0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n002.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:45:40 CDT 2018 0.03/0.23 % CPUTime : 1.35/1.61 ============================== Prover9 =============================== 1.35/1.61 Prover9 (32) version 2009-11A, November 2009. 1.35/1.61 Process 64561 was started by sandbox2 on n002.star.cs.uiowa.edu, 1.35/1.61 Sat Jul 14 05:45:41 2018 1.35/1.61 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_64529_n002.star.cs.uiowa.edu". 1.35/1.61 ============================== end of head =========================== 1.35/1.61 1.35/1.61 ============================== INPUT ================================= 1.35/1.61 1.35/1.61 % Reading from file /tmp/Prover9_64529_n002.star.cs.uiowa.edu 1.35/1.61 1.35/1.61 set(prolog_style_variables). 1.35/1.61 set(auto2). 1.35/1.61 % set(auto2) -> set(auto). 1.35/1.61 % set(auto) -> set(auto_inference). 1.35/1.61 % set(auto) -> set(auto_setup). 1.35/1.61 % set(auto_setup) -> set(predicate_elim). 1.35/1.61 % set(auto_setup) -> assign(eq_defs, unfold). 1.35/1.61 % set(auto) -> set(auto_limits). 1.35/1.61 % set(auto_limits) -> assign(max_weight, "100.000"). 1.35/1.61 % set(auto_limits) -> assign(sos_limit, 20000). 1.35/1.61 % set(auto) -> set(auto_denials). 1.35/1.61 % set(auto) -> set(auto_process). 1.35/1.61 % set(auto2) -> assign(new_constants, 1). 1.35/1.61 % set(auto2) -> assign(fold_denial_max, 3). 1.35/1.61 % set(auto2) -> assign(max_weight, "200.000"). 1.35/1.61 % set(auto2) -> assign(max_hours, 1). 1.35/1.61 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.35/1.61 % set(auto2) -> assign(max_seconds, 0). 1.35/1.61 % set(auto2) -> assign(max_minutes, 5). 1.35/1.61 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.35/1.61 % set(auto2) -> set(sort_initial_sos). 1.35/1.61 % set(auto2) -> assign(sos_limit, -1). 1.35/1.61 % set(auto2) -> assign(lrs_ticks, 3000). 1.35/1.61 % set(auto2) -> assign(max_megs, 400). 1.35/1.61 % set(auto2) -> assign(stats, some). 1.35/1.61 % set(auto2) -> clear(echo_input). 1.35/1.61 % set(auto2) -> set(quiet). 1.35/1.61 % set(auto2) -> clear(print_initial_clauses). 1.35/1.61 % set(auto2) -> clear(print_given). 1.35/1.61 assign(lrs_ticks,-1). 1.35/1.61 assign(sos_limit,10000). 1.35/1.61 assign(order,kbo). 1.35/1.61 set(lex_order_vars). 1.35/1.61 clear(print_given). 1.35/1.61 1.35/1.61 % formulas(sos). % not echoed (622 formulas) 1.35/1.61 1.35/1.61 ============================== end of input ========================== 1.35/1.61 1.35/1.61 % From the command line: assign(max_seconds, 300). 1.35/1.61 1.35/1.61 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.35/1.61 1.35/1.61 % Formulas that are not ordinary clauses: 1.35/1.61 1 (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),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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2)),Z)))))) # label(fact_218_le__sup__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 2 (all Fun_1 all Com_2 all Fun all Com_1 (hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1) = hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2) <-> Fun_1 = Fun & Com_2 = Com_1)) # label(fact_246_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 3 (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]. 1.35/1.61 4 (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]. 1.35/1.61 5 (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]. 1.35/1.61 6 (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]. 1.35/1.61 7 (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]. 1.35/1.61 8 (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]. 1.35/1.61 9 (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]. 1.35/1.61 10 (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_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)) = 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)))))) # label(fact_481_inj__on__image__Int) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 11 (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]. 1.35/1.61 12 (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]. 1.35/1.61 13 (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]. 1.35/1.61 14 (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]. 1.35/1.61 15 (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,Xa) = hAPP(X_a,X_b,F,X_1) -> ti(X_a,X_1) = ti(X_a,Xa)))))))) # label(fact_486_inj__on__def) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 16 (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_65_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 17 (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,A_3) = ti(X_a,B_1))) # label(fact_64_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 18 (all X_a all A_3 all B all 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)) = 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)) # label(fact_131_Un__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 19 (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]. 1.35/1.61 20 (all X_a all X_2 ti(X_a,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))) # label(fact_260_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 21 (all X_a all A_3 all 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)) = 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))) # label(fact_42_insert__Collect) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 22 (all X_a all X_b (ord(X_a) & ord(X_b) -> (all C_1 all A_3 all F all B_1 (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),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]. 1.35/1.61 23 (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]. 1.35/1.61 24 (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)) -> (C_2 = B_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]. 1.35/1.61 25 (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]. 1.35/1.61 26 (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]. 1.35/1.61 27 (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]. 1.35/1.61 28 (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]. 1.35/1.61 29 (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]. 1.35/1.61 30 (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]. 1.35/1.61 31 (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)) -> (bot_bot(fun(X_a,bool)) != ti(fun(X_a,bool),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,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_230_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 32 (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]. 1.35/1.61 33 (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]. 1.35/1.61 34 (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]. 1.35/1.61 35 (all X_a all R_1 all S 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_inf_inf(fun(X_a,bool)),R_1),S))) <-> 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)))) # label(fact_322_inf__Int__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 36 (all X_a all X_b fold_graph(X_a,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))) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 37 (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]. 1.35/1.61 38 (all X_a all A_1 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)),bot_bot(fun(X_a,bool))),A_1)) # label(fact_421_empty__Diff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 39 (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]. 1.35/1.61 40 (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]. 1.35/1.61 41 (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]. 1.35/1.61 42 (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]. 1.35/1.61 43 (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]. 1.35/1.61 44 (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]. 1.35/1.61 45 (all X_b all X_a all F all X_2 all Y_2 ti(X_a,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)) # label(fact_466_fun__upd__same) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 46 (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),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))) # label(fact_206_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 47 (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]. 1.35/1.61 48 (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]. 1.35/1.61 49 (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]. 1.35/1.61 50 (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]. 1.35/1.61 51 (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]. 1.35/1.61 52 (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]. 1.35/1.61 53 (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]. 1.35/1.61 54 (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)) -> ti(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),B))) # label(fact_332_Int__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 55 (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]. 1.35/1.61 56 (all Fun all Com_1 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun),Com_1) != skip) # label(fact_250_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.61 57 (all X_a (ord(X_a) -> (all C_2 all A_6 all B_2 (B_2 = A_6 -> (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]. 1.35/1.61 58 (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]. 1.35/1.61 59 (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)) -> (bot_bot(fun(X_a,bool)) != ti(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),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]. 1.45/1.61 60 (all X_a all A_1 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),A_1)) # label(fact_419_Diff__cancel) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 61 (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]. 1.45/1.61 62 (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)),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_122_Un__left__absorb) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 63 (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]. 1.45/1.61 64 (all X_a all A_1 ti(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),A_1)) # label(fact_125_Un__absorb) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 65 (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]. 1.45/1.61 66 (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]. 1.45/1.61 67 (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]. 1.45/1.61 68 (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]. 