)),fun(fun(X_a,option(X_b)),fun(X_a,fun(option(X_b),bool))),combb(option(X_b),fun(option(X_b),bool),X_a),fequal(option(X_b))),M)),none(X_b))))) # label(fact_490_dom__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 536 (all X_a all X_b all A_3 all M (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M))) <-> hAPP(X_a,option(X_b),M,A_3) != none(X_b))) # label(fact_491_domIff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 537 (all X_a all X_2 (ti(option(X_a),X_2) != none(X_a) <-> (exists Y_1 ti(option(X_a),X_2) = hAPP(X_a,option(X_a),some(X_a),Y_1)))) # label(fact_492_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 538 (all X_a all X_2 ((all Y_1 ti(option(X_a),X_2) != hAPP(X_a,option(X_a),some(X_a),Y_1)) <-> ti(option(X_a),X_2) = none(X_a))) # label(fact_493_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 539 (all X_a all A_2 hAPP(X_a,option(X_a),some(X_a),A_2) != none(X_a)) # label(fact_494_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 540 (all X_a all A_2 none(X_a) != hAPP(X_a,option(X_a),some(X_a),A_2)) # label(fact_495_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 541 (all X_b all X_a all F1 all F2 hAPP(option(X_b),X_a,hAPP(fun(X_b,X_a),fun(option(X_b),X_a),hAPP(X_a,fun(fun(X_b,X_a),fun(option(X_b),X_a)),option_rec(X_a,X_b),F1),F2),none(X_b)) = ti(X_a,F1)) # label(fact_496_option_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 542 (all X_a all X_b all F (hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F) = bot_bot(fun(X_a,bool)) <-> (all X_1 hAPP(X_a,option(X_b),F,X_1) = none(X_b)))) # label(fact_497_dom__eq__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 543 (all X_a all X_b all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),inj_on(X_b,X_a),F),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_498_finite__imageD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 544 (all T_2 all T_1 (bounded_lattice(T_1) -> bounded_lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Obounded__lattice) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 545 (all T_2 all T_1 (bounded_lattice(T_1) -> bounded_lattice_bot(fun(T_2,T_1)))) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 546 (all T_2 all T_1 (lattice(T_1) -> semilattice_sup(fun(T_2,T_1)))) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 547 (all T_2 all T_1 (lattice(T_1) -> semilattice_inf(fun(T_2,T_1)))) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 548 (all T_2 all T_1 (distrib_lattice(T_1) -> distrib_lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Odistrib__lattice) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 549 (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].
% 1.49/1.92 550 (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].
% 1.49/1.92 551 (all T_2 all T_1 (lattice(T_1) -> lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Olattice) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 552 (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].
% 1.49/1.92 553 (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].
% 1.49/1.92 554 (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].
% 1.49/1.92 555 (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].
% 1.49/1.92 556 (all T_1 (finite_finite_1(T_1) -> finite_finite_1(option(T_1)))) # label(arity_Option_Ooption___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 557 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 558 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 559 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 560 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 561 (all X_a all X all P (-hBOOL(hAPP(fun(X_a,bool),bool,fAll(X_a),P)) | hBOOL(hAPP(X_a,bool,P,X)))) # label(help_fAll_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 562 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 563 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 564 (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].
% 1.49/1.92 565 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 566 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 567 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 568 (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].
% 1.49/1.92 569 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.92 570 (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].
% 1.49/1.92 571 (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].
% 1.49/1.92 572 (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].
% 1.49/1.92 573 (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].
% 1.49/1.92 574 (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].
% 1.49/1.95 575 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.95 576 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.95 577 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.95 578 (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].
% 1.49/1.95 579 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.95 580 (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].
% 1.49/1.95
% 1.49/1.95 ============================== end of process non-clausal formulas ===
% 1.49/1.95
% 1.49/1.95 ============================== PROCESS INITIAL CLAUSES ===============
% 1.49/1.95
% 1.49/1.95 ============================== PREDICATE ELIMINATION =================
% 1.49/1.95 581 -lattice(A) | semilattice_inf(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom). [clausify(547)].
% 1.49/1.95 582 -semilattice_inf(A) | semilattice_inf_inf(A) = ti(fun(A,fun(A,A)),semilattice_inf_inf(A)) # label(tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) # label(axiom). [clausify(24)].
% 1.49/1.95 583 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),B)) # label(fact_344_inf__le1) # label(axiom). [clausify(389)].
% 1.49/1.95 584 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),C)) # label(fact_346_inf__le2) # label(axiom). [clausify(391)].
% 1.49/1.95 585 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = ti(A,B) # label(fact_347_le__iff__inf) # label(axiom). [clausify(392)].
% 1.49/1.95 586 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) != ti(A,B) # label(fact_347_le__iff__inf) # label(axiom). [clausify(392)].
% 1.49/1.95 587 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_348_le__inf__iff) # label(axiom). [clausify(393)].
% 1.49/1.95 588 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_348_le__inf__iff) # label(axiom). [clausify(393)].
% 1.49/1.95 589 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_348_le__inf__iff) # label(axiom). [clausify(393)].
% 1.49/1.95 590 -semilattice_inf(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),semilattice_inf_inf(A),B),D)),C)) # label(fact_349_le__infI1) # label(axiom). [clausify(394)].
% 1.49/1.95 591 -semilattice_inf(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),semilattice_inf_inf(A),D),B)),C)) # label(fact_350_le__infI2) # label(axiom). [clausify(395)].
% 1.49/1.95 592 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = ti(A,B) # label(fact_351_inf__absorb1) # label(axiom). [clausify(396)].
% 1.49/1.95 593 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) = ti(A,B) # label(fact_352_inf__absorb2) # label(axiom). [clausify(397)].
% 1.49/1.95 594 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) # label(fact_353_le__infI) # label(axiom). [clausify(398)].
% 1.49/1.95 595 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) # label(fact_354_inf__greatest) # label(axiom). [clausify(399)].
% 1.49/1.95 596 -semilattice_inf(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),semilattice_inf_inf(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),E))) # label(fact_355_inf__mono) # label(axiom). [clausify(400)].
% 1.49/1.95 597 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_356_le__infE) # label(axiom). [clausify(401)].
% 1.49/1.95 598 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_356_le__infE) # label(axiom). [clausify(401)].
% 1.49/1.95 599 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_365_inf_Oidem) # label(axiom). [clausify(410)].
% 1.49/1.95 600 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) = ti(A,B) # label(fact_366_inf__idem) # label(axiom). [clausify(411)].
% 1.49/1.95 601 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) # label(fact_368_inf_Ocommute) # label(axiom). [clausify(413)].
% 1.49/1.95 602 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) # label(fact_370_inf__commute) # label(axiom). [clausify(415)].
% 1.49/1.95 603 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) # label(fact_371_inf_Oleft__idem) # label(axiom). [clausify(416)].
% 1.49/1.95 604 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) # label(fact_373_inf__left__idem) # label(axiom). [clausify(418)].
% 1.49/1.95 605 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)) # label(fact_374_inf_Oleft__commute) # label(axiom). [clausify(419)].
% 1.49/1.95 606 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),D)) # label(fact_376_inf__left__commute) # label(axiom). [clausify(421)].
% 1.49/1.95 607 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) # label(fact_377_inf_Oassoc) # label(axiom). [clausify(422)].
% 1.49/1.95 608 -semilattice_inf(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),D)) # label(fact_379_inf__assoc) # label(axiom). [clausify(424)].
% 1.49/1.95 609 -semilattice_inf(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_inf_inf(A))) # label(fact_453_comp__fun__idem__inf) # label(axiom). [clausify(498)].
% 1.49/1.95 Derived: -lattice(A) | semilattice_inf_inf(fun(B,A)) = ti(fun(fun(B,A),fun(fun(B,A),fun(B,A))),semilattice_inf_inf(fun(B,A))). [resolve(581,b,582,a)].
% 1.49/1.95 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),C)). [resolve(581,b,583,a)].
% 1.49/1.95 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),D)). [resolve(581,b,584,a)].
% 1.49/1.95 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) = ti(fun(B,A),C). [resolve(581,b,585,a)].
% 1.49/1.95 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) != ti(fun(B,A),C). [resolve(581,b,586,a)].
% 1.49/1.95 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)). [resolve(581,b,587,a)].
% 1.49/1.95 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(581,b,588,a)].
% 1.49/1.95 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E))) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(581,b,589,a)].
% 1.49/1.95 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)),D)). [resolve(581,b,590,a)].