1.45/1.61 69 (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]. 1.45/1.61 70 (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]. 1.45/1.61 71 (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]. 1.45/1.61 72 (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]. 1.45/1.61 73 (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,C_2) = ti(X_a,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_149_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 74 (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)),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)) = 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))) # label(fact_325_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 75 (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]. 1.45/1.61 76 (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]. 1.45/1.61 77 (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),G),N_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)))) # label(fact_274_image__cong) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 78 (all X_a (bounded_lattice_bot(X_a) -> (all X bot_bot(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),bot_bot(X_a)),X)))) # label(fact_364_inf__bot__left) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 79 (all X_a all X_b all F all X_2 ((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))) <-> 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))))) # label(fact_473_dom__eq__singleton__conv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 80 (all P all Q (hBOOL(Q) | -hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.61 81 (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]. 1.45/1.61 82 (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)),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(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B))) # label(fact_423_insert__Diff1) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 83 (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]. 1.45/1.62 84 (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)) -> ti(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))) # label(fact_333_Int__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 85 (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]. 1.45/1.62 86 (all X_a undefined(X_a) = ti(X_a,undefined(X_a))) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 87 (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]. 1.45/1.62 88 (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]. 1.45/1.62 89 (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]. 1.45/1.62 90 (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,Y_2) != ti(X_a,X_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,Y_2) != hAPP(X_a,X_b,F,X_2)))))) # label(fact_485_inj__on__contraD) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 91 (all X_a all Fun1_1 all Com_2 all Fun2_1 all Fun1_2 all Com_1 all Fun2_2 (Fun1_2 = Fun1_1 & Com_1 = Com_2 & Fun2_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_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))) # label(fact_114_triple_Oinject) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 92 (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),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)) = 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))))) # label(fact_360_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 93 (all X_a all X_b all F all G 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)),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))))) = 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))) # label(fact_443_dom__override__on) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 94 (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]. 1.45/1.62 95 (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)) -> ti(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)),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)))))) # label(fact_406_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 96 (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)),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)) = 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_121_Un__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 97 (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]. 1.45/1.62 98 (all X_a all X_2 (none(X_a) != ti(option(X_a),X_2) <-> (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]. 1.45/1.62 99 (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]. 1.45/1.62 100 (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)) -> (ti(fun(X_a,bool),B) = 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),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_37_insert__ident) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 101 (all X_a (semilattice_sup(X_a) -> (all A_6 ti(X_a,A_6) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_6),A_6)))) # label(fact_209_sup_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 102 (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]. 1.45/1.62 103 (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]. 1.45/1.62 104 (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]. 1.45/1.62 105 (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]. 1.45/1.62 106 (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]. 1.45/1.62 107 (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]. 1.45/1.62 108 (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),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),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),Z_1)),X)))) # label(fact_362_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 109 (all X_a all X_b fun_upd(X_a,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))) # label(tsy_c_Fun_Ofun__upd_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 110 (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]. 1.45/1.62 111 (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]. 1.45/1.62 112 (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]. 1.45/1.62 113 (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)) -> (ti(X_a,C_1) = hAPP(X_a,X_a,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_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]. 1.45/1.62 114 (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]. 1.45/1.62 115 (all Com1_3 all Com2_3 all Com1_2 all Com2_2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_3),Com2_3) <-> Com1_2 = Com1_3 & Com2_2 = Com2_3)) # label(fact_245_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 116 (all X_a fequal(X_a) = ti(fun(X_a,fun(X_a,bool)),fequal(X_a))) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 117 (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)),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)) = 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))) # label(fact_401_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 118 (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)) -> ti(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),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)))) # label(fact_414_Diff__partition) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 119 (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]. 1.45/1.62 120 (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]. 1.45/1.62 121 (all X_a the_elem(X_a) = ti(fun(fun(X_a,bool),X_a),the_elem(X_a))) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 122 (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]. 1.45/1.62 123 (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]. 1.45/1.62 124 (all X_a all P_1 all A_3 ((-hBOOL(hAPP(X_a,bool,P_1,A_3)) -> bot_bot(fun(X_a,bool)) = 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))) & (hBOOL(hAPP(X_a,bool,P_1,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))) = 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))))) # label(fact_88_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 125 (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]. 1.45/1.62 126 (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]. 1.45/1.62 127 (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]. 1.45/1.62 128 (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]. 1.45/1.62 129 (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]. 1.45/1.62 130 (all X_a all A_3 all 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))) = 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_43_insert__compr) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 131 (all X_b all X_a all F 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),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)) = 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))) # label(fact_83_image__insert) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 132 (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]. 1.45/1.62 133 (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),X),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]. 1.45/1.62 134 (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]. 1.45/1.62 135 (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]. 1.45/1.62 136 (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]. 1.45/1.62 137 (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]. 1.45/1.62 138 (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]. 1.45/1.62 139 (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]. 1.45/1.62 140 (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]. 1.45/1.62 141 (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]. 1.45/1.62 142 (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,A_3) = 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_266_theI) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 143 (all X_a all A_1 all 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) -> ti(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)),A_1),B))) # label(fact_412_Diff__triv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 144 (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]. 1.45/1.62 145 (all X_a (semilattice_sup(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),X)))) # label(fact_208_sup__idem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 146 (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]. 1.45/1.62 147 (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]. 1.45/1.62 148 (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]. 1.45/1.62 149 (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]. 