% 1.49/1.95 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),E),C)),D)). [resolve(581,b,591,a)].
% 1.49/1.95 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),C) = ti(fun(B,A),C). [resolve(581,b,593,a)].
% 1.49/1.95 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),E),F)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),F))). [resolve(581,b,596,a)].
% 1.49/1.95 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),C) = ti(fun(B,A),C). [resolve(581,b,599,a)].
% 1.49/1.95 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),C). [resolve(581,b,601,a)].
% 1.49/1.95 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D). [resolve(581,b,603,a)].
% 1.49/1.95 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),E)). [resolve(581,b,605,a)].
% 1.49/1.95 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),D)),E) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),D),E)). [resolve(581,b,607,a)].
% 1.49/1.95 Derived: -lattice(A) | hBOOL(hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),bool,finite_comp_fun_idem(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)))). [resolve(581,b,609,a)].
% 1.49/1.95 610 semilattice_inf(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__inf) # label(axiom). [assumption].
% 1.49/1.95 Derived: semilattice_inf_inf(bool) = ti(fun(bool,fun(bool,bool)),semilattice_inf_inf(bool)). [resolve(610,a,582,a)].
% 1.49/1.95 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),A)). [resolve(610,a,583,a)].
% 1.49/1.95 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),B)). [resolve(610,a,584,a)].
% 1.49/1.95 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) = ti(bool,A). [resolve(610,a,585,a)].
% 1.49/1.95 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) != ti(bool,A). [resolve(610,a,586,a)].
% 1.49/1.95 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)). [resolve(610,a,587,a)].
% 1.49/1.95 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(610,a,588,a)].
% 1.49/1.95 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C))) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(610,a,589,a)].
% 1.49/1.95 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)),B)). [resolve(610,a,590,a)].
% 1.49/1.95 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),C),A)),B)). [resolve(610,a,591,a)].
% 1.49/1.95 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),A) = ti(bool,A). [resolve(610,a,593,a)].
% 1.49/1.95 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),C),D)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),D))). [resolve(610,a,596,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),A) = ti(bool,A). [resolve(610,a,599,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),A). [resolve(610,a,601,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B). [resolve(610,a,603,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),C)). [resolve(610,a,605,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B)),C) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),C)). [resolve(610,a,607,a)].
% 1.49/1.98 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_inf_inf(bool))). [resolve(610,a,609,a)].
% 1.49/1.98 611 -lattice(A) | semilattice_sup(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom). [clausify(546)].
% 1.49/1.98 612 -semilattice_sup(A) | semilattice_sup_sup(A) = ti(fun(A,fun(A,A)),semilattice_sup_sup(A)) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom). [clausify(25)].
% 1.49/1.98 613 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) # label(fact_196_sup__assoc) # label(axiom). [clausify(242)].
% 1.49/1.98 614 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) # label(fact_198_sup_Oassoc) # label(axiom). [clausify(244)].
% 1.49/1.98 615 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)) # label(fact_199_sup__left__commute) # label(axiom). [clausify(245)].
% 1.49/1.98 616 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)) # label(fact_201_sup_Oleft__commute) # label(axiom). [clausify(247)].
% 1.49/1.98 617 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_202_sup__left__idem) # label(axiom). [clausify(248)].
% 1.49/1.98 618 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_204_sup_Oleft__idem) # label(axiom). [clausify(250)].
% 1.49/1.98 619 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) # label(fact_205_sup__commute) # label(axiom). [clausify(251)].
% 1.49/1.98 620 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) # label(fact_207_sup_Ocommute) # label(axiom). [clausify(253)].
% 1.49/1.98 621 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_208_sup__idem) # label(axiom). [clausify(254)].
% 1.49/1.98 622 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_209_sup_Oidem) # label(axiom). [clausify(255)].
% 1.49/1.98 623 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_210_le__supE) # label(axiom). [clausify(256)].
% 1.49/1.98 624 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_210_le__supE) # label(axiom). [clausify(256)].
% 1.49/1.98 625 -semilattice_sup(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),semilattice_sup_sup(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),E))) # label(fact_211_sup__mono) # label(axiom). [clausify(257)].
% 1.49/1.98 626 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),C)) # label(fact_212_sup__least) # label(axiom). [clausify(258)].
% 1.49/1.98 627 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),C)) # label(fact_213_le__supI) # label(axiom). [clausify(259)].
% 1.49/1.98 628 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) = ti(A,C) # label(fact_214_sup__absorb1) # label(axiom). [clausify(260)].
% 1.49/1.98 629 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = ti(A,C) # label(fact_215_sup__absorb2) # label(axiom). [clausify(261)].
% 1.49/1.98 630 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),C))) # label(fact_216_le__supI2) # label(axiom). [clausify(262)].
% 1.49/1.98 631 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D))) # label(fact_217_le__supI1) # label(axiom). [clausify(263)].
% 1.49/1.98 632 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_218_le__sup__iff) # label(axiom). [clausify(264)].
% 1.49/1.98 633 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_218_le__sup__iff) # label(axiom). [clausify(264)].
% 1.49/1.98 634 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_218_le__sup__iff) # label(axiom). [clausify(264)].
% 1.49/1.98 635 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = ti(A,C) # label(fact_219_le__iff__sup) # label(axiom). [clausify(265)].
% 1.49/1.98 636 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) != ti(A,C) # label(fact_219_le__iff__sup) # label(axiom). [clausify(265)].
% 1.49/1.98 637 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B))) # label(fact_220_sup__ge2) # label(axiom). [clausify(266)].
% 1.49/1.98 638 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C))) # label(fact_222_sup__ge1) # label(axiom). [clausify(268)].
% 1.49/1.98 639 -semilattice_sup(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),semilattice_sup_sup(A))) # label(fact_454_comp__fun__idem__sup) # label(axiom). [clausify(499)].
% 1.49/1.98 Derived: -lattice(A) | semilattice_sup_sup(fun(B,A)) = ti(fun(fun(B,A),fun(fun(B,A),fun(B,A))),semilattice_sup_sup(fun(B,A))). [resolve(611,b,612,a)].
% 1.49/1.98 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)),E) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E)). [resolve(611,b,613,a)].
% 1.49/1.98 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),E)). [resolve(611,b,615,a)].
% 1.49/1.98 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D). [resolve(611,b,617,a)].
% 1.49/1.98 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C). [resolve(611,b,619,a)].
% 1.49/1.98 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),C) = ti(fun(B,A),C). [resolve(611,b,621,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)),E)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),E)). [resolve(611,b,623,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)),E)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),D),E)). [resolve(611,b,624,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),E),F)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),E)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),F))). [resolve(611,b,625,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),E),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),E)),D)). [resolve(611,b,626,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C) = ti(fun(B,A),D). [resolve(611,b,628,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) = ti(fun(B,A),D). [resolve(611,b,629,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),E),D))). [resolve(611,b,630,a)].
% 1.49/1.98 Derived: -lattice(A) | -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E))). [resolve(611,b,631,a)].
% 1.49/1.98 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),D)) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) != ti(fun(B,A),D). [resolve(611,b,636,a)].
% 1.49/1.98 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C))). [resolve(611,b,637,a)].
% 1.49/1.98 Derived: -lattice(A) | hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_eq(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D))). [resolve(611,b,638,a)].
% 1.49/1.98 Derived: -lattice(A) | hBOOL(hAPP(fun(fun(B,A),fun(fun(B,A),fun(B,A))),bool,finite_comp_fun_idem(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)))). [resolve(611,b,639,a)].
% 1.49/1.98 640 semilattice_sup(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 1.49/1.98 Derived: semilattice_sup_sup(bool) = ti(fun(bool,fun(bool,bool)),semilattice_sup_sup(bool)). [resolve(640,a,612,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C)). [resolve(640,a,613,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),C)). [resolve(640,a,615,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B). [resolve(640,a,617,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A). [resolve(640,a,619,a)].
% 1.49/1.98 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),A) = ti(bool,A). [resolve(640,a,621,a)].
% 1.49/1.98 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),C)). [resolve(640,a,623,a)].
% 1.49/1.98 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),B),C)). [resolve(640,a,624,a)].
% 1.49/1.98 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),C),D)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),C)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),D))). [resolve(640,a,625,a)].
% 1.49/2.04 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),C),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),C)),B)). [resolve(640,a,626,a)].
% 1.49/2.04 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A) = ti(bool,B). [resolve(640,a,628,a)].
% 1.49/2.04 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = ti(bool,B). [resolve(640,a,629,a)].
% 1.49/2.04 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),C),B))). [resolve(640,a,630,a)].