1.45/1.62 150 (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)),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)),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_329_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 151 (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)) -> ((S_1 = T_3 -> 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]. 1.45/1.62 152 (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),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),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_199_sup__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 153 (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]. 1.45/1.62 154 (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]. 1.45/1.62 155 (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]. 1.45/1.62 156 (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]. 1.45/1.62 157 (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]. 1.45/1.62 158 (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]. 1.45/1.62 159 (all X_a all X_2 all Xo (ti(option(X_a),Xo) = hAPP(X_a,option(X_a),some(X_a),X_2) <-> 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))))) # label(fact_190_elem__set) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 160 (all X_a all A_1 (bot_bot(fun(X_a,bool)) = ti(fun(X_a,bool),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))))) # label(fact_31_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 161 (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]. 1.45/1.62 162 (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]. 1.45/1.62 163 (all X_a all A_2 hAPP(X_a,option(X_a),some(X_a),A_2) != none(X_a)) # label(fact_495_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 164 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 165 (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) = hAPP(X_a,X_b,F,X_1)) & (ti(X_a,X_1) = ti(X_a,A_3) -> ti(X_b,B_1) = 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)))) # label(fact_471_fun__upd__def) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 166 (all X_a all X_b combk(X_a,X_b) = ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 167 (all X_a all X_b all F ((all X_1 hAPP(X_a,option(X_b),F,X_1) = none(X_b)) <-> bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),F))) # label(fact_497_dom__eq__empty__conv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 168 (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]. 1.45/1.62 169 (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_67_finite__insert) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 170 (all P all Q (hBOOL(Q) | hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 171 (all X_a all P_1 all A_1 all B ((exists X_1 (hBOOL(hAPP(X_a,bool,P_1,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))))) <-> (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]. 1.45/1.62 172 (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)) -> ti(X_a,A_3) = hAPP(fun(X_a,bool),X_a,the_1(X_a),P_1)))) # label(fact_265_the1__equality) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 173 (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]. 1.45/1.62 174 (all X_b all X_a all F1 all Fun1_1 all Com_2 all 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) = 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))) # label(fact_188_triple_Orecs) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 175 (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]. 1.45/1.62 176 (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]. 1.45/1.62 177 (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]. 1.45/1.62 178 (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]. 1.45/1.62 179 (all X_a (lattice(X_a) -> (all X all Y ti(X_a,X) = 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))))) # label(fact_357_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 180 (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]. 1.45/1.62 181 (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]. 1.45/1.62 182 (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]. 1.45/1.62 183 (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]. 1.45/1.62 184 (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]. 1.45/1.62 185 (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]. 1.45/1.62 186 (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]. 1.45/1.62 187 (all X_a finite2073411215e_idem(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))) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 188 (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]. 1.45/1.62 189 (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,C_1) = ti(X_a,D) <-> ti(X_a,B_1) = ti(X_a,A_3)))))) # label(fact_446_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 190 (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),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),A_3),bot_bot(fun(X_a,bool))) -> ti(X_a,B_1) = ti(X_a,A_3))) # label(fact_61_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 191 (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),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)))) # label(fact_205_sup__commute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 192 (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),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_inf_inf(X_a),Y),Z_1))))) # label(fact_375_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 193 (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]. 1.45/1.62 194 (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]. 1.45/1.62 195 (all X_a all B ti(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)),bot_bot(fun(X_a,bool))),B)) # label(fact_128_Un__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 196 (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]. 1.45/1.62 197 (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]. 1.45/1.62 198 (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]. 1.45/1.62 199 (all Com1 all Com2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_256_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 200 (all X_a (bounded_lattice_bot(X_a) -> (all X bot_bot(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),bot_bot(X_a))))) # label(fact_363_inf__bot__right) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 201 (all X_a (ord(X_a) -> ord_less_eq(X_a) = ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 202 (all X_a all X all Y (ti(X_a,X) = ti(X_a,Y) | -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.45/1.62 203 (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]. 1.45/1.62 204 (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]. 1.45/1.62 205 (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]. 1.45/1.62 206 (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]. 1.45/1.63 207 (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]. 1.45/1.63 208 (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]. 1.45/1.63 209 (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),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)) & 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_472_inj__on__Un) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 210 (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]. 1.45/1.63 211 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 212 (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]. 1.45/1.63 213 (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]. 1.45/1.63 214 (all X_a all X all Y ti(X_a,X) = 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)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 215 (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]. 1.45/1.63 216 (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]. 1.45/1.63 217 (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(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_80_insert__subset) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 218 (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]. 1.45/1.63 219 (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]. 1.45/1.63 220 (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]. 1.45/1.63 221 (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,A_3) = ti(X_a,X_1))) -> 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]. 1.45/1.63 222 (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]. 1.45/1.63 223 (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]. 1.45/1.63 224 (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]. 1.45/1.63 225 (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]. 1.45/1.63 226 (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]. 1.45/1.63 227 (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]. 1.45/1.63 228 (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]. 1.45/1.63 229 (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]. 1.45/1.63 230 (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) -> ti(X_b,Y_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_a,X_2) != ti(X_a,Z) -> 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]. 1.45/1.63 231 (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]. 1.45/1.63 232 (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]. 1.45/1.63 233 (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]. 1.45/1.63 234 (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)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y))))) # label(fact_351_inf__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 235 (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]. 1.45/1.63 236 (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,B_1) != ti(X_a,A_3) -> 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]. 1.45/1.63 237 (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]. 1.45/1.63 238 (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]. 1.45/1.63 239 (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]. 1.45/1.63 240 (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]. 1.45/1.63 241 (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)) -> 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),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))))))) # label(fact_405_insert__Diff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 242 (all X_b all X_a all F 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_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)),semilattice_sup_sup(fun(X_b,bool)),A_1),B))) # label(fact_140_image__Un) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 243 (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]. 1.45/1.63 244 (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]. 1.45/1.63 245 (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]. 1.45/1.63 246 (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]. 1.45/1.63 247 (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,A_1)),hAPP(fun(X_a,bool),X_a,Fa,B)) = 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)))))))) # label(fact_301_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 248 (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]. 1.45/1.63 249 (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),A_1)) & hBOOL(hAPP(X_a,bool,P_1,X_2)) <-> 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)))))) # label(fact_321_Int__Collect) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 250 (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]. 1.45/1.63 251 (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]. 1.45/1.63 252 (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]. 1.45/1.63 253 (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),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))))))) # label(fact_6_derivs__insertD) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 254 (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)),R_1),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))))) # label(fact_183_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 255 (all X_a if(X_a) = ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 256 (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(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,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1)))))) # label(fact_393_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 257 (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]. 1.45/1.63 258 (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]. 1.45/1.63 259 (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]. 1.45/1.63 260 (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]. 1.45/1.63 261 (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]. 1.45/1.63 262 (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]. 1.45/1.63 263 (all X_b all X_a all P_1 all F all G all 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))))) = 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)) # label(fact_385_if__image__distrib) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 264 (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]. 1.45/1.63 265 (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]. 1.45/1.63 266 (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]. 1.45/1.63 267 (all X_b all X_a all F1 all F2 ti(X_a,F1) = 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))) # label(fact_496_option_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 268 (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),Y)) -> ti(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_215_sup__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 269 (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(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)))))) = hAPP(fun(X_b,bool),X_a,Fa,A_1))))) # label(fact_440_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 270 (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)) & (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_341_Int__insert__left) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 271 (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)),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(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))))) # label(fact_438_subset__insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 272 (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]. 1.45/1.63 273 (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]. 1.45/1.63 274 (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))))) -> 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))) = ti(fun(X_a,bool),A_1))) # label(fact_18_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 275 (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),Z) = 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)))) # label(fact_452_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 276 (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]. 1.45/1.63 277 (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]. 1.45/1.63 278 (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]. 1.45/1.63 279 (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]. 1.45/1.63 280 (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)))) -> (hAPP(X_a,option(X_a),some(X_a),X_2) = ti(option(X_a),A_1) -> hBOOL(hAPP(X_a,bool,P_1,X_2))))) # label(fact_191_ospec) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 281 (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),X),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]. 1.45/1.63 282 (all X_a all X_b (ord(X_a) & ord(X_b) -> (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)) -> (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),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]. 1.45/1.63 283 (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]. 1.45/1.63 284 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(P))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 285 (all T_2 all T_1 (finite_finite_1(T_2) & finite_finite_1(T_1) -> finite_finite_1(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 286 (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]. 1.45/1.63 287 (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]. 1.45/1.63 288 (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),A_6),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),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))))) # label(fact_201_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 289 (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]. 1.45/1.63 290 (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),Y)),Z_1)))) # label(fact_196_sup__assoc) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 291 (all X_a all X_b all X_c combs(X_a,X_b,X_c) = ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c))) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 292 (all X_a insert(X_a) = ti(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),insert(X_a))) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 293 (all X_a (semilattice_inf(X_a) -> (all A_6 ti(X_a,A_6) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),A_6)))) # label(fact_365_inf_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 294 (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]. 1.45/1.63 295 (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]. 1.45/1.63 296 (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))) -> (ti(fun(X_a,bool),B) = ti(fun(X_a,bool),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) = 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_482_inj__on__Un__image__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 297 (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]. 1.45/1.63 298 (all X_a all A_1 all B ti(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)),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))) # label(fact_418_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 299 (all Com1_3 all Com2_3 all Fun all Com_1 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_243_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 300 (all X_a all X_b all 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)))) = hAPP(fun(X_a,option(X_b)),fun(X_a,bool),dom(X_a,X_b),M)) # label(fact_490_dom__def) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 301 (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]. 1.45/1.63 302 (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]. 1.45/1.63 303 (all X_a (semilattice_sup(X_a) -> semilattice_sup_sup(X_a) = ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a)))) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 304 (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]. 1.45/1.63 305 (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),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)))))) # label(fact_155_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 306 (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]. 1.45/1.63 307 (all P (fTrue = ti(bool,P) | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 308 (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]. 1.45/1.63 309 (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)) -> ti(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_136_Un__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 310 (all X_a all X_2 ((all Y_1 hAPP(X_a,option(X_a),some(X_a),Y_1) != ti(option(X_a),X_2)) <-> none(X_a) = ti(option(X_a),X_2))) # label(fact_493_not__Some__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.63 311 (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]. 1.45/1.64 312 (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_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_389_distrib__imp2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 313 (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_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)) = 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))) # label(fact_328_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 314 (all X_a all 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))) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3))) # label(fact_90_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 315 (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]. 1.45/1.64 316 (all X_a hoare_2027193591valids(X_a) = ti(fun(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool)),hoare_2027193591valids(X_a))) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 317 (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)) -> (hAPP(X_a,X_b,F,X_2) = ti(X_b,B_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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]. 1.45/1.64 318 (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]. 1.45/1.64 319 (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]. 1.45/1.64 320 (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]. 1.45/1.64 321 (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]. 