% 1.49/2.04 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C))). [resolve(640,a,631,a)].
% 1.49/2.04 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) != ti(bool,B). [resolve(640,a,636,a)].
% 1.49/2.04 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A))). [resolve(640,a,637,a)].
% 1.49/2.04 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B))). [resolve(640,a,638,a)].
% 1.49/2.04 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_sup_sup(bool))). [resolve(640,a,639,a)].
% 1.49/2.04 641 -bounded_lattice(A) | bounded_lattice_bot(fun(B,A)) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom). [clausify(545)].
% 1.49/2.04 642 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) != bot_bot(A) | bot_bot(A) = ti(A,B) # label(fact_224_sup__eq__bot__iff) # label(axiom). [clausify(270)].
% 1.49/2.04 643 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) != bot_bot(A) | bot_bot(A) = ti(A,C) # label(fact_224_sup__eq__bot__iff) # label(axiom). [clausify(270)].
% 1.49/2.04 644 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = bot_bot(A) | bot_bot(A) != ti(A,B) | bot_bot(A) != ti(A,C) # label(fact_224_sup__eq__bot__iff) # label(axiom). [clausify(270)].
% 1.49/2.04 645 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),bot_bot(A)) = ti(A,B) # label(fact_225_sup__bot__right) # label(axiom). [clausify(271)].
% 1.49/2.04 646 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),bot_bot(A)),B) = ti(A,B) # label(fact_226_sup__bot__left) # label(axiom). [clausify(272)].
% 1.49/2.04 647 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),bot_bot(A)) = bot_bot(A) # label(fact_363_inf__bot__right) # label(axiom). [clausify(408)].
% 1.49/2.04 648 -bounded_lattice_bot(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),bot_bot(A)),B) = bot_bot(A) # label(fact_364_inf__bot__left) # label(axiom). [clausify(409)].
% 1.49/2.04 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) != bot_bot(fun(B,A)) | bot_bot(fun(B,A)) = ti(fun(B,A),C). [resolve(641,b,642,a)].
% 1.49/2.04 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) != bot_bot(fun(B,A)) | bot_bot(fun(B,A)) = ti(fun(B,A),D). [resolve(641,b,643,a)].
% 1.49/2.04 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) = bot_bot(fun(B,A)) | bot_bot(fun(B,A)) != ti(fun(B,A),C) | bot_bot(fun(B,A)) != ti(fun(B,A),D). [resolve(641,b,644,a)].
% 1.49/2.04 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),bot_bot(fun(B,A))) = ti(fun(B,A),C). [resolve(641,b,645,a)].
% 3.91/4.14 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),bot_bot(fun(B,A))),C) = ti(fun(B,A),C). [resolve(641,b,646,a)].
% 3.91/4.14 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),C),bot_bot(fun(B,A))) = bot_bot(fun(B,A)). [resolve(641,b,647,a)].
% 3.91/4.14 Derived: -bounded_lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_inf_inf(fun(B,A)),bot_bot(fun(B,A))),C) = bot_bot(fun(B,A)). [resolve(641,b,648,a)].
% 3.91/4.14 649 bounded_lattice_bot(bool) # label(arity_HOL_Obool___Lattices_Obounded__lattice__bot) # label(axiom). [assumption].
% 3.91/4.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) != bot_bot(bool) | bot_bot(bool) = ti(bool,A). [resolve(649,a,642,a)].
% 3.91/4.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) != bot_bot(bool) | bot_bot(bool) = ti(bool,B). [resolve(649,a,643,a)].
% 3.91/4.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = bot_bot(bool) | bot_bot(bool) != ti(bool,A) | bot_bot(bool) != ti(bool,B). [resolve(649,a,644,a)].
% 3.91/4.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),bot_bot(bool)) = ti(bool,A). [resolve(649,a,645,a)].
% 3.91/4.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),bot_bot(bool)),A) = ti(bool,A). [resolve(649,a,646,a)].
% 3.91/4.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),bot_bot(bool)) = bot_bot(bool). [resolve(649,a,647,a)].
% 3.91/4.14 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),bot_bot(bool)),A) = bot_bot(bool). [resolve(649,a,648,a)].
% 3.91/4.14
% 3.91/4.14 ============================== end predicate elimination =============
% 3.91/4.14
% 3.91/4.14 Auto_denials: (non-Horn, no changes).