1.45/1.64 322 (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]. 1.45/1.64 323 (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]. 1.45/1.64 324 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)) = hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R)) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 325 (all X_a all A_1 all 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))) = 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_124_Un__def) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 326 (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]. 1.45/1.64 327 (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]. 1.45/1.64 328 (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]. 1.45/1.64 329 (all X_a all A_1 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),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),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_132_Un__insert__right) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 330 (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]. 1.45/1.64 331 (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]. 1.45/1.64 332 (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)) -> (bot_bot(fun(X_a,bool)) != ti(fun(X_a,bool),A_1) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) -> (bot_bot(fun(X_a,bool)) != ti(fun(X_a,bool),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)) = 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)))))))) # label(fact_227_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 333 (all X_b all X_a all F all X_2 ti(fun(X_a,X_b),F) = 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))) # label(fact_458_fun__upd__triv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 334 (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]. 1.45/1.64 335 (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]. 1.45/1.64 336 (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]. 1.45/1.64 337 (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]. 1.45/1.64 338 (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]. 1.45/1.64 339 (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]. 1.45/1.64 340 (all X_a all X_b all Z all F all A_1 ((exists X_1 (hAPP(X_b,X_a,F,X_1) = ti(X_a,Z) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)))) <-> hBOOL(hAPP(fun(X_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))))) # label(fact_56_image__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 341 (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]. 1.45/1.64 342 (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]. 1.45/1.64 343 (all X_a all P_1 all 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)) = 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_320_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 344 (all X_a hoare_279057269derivs(X_a) = ti(fun(fun(hoare_1656922687triple(X_a),bool),fun(fun(hoare_1656922687triple(X_a),bool),bool)),hoare_279057269derivs(X_a))) # label(tsy_c_Hoare__Mirabelle__nrugjuseim_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 345 (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]. 1.45/1.64 346 (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]. 1.45/1.64 347 (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]. 1.45/1.64 348 (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]. 1.45/1.64 349 (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)) <-> ti(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_137_subset__Un__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 350 (all X_a all 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)),bot_bot(fun(X_a,bool))),B)) # label(fact_310_Int__empty__left) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 351 (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)),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) = 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))) # label(fact_408_Diff__insert2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 352 (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]. 1.45/1.64 353 (all P (fFalse = ti(bool,P) | fTrue = ti(bool,P))) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 354 (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)) -> (bot_bot(fun(X_a,bool)) != ti(fun(X_a,bool),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)) = hAPP(X_a,X_a,H,hAPP(fun(X_a,bool),X_a,Fa,N_1))))))) # label(fact_237_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 355 (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]. 1.45/1.64 356 (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]. 1.45/1.64 357 hBOOL(hoare_1924220188gleton) -> (all T_5 -(all S_3 T_5 = S_3)) # label(fact_194_single__stateE) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 358 (all X_a all A_3 all A_1 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),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)),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))) # label(fact_340_insert__inter__insert) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 359 (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]. 1.45/1.64 360 (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]. 1.45/1.64 361 (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)),B),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)) <-> ti(fun(X_a,bool),B) = ti(fun(X_a,bool),A_1))) # label(fact_52_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 362 (all X_b all X_a all F 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),bot_bot(fun(X_b,bool)))) # label(fact_70_image__empty) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 363 (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]. 1.45/1.64 364 (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),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),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))) & (-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]. 1.45/1.64 365 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(Q))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 366 (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 (hAPP(X_b,X_a,F,X_1) = ti(X_a,B_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]. 1.45/1.64 367 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)) = hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R)) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 368 (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]. 1.45/1.64 369 (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]. 1.45/1.64 370 (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]. 1.45/1.64 371 (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]. 1.45/1.64 372 (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]. 1.45/1.64 373 (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]. 1.45/1.64 374 (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]. 1.45/1.64 375 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 376 (all X_a fAll(X_a) = ti(fun(fun(X_a,bool),bool),fAll(X_a))) # label(tsy_c_fAll_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 377 (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]. 1.45/1.64 378 (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]. 1.45/1.64 379 (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]. 1.45/1.64 380 (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,G,X_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)) & (-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,F,X_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)))) # label(fact_449_override__on__def) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 381 (all X_a all X_b (order(X_a) & order(X_b) -> (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]. 1.45/1.64 382 (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]. 1.45/1.64 383 (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]. 1.45/1.64 384 (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]. 1.45/1.64 385 (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)) -> (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),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)) = 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))))))) # label(fact_390_folding__image__simple_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 386 (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))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) | ti(X_a,A_3) = ti(X_a,B_1))) # label(fact_39_insert__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 387 (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]. 1.45/1.64 388 (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]. 1.45/1.64 389 (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]. 1.45/1.64 390 (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]. 1.45/1.64 391 (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]. 1.45/1.64 392 (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]. 1.45/1.64 393 (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]. 1.45/1.64 394 (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]. 1.45/1.64 395 (all X_b none(X_b) = ti(option(X_b),none(X_b))) # label(tsy_c_Option_Ooption_ONone_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 396 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 397 (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(fun(X_b,bool),X_a,Fa,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)))))) # label(fact_269_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 398 (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),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_429_Diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 399 (all X_b all X_a all M all B_1 all D all A_3 all C_1 (ti(X_a,C_1) != ti(X_a,A_3) -> 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]. 1.45/1.64 400 (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]. 1.45/1.64 401 (all X_b all X_a all M all A_3 all B_1 all X_2 all Y_2 (hAPP(X_a,option(X_a),some(X_a),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) <-> ti(X_a,Y_2) = ti(X_a,B_1) & ti(X_b,A_3) = ti(X_b,X_2) | hAPP(X_a,option(X_a),some(X_a),Y_2) = hAPP(X_b,option(X_a),M,X_2) & ti(X_b,X_2) != ti(X_b,A_3))) # label(fact_462_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption]. 1.45/1.64 402 (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]. 1.45/1.64 403 (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]. 1.45/1.64 404 (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]. 