% 3.91/4.14
% 3.91/4.14 Term ordering decisions:
% 3.91/4.14 Function symbol KB weights: bool=1. state=1. com=1. pname=1. evalc=1. body_1=1. while=1. fconj=1. body=1. wt=1. hoare_Mirabelle_MGT=1. semi=1. fdisj=1. fimplies=1. fNot=1. hoare_1924220188gleton=1. fFalse=1. skip=1. fTrue=1. fa=1. wT_bodies=1. pn=1. y=1. c1=1. c2=1. fun=1. ti=1. image=1. inj_on=1. fun_upd=1. dom=1. combk=1. finite1357897459simple=1. finite_comp_fun_idem=1. override_on=1. finite908156982e_idem=1. fold_graph=1. option_rec=1. hoare_1312322281e_case=1. hoare_1632998903le_rec=1. f1=1. f2=1. f3=1. f4=1. f8=1. f17=1. f18=1. f22=1. f23=1. f55=1. f56=1. f57=1. f63=1. f99=1. f100=1. hoare_1656922687triple=1. ord_less_eq=1. option=1. bot_bot=1. member=1. semilattice_sup_sup=1. semilattice_inf_inf=1. insert=1. finite_finite=1. minus_minus=1. hoare_279057269derivs=1. hoare_246368825triple=1. collect=1. some=1. fequal=1. the_1=1. none=1. the=1. finite_folding_one=1. finite2073411215e_idem=1. hoare_2027193591valids=1. if=1. set=1. combi=1. fAll=1. partial_flat_lub=1. the_elem=1. undefined=1. f12=1. f43=1. combb=1. combs=1. combc=1. f13=1. f15=1. f16=1. f44=1. f45=1. f46=1. f49=1. f52=1. f54=1. f59=1. f60=1. f61=1. f62=1. f82=1. f83=1. f93=1. f94=1. f101=1. hAPP=1. f6=1. f10=1. f11=1. f19=1. f20=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f41=1. f42=1. f50=1. f51=1. f53=1. f64=1. f65=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f95=1. f97=1. f98=1. f5=1. f7=1. f9=1. f14=1. f21=1. f32=1. f33=1. f47=1. f48=1. f70=1. f71=1. f74=1. f75=1. f84=1. f96=1. f34=1. f35=1. f36=1. f37=1. f58=1. f66=1. f67=1. f68=1. f69=1. f72=1. f73=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f38=1. f39=1. f40=1. f92=1. f91=1. f31=1.
% 3.91/4.14
% 3.91/4.14 ============================== end of process initial clauses ========
% 3.91/4.14
% 3.91/4.14 ============================== CLAUSES FOR SEARCH ====================
% 3.91/4.14
% 3.91/4.14 ============================== end of clauses for search =============
% 3.91/4.14
% 3.91/4.14 ============================== SEARCH ================================
% 3.91/4.14
% 3.91/4.14 % Starting search at 0.70 seconds.
% 3.91/4.14
% 3.91/4.14 Low Water (keep): wt=178.000, iters=3518
% 3.91/4.14
% 3.91/4.14 Low Water (keep): wt=175.000, iters=3466
% 3.91/4.14
% 3.91/4.14 Low Water (keep): wt=173.000, iters=3414
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=165.000, iters=3377
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=162.000, iters=3505
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=154.000, iters=3343
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=151.000, iters=3413
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=149.000, iters=3366
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=148.000, iters=3359
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=145.000, iters=3733
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=143.000, iters=3792
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=123.000, iters=3339
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=121.000, iters=3357
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=120.000, iters=3505
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=118.000, iters=3493
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=116.000, iters=3460
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=114.000, iters=3683
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=108.000, iters=3402
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=107.000, iters=3365
% 201.15/201.42
% 201.15/201.42 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 56 (0.00 of 3.41 sec).
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=106.000, iters=3371
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=103.000, iters=3362
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=101.000, iters=3354
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=100.000, iters=3538
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=95.000, iters=3337
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=94.000, iters=3390
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=92.000, iters=3350
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=90.000, iters=3350
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=89.000, iters=3368
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=88.000, iters=3363
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=86.000, iters=3345
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=85.000, iters=3382
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=83.000, iters=3379
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=81.000, iters=3334
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=80.000, iters=3360
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=79.000, iters=3399
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=78.000, iters=3422
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=77.000, iters=3494
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=76.000, iters=3395
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=74.000, iters=3346
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=70.000, iters=3387
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=68.000, iters=3333
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=67.000, iters=3367
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=65.000, iters=3372
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=64.000, iters=3342
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=63.000, iters=3420
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=61.000, iters=3343
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=59.000, iters=3459
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=58.000, iters=3407
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=57.000, iters=3490
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=56.000, iters=3480
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=54.000, iters=3425
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=50.000, iters=3408
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=47.000, iters=3587
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=46.000, iters=3704
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=41.000, iters=3350
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=40.000, iters=3466
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=37.000, iters=3452
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=5172, wt=200.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=5233, wt=199.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=5093, wt=198.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=4567, wt=197.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=5235, wt=196.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=5328, wt=194.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=13542, wt=14.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=13582, wt=13.000
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=13586, wt=12.000
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=36.000, iters=3654
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=13814, wt=11.000
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=34.000, iters=3648
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=32.000, iters=3521
% 201.15/201.42
% 201.15/201.42 Low Water (displace): id=14678, wt=10.000
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=31.000, iters=3489
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=29.000, iters=3441
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=26.000, iters=3359
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=25.000, iters=3333
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=24.000, iters=3448
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=23.000, iters=3539
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=22.000, iters=3386
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=21.000, iters=3498
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=18.000, iters=3337
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=17.000, iters=3337
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=16.000, iters=3333
% 201.15/201.42
% 201.15/201.42 Low Water (keep): wt=15.000, iters=3334
% 201.15/201.42
% 201.15/201.42 ============================== STATISTICS ============================
% 201.15/201.42
% 201.15/201.42 Given=21290. Generated=8890452. Kept=209747. proofs=0.