1.45/1.64 405 (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]. 1.45/1.64 406 (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),X),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]. 1.45/1.64 407 (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]. 1.45/1.64 408 (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]. 1.45/1.64 409 (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]. 1.45/1.64 410 (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]. 1.45/1.64 411 (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]. 1.45/1.64 412 (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),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),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)))))) # label(fact_117_ball__Un) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 413 (all P all Q (hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 414 (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]. 1.45/1.65 415 (all X_a all X all P (hBOOL(hAPP(X_a,bool,P,X)) | -hBOOL(hAPP(fun(X_a,bool),bool,fAll(X_a),P)))) # label(help_fAll_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 416 (all Pname_1 all Fun_1 all Com_2 hAPP(com,com,hAPP(fun(state,bool),fun(com,com),while,Fun_1),Com_2) != hAPP(pname,com,body_1,Pname_1)) # label(fact_247_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 417 (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]. 1.45/1.65 418 (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]. 1.45/1.65 419 (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]. 1.45/1.65 420 (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]. 1.45/1.65 421 (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),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X),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_200_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 422 (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),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)) = 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)) # label(fact_326_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 423 (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]. 1.45/1.65 424 (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]. 1.45/1.65 425 (all X_a all 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))))) = hAPP(fun(X_a,bool),X_a,the_elem(X_a),X_3)) # label(fact_240_the__elem__def) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 426 (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)),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)),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)))) # label(fact_384_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 427 (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(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)))))) = 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))))) # label(fact_441_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 428 (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]. 1.45/1.65 429 (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]. 1.45/1.65 430 (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]. 1.45/1.65 431 (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]. 1.45/1.65 432 (all X_a all P_1 ((all X_1 -hBOOL(hAPP(X_a,bool,P_1,X_1))) <-> bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) # label(fact_27_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 433 (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]. 1.45/1.65 434 (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]. 1.45/1.65 435 (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)),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)) = 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_315_Int__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 436 (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)) <-> ti(X_a,X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X_2),Y_2))))) # label(fact_347_le__iff__inf) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 437 (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)),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)) = 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))) # label(fact_416_Diff__Int) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 438 (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),A_6),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]. 1.45/1.65 439 (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(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_79_subset__insert) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 440 (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]. 1.45/1.65 441 (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]. 1.45/1.65 442 (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]. 1.45/1.65 443 (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(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)) = 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))) # label(fact_336_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 444 (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]. 1.45/1.65 445 (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_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))) = 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))) # label(fact_15_image__constant) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 446 (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)) <-> ti(X_a,Y_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_2),Y_2))))) # label(fact_219_le__iff__sup) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 447 (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]. 1.45/1.65 448 (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))) -> bot_bot(fun(X_a,bool)) = ti(fun(X_a,bool),A_1))) # label(fact_279_equals0I) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 449 (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]. 1.45/1.65 450 (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]. 1.45/1.65 451 (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]. 1.45/1.65 452 (exists S_3 exists T_5 S_3 != T_5) <-> hBOOL(hoare_1924220188gleton) # label(fact_195_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 453 (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]. 1.45/1.65 454 (all X_a all A_3 all B_1 all C_1 all D (ti(X_a,C_1) = ti(X_a,B_1) & ti(X_a,A_3) = ti(X_a,D) | ti(X_a,A_3) = ti(X_a,C_1) & ti(X_a,D) = ti(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),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)))))) # label(fact_63_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 455 (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]. 1.45/1.65 456 (all X_a all A_1 all 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) <-> (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,Xa) != ti(X_a,X_1))))))) # label(fact_308_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 457 (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,A_1)),hAPP(fun(X_b,bool),X_a,Fa,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))))))) # label(fact_391_folding__image__simple_Ounion__inter) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 458 (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]. 1.45/1.65 459 (all X_b all X_a all C_1 all A_1 ((bot_bot(fun(X_a,bool)) != ti(fun(X_a,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),C_1),bot_bot(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),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1)) & (bot_bot(fun(X_a,bool)) = ti(fun(X_a,bool),A_1) -> bot_bot(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),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1)))) # label(fact_14_image__constant__conv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 460 (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]. 1.45/1.65 461 (all X_b all X_a all T_3 all K all X_2 (hAPP(X_a,option(X_a),some(X_a),X_2) = hAPP(X_b,option(X_a),T_3,K) -> ti(fun(X_b,option(X_a)),T_3) = 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)))) # label(fact_461_map__upd__triv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 462 (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(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)) = 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)))) # label(fact_337_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 463 (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]. 1.45/1.65 464 (all X_a all A_1 ti(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),bot_bot(fun(X_a,bool)))) # label(fact_127_Un__empty__right) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 465 (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),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),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)))))) # label(fact_57_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 466 (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)) -> (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),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)))) -> 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))))))) & (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)) -> ti(X_a,X_2) = hAPP(fun(X_a,bool),X_a,Fa,A_1)))))) # label(fact_396_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 467 (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),X),Y)),Z_1)))) # label(fact_378_inf__sup__aci_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 468 (all X_b all X_a dom(X_b,X_a) = ti(fun(fun(X_b,option(X_a)),fun(X_b,bool)),dom(X_b,X_a))) # label(tsy_c_Map_Odom_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 469 (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]. 1.45/1.65 470 (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(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)) = 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)))))) # label(fact_268_folding__image__simple__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 471 (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]. 1.45/1.65 472 (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]. 1.45/1.65 473 (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]. 1.45/1.65 474 (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]. 1.45/1.65 475 (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_7) = ti(X_a,A_3))) # label(fact_157_option_Oinject) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 476 (all X_b all X_a all F all X_2 all Y_2 (ti(X_a,Y_2) = hAPP(X_b,X_a,F,X_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]. 1.45/1.65 477 (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]. 1.45/1.65 478 (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)) <-> hBOOL(hAPP(X_a,bool,A_1,X_2)) | ti(X_a,Y_2) = ti(X_a,X_2))) # label(fact_38_insert__code) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 479 (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]. 1.45/1.65 480 (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)) -> (bot_bot(fun(X_a,bool)) != ti(fun(X_a,bool),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_231_finite__ne__induct) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 481 (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]. 1.45/1.65 482 (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]. 1.45/1.65 483 (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) = 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))))))) & (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)))) # label(fact_450_flat__lub__def) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 484 (all X_a all X_b all F all A_1 (ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,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) = bot_bot(fun(X_a,bool)))) # label(fact_71_empty__is__image) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 485 (all Pname_2 all Pname_1 (ti(pname,Pname_2) = ti(pname,Pname_1) <-> hAPP(pname,com,body_1,Pname_2) = hAPP(pname,com,body_1,Pname_1))) # label(fact_102_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 486 (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]. 1.45/1.65 487 (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]. 1.45/1.65 488 (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]. 1.45/1.65 489 (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)) -> (bot_bot(fun(X_a,bool)) != ti(fun(X_a,bool),A_1) -> 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]. 1.45/1.65 490 (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]. 1.45/1.65 491 (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]. 1.45/1.65 492 (all X_a (bounded_lattice_bot(X_a) -> (all X_2 all Y_2 (bot_bot(X_a) = ti(X_a,X_2) & ti(X_a,Y_2) = bot_bot(X_a) <-> 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))))) # label(fact_224_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 493 (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]. 1.45/1.65 494 (all X_a all A_1 all B (bot_bot(fun(X_a,bool)) = ti(fun(X_a,bool),B) & bot_bot(fun(X_a,bool)) = ti(fun(X_a,bool),A_1) <-> 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_sup_sup(fun(X_a,bool)),A_1),B))) # label(fact_126_Un__empty) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 495 (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]. 1.45/1.65 496 (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]. 1.45/1.65 497 (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]. 1.45/1.65 498 (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]. 1.45/1.65 499 (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]. 1.45/1.65 500 (all X_a all A_1 all 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),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))) # label(fact_411_Diff__disjoint) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 501 (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]. 1.45/1.65 502 (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),G) = ti(fun(X_a,X_b),F))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 503 (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))) <-> none(X_b) != hAPP(X_a,option(X_b),M,A_3))) # label(fact_491_domIff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 504 (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]. 1.45/1.65 505 (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]. 1.45/1.65 506 (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]. 1.45/1.65 507 (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 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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))))) # label(fact_277_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 508 (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)) -> ti(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_135_Un__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 509 (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]. 1.45/1.65 510 (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]. 1.45/1.65 511 (all X_a all X ti(X_a,X) = hAPP(option(X_a),X_a,the(X_a),hAPP(X_a,option(X_a),some(X_a),X))) # label(fact_109_the_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 512 (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]. 1.45/1.65 513 (all P all Q (hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 514 (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]. 1.45/1.65 515 (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)),M),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))) # label(fact_459_image__map__upd) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 516 (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]. 1.45/1.65 517 (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),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)))))) # label(fact_348_le__inf__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 518 (all X_a all A_1 (ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) <-> (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))))) # label(fact_30_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 519 (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]. 1.45/1.65 520 (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]. 1.45/1.65 521 (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),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),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]. 1.45/1.65 522 (all Com1 all Com2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != skip) # label(fact_255_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 523 (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]. 1.45/1.65 524 (all X_a all X_b all T_3 all K all X_2 -(all X_1 none(X_b) = 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))) # label(fact_476_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 525 (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]. 1.45/1.65 526 (all X_a all A_3 ti(X_a,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))) # label(fact_259_the__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 1.45/1.65 527 (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]. 1.45/1.65 528 (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]. 1.45/1.65 529 (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]. 1.45/1.65 530 (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]. 1.45/1.65 531 (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,B_1) = ti(X_a,A_3)) -> 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]. 1.45/1.65 532 (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]. 1.45/1.65 533 (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]. 1.45/1.66 534 (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]. 1.45/1.66 535 (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]. 1.45/1.66 536 (all Pname all Com1_1 all Com2_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) != hAPP(pname,com,body_1,Pname)) # label(fact_252_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 537 (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]. 1.45/1.66 538 (all X_b all X_a all X_c all F all G all 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) = 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))) # label(fact_60_image__image) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 539 (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]. 1.45/1.66 540 (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),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_inf_inf(X_a),Y),Z_1))))) # label(fact_376_inf__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 541 (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]. 1.45/1.66 542 (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]. 1.45/1.66 543 (all Pname skip != hAPP(pname,com,body_1,Pname)) # label(fact_234_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 544 (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]. 1.45/1.66 545 (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)) = 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))))))) & (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)) -> ti(X_a,X_2) = 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)))))) # label(fact_397_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 546 (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]. 1.45/1.66 547 (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]. 1.45/1.66 548 (all X_b all X_a all M all A_3 all B_1 (hAPP(X_a,option(X_a),some(X_a),B_1) = hAPP(X_b,option(X_a),M,A_3) -> 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]. 1.45/1.66 549 (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]. 1.45/1.66 550 (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]. 1.45/1.66 551 (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]. 1.45/1.66 552 (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]. 1.45/1.66 553 (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]. 1.45/1.66 554 (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]. 1.45/1.66 555 (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]. 1.45/1.66 556 (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]. 1.45/1.66 557 (all X_a all X_2 ti(X_a,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))))) # label(fact_105_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 558 (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]. 1.45/1.66 559 (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_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)))))) = 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)) & (-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]. 1.45/1.66 560 (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]. 1.45/1.66 561 (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),B_2),A_6) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_inf_inf(X_a),A_6),B_2)))) # label(fact_368_inf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 562 (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]. 