% 201.15/201.42 Usable=21173. Sos=9998. Demods=455. Limbo=12045, Disabled=167444. Hints=0.
% 201.15/201.42 Kept_by_rule=0, Deleted_by_rule=282959.
% 201.15/201.42 Forward_subsumed=232824. Back_subsumed=113.
% 201.15/201.42 Sos_limit_deleted=8164922. Sos_displaced=164820. Sos_removed=0.
% 201.15/201.42 New_demodulators=828 (0 lex), Back_demodulated=1468. Back_unit_deleted=129.
% 201.15/201.42 Demod_attempts=322257936. Demod_rewrites=374872.
% 201.15/201.42 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 201.15/201.42 Nonunit_fsub_feature_tests=1809030. Nonunit_bsub_feature_tests=19941.
% 201.15/201.42 Megabytes=419.43.
% 201.15/201.42 User_CPU=195.04, System_CPU=4.67, Wall_clock=200.
% 201.15/201.42
% 201.15/201.42 Megs malloced by palloc(): 400.
% 201.15/201.42 type (bytes each) gets frees in use bytes
% 201.15/201.42 chunk ( 104) 56559 56559 0 0.0 K
% 201.15/201.42 string_buf ( 8) 50838 50838 0 0.0 K
% 201.15/201.42 token ( 20) 129071 129071 0 0.0 K
% 201.15/201.42 pterm ( 16) 91898 91898 0 0.0 K
% 201.15/201.42 hashtab ( 8) 580 580 0 0.0 K
% 201.15/201.42 hashnode ( 8) 2169 2169 0 0.0 K
% 201.15/201.42 term ( 20) 356042664 345371893 10670771 208413.5 K
% 201.15/201.42 term arg arrays: 48833.0 K
% 201.15/201.42 attribute ( 12) 4328 128 4200 49.2 K
% 201.15/201.42 ilist ( 8) 619341152 618376085 965067 7539.6 K
% 201.15/201.42 plist ( 8) 7920311 7654330 265981 2078.0 K
% 201.15/201.42 i2list ( 12) 10524422 10524422 0 0.0 K
% 201.15/201.42 just ( 12) 9176092 8953269 222823 2611.2 K
% 201.15/201.42 parajust ( 16) 571287 497309 73978 1155.9 K
% 201.15/201.42 instancejust ( 8) 0 0 0 0.0 K
% 201.15/201.42 ivyjust ( 24) 0 0 0 0.0 K
% 201.15/201.42 formula ( 28) 23572 14684 8888 243.0 K
% 201.15/201.42 formula arg arrays: 30.2 K
% 201.15/201.42 topform ( 52) 8891986 8680705 211281 10729.1 K
% 201.15/201.42 clist_pos ( 20) 598676 387561 211115 4123.3 K
% 201.15/201.42 clist ( 16) 8 1 7 0.1 K
% 201.15/201.42 context ( 808) 32250715 32250713 2 1.6 K
% 201.15/201.42 trail ( 12) 32444707 32444703 4 0.0 K
% 201.15/201.42 ac_match_pos (70044) 0 0 0 0.0 K
% 201.15/201.42 ac_match_free_vars_pos (20020)
% 201.15/201.42 0 0 0 0.0 K
% 201.15/201.42 btm_state ( 60) 0 0 0 0.0 K
% 201.15/201.42 btu_state ( 60) 0 0 0 0.0 K
% 201.15/201.42 ac_position (285432) 0 0 0 0.0 K
% 201.15/201.42 fpa_trie ( 20) 2723292 2398545 324747 6342.7 K
% 201.15/201.42 fpa_state ( 28) 10042522 10042522 0 0.0 K
% 201.15/201.42 fpa_index ( 12) 10 0 10 0.1 K
% 201.15/201.42 fpa_chunk ( 20) 3969262 3752613 216649 4231.4 K
% 201.15/201.42 fpa_list ( 16) 2489744 0 2489744 38902.2 K
% 201.15/201.42 fpa_list chunks: 24512.8 K
% 201.15/201.42 discrim ( 12) 3372343 2757414 614929 7206.2 K
% 201.15/201.42 discrim_pos ( 16) 568448 568448 0 0.0 K
% 201.15/201.42 flat2 ( 32) 86797340 86797340 0 0.0 K
% 201.15/201.42 flat ( 48) 0 0 0 0.0 K
% 201.15/201.42 flatterm ( 32) 382244917 382244917 0 0.0 K
% 201.15/201.42 mindex ( 28) 13 0 13 0.4 K
% 201.15/201.42 mindex_pos ( 56) 12678443 12678443 0 0.0 K
% 201.15/201.42 lindex ( 12) 5 0 5 0.1 K
% 201.15/201.42 clash ( 40) 0 0 0 0.0 K
% 201.15/201.42 di_tree ( 12) 14637037 10944642 3692395 43270.3 K
% 201.15/201.42 avl_node ( 20) 394289 374293 19996 390.5 K
% 201.15/201.42
% 201.15/201.42 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 201.15/201.42 List 1, length 9, 0.0 K
% 201.15/201.42 List 5, length 63, 1.2 K
% 201.15/201.42 List 6, length 40, 0.9 K
% 201.15/201.42 List 7, length 198, 5.4 K
% 201.15/201.42 List 8, length 134, 4.2 K
% 201.15/201.42 List 9, length 6, 0.2 K
% 201.15/201.42 List 11, length 8, 0.3 K
% 201.15/201.42 List 12, length 8, 0.4 K
% 201.15/201.42 List 14, length 13, 0.7 K
% 201.15/201.42 List 16, length 103, 6.4 K
% 201.15/201.42 List 26, length 768, 78.0 K
% 201.15/201.42 List 32, length 254, 31.8 K
% 201.15/201.42 List 128, length 131, 65.5 K
% 201.15/201.42 List 202, length 2, 1.6 K
% 201.15/201.42
% 201.15/201.42 ============================== SELECTOR REPORT =======================
% 201.15/201.42 Sos_deleted=8164922, Sos_displaced=164820, Sos_size=9998
% 201.15/201.42 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 201.15/201.42 I 2147483647 high age 0 769
% 201.15/201.42 H 1 high weight 0 0
% 201.15/201.42 A 1 low age 9998 2281
% 201.15/201.42 F 4 low weight 2873 9120
% 201.15/201.42 T 4 low weight 7125 9120
% 201.15/201.43 ============================== end of selector report ================
% 201.15/201.43
% 201.15/201.43 ============================== end of statistics =====================
% 201.15/201.43
% 201.15/201.43 Exiting with failure.
% 201.15/201.43
% 201.15/201.43 Process 24199 exit (max_megs) Sat Jun 4 15:15:43 2022
% 201.15/201.43 Prover9 interrupted
%------------------------------------------------------------------------------