1.45/1.66 563 (all X_a all X_b finite_comp_fun_idem(X_a,X_b) = ti(fun(fun(X_a,fun(X_b,X_b)),bool),finite_comp_fun_idem(X_a,X_b))) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 564 (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_b,option(X_b),some(X_b),B_4) = hAPP(X_a,option(X_b),M,A_3)))) # label(fact_104_domD) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 565 (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]. 1.45/1.66 566 (all Pname hAPP(pname,com,body_1,Pname) != skip) # label(fact_233_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 567 (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),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_120_Un__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 568 (all X_a all A_3 (bot_bot(fun(X_a,bool)) = ti(fun(X_a,bool),A_3) | (exists A_4 exists A_5 (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) = ti(fun(X_a,bool),A_3) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_4)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_3)))) # label(fact_100_finite_Osimps) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 569 (all X_a all A_1 all B (ti(fun(X_a,bool),B) = ti(fun(X_a,bool),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)))) # label(fact_50_equalityD2) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 570 (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),G_1)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)))) # label(fact_130_finite__Un) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 571 (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]. 1.45/1.66 572 (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]. 1.45/1.66 573 (all X_a all A_1 ((exists X_1 exists 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)) & 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) = ti(fun(X_a,bool),A_1))) <-> ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)))) # label(fact_108_nonempty__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.66 574 (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]. 1.45/1.66 575 (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]. 1.45/1.66 576 (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]. 1.45/1.66 577 (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]. 1.45/1.67 578 (all X_b all X_a all F all X_2 all Y_2 (ti(X_b,Y_2) = hAPP(X_a,X_b,F,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),Y_2) = ti(fun(X_a,X_b),F))) # label(fact_464_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption]. 1.45/1.67 579 (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))) -> bot_bot(X_a) = ti(X_a,A_6))))) # label(fact_160_le__bot) # label(axiom) # label(non_clause). [assumption]. 1.45/1.67 580 (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]. 1.45/1.67 1.45/1.67 ============================== end of process non-clausal formulas === 1.45/1.67 1.45/1.67 ============================== PROCESS INITIAL CLAUSES =============== 1.45/1.67 1.45/1.67 ============================== PREDICATE ELIMINATION ================= 1.45/1.67 581 semilattice_sup(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__sup) # label(axiom). [assumption]. 1.45/1.67 582 -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),D),B)),C)) # label(fact_218_le__sup__iff) # label(axiom). [clausify(1)]. 1.45/1.67 583 -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),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),D),B)),C)) # label(fact_218_le__sup__iff) # label(axiom). [clausify(1)]. 1.45/1.67 584 -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),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)),C)) # label(fact_218_le__sup__iff) # label(axiom). [clausify(1)]. 1.45/1.67 585 -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(26)]. 1.45/1.67 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),C),A)),B)). [resolve(581,a,582,a)]. 1.45/1.67 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_sup_sup(bool),C),A)),B)). [resolve(581,a,583,a)]. 1.45/1.67 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_sup_sup(bool),A),C)),B)). [resolve(581,a,584,a)]. 1.45/1.67 586 -lattice(A) | semilattice_sup(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom). [clausify(44)]. 1.45/1.67 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)),E),C)),D)). [resolve(586,b,582,a)]. 1.45/1.67 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_sup_sup(fun(B,A)),E),C)),D)). [resolve(586,b,583,a)]. 1.45/1.67 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_sup_sup(fun(B,A)),C),E)),D)). [resolve(586,b,584,a)]. 1.45/1.67 587 -semilattice_sup(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) # label(fact_209_sup_Oidem) # label(axiom). [clausify(101)]. 1.45/1.67 Derived: ti(bool,A) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),A). [resolve(587,a,581,a)]. 1.45/1.67 Derived: ti(fun(A,B),C) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),C) | -lattice(B). [resolve(587,a,586,b)]. 1.45/1.67 588 -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(114)]. 1.45/1.67 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(588,a,581,a)]. 1.45/1.67 Derived: hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),C))) | -lattice(B). [resolve(588,a,586,b)]. 1.45/1.67 589 -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(133)]. 1.45/1.67 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(589,a,581,a)]. 1.45/1.67 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D)) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D) | -lattice(B). [resolve(589,a,586,b)]. 1.45/1.67 590 -semilattice_sup(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) # label(fact_208_sup__idem) # label(axiom). [clausify(145)]. 1.45/1.67 591 -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(152)]. 1.45/1.67 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(591,a,581,a)]. 1.45/1.67 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),E)) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),E)) | -lattice(B). [resolve(591,a,586,b)]. 1.45/1.67 592 -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(191)]. 1.45/1.67 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(592,a,581,a)]. 1.45/1.67 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),C) | -lattice(B). [resolve(592,a,586,b)]. 1.45/1.68 593 -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(210)]. 1.45/1.68 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(593,a,581,a)]. 1.45/1.68 Derived: hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D))) | -lattice(B). [resolve(593,a,586,b)]. 1.45/1.68 594 -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(226)]. 1.45/1.68 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(594,a,581,a)]. 1.45/1.68 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),E))) | -lattice(B). [resolve(594,a,586,b)]. 1.45/1.68 595 -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(262)]. 1.45/1.68 596 -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(266)]. 1.45/1.68 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(596,a,581,a)]. 1.45/1.68 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),E),D))) | -lattice(B). [resolve(596,a,586,b)]. 1.45/1.68 597 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_215_sup__absorb2) # label(axiom). [clausify(268)]. 1.45/1.68 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | ti(bool,B) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B). [resolve(597,a,581,a)]. 1.45/1.68 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | ti(fun(A,B),D) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D) | -lattice(B). [resolve(597,a,586,b)]. 1.45/1.68 598 -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(288)]. 1.45/1.68 599 -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(290)]. 1.45/1.68 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(599,a,581,a)]. 1.45/1.68 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D)),E) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),E)) | -lattice(B). [resolve(599,a,586,b)]. 1.45/1.68 600 -semilattice_sup(A) | ti(fun(A,fun(A,A)),semilattice_sup_sup(A)) = semilattice_sup_sup(A) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom). [clausify(303)]. 1.45/1.68 Derived: ti(fun(bool,fun(bool,bool)),semilattice_sup_sup(bool)) = semilattice_sup_sup(bool). [resolve(600,a,581,a)]. 1.45/1.68 Derived: ti(fun(fun(A,B),fun(fun(A,B),fun(A,B))),semilattice_sup_sup(fun(A,B))) = semilattice_sup_sup(fun(A,B)) | -lattice(B). [resolve(600,a,586,b)]. 1.45/1.68 601 -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(330)]. 1.45/1.68 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(601,a,581,a)]. 1.45/1.68 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),E),F)) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),E)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),F))) | -lattice(B). [resolve(601,a,586,b)]. 1.45/1.68 602 -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(336)]. 1.45/1.68 603 -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(336)]. 1.45/1.68 604 -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(372)]. 1.45/1.68 605 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) # label(fact_214_sup__absorb1) # label(axiom). [clausify(374)]. 1.45/1.68 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | ti(bool,B) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A). [resolve(605,a,581,a)]. 1.45/1.68 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | ti(fun(A,B),D) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),C) | -lattice(B). [resolve(605,a,586,b)]. 1.45/1.68 606 -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(382)]. 1.45/1.68 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_sup_sup(bool))). [resolve(606,a,581,a)]. 1.52/1.72 Derived: hBOOL(hAPP(fun(fun(A,B),fun(fun(A,B),fun(A,B))),bool,finite_comp_fun_idem(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)))) | -lattice(B). [resolve(606,a,586,b)]. 1.52/1.72 607 -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(438)]. 1.52/1.72 608 -semilattice_sup(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_219_le__iff__sup) # label(axiom). [clausify(446)]. 1.52/1.72 609 -semilattice_sup(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_219_le__iff__sup) # label(axiom). [clausify(446)]. 1.52/1.72 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | ti(bool,B) != hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B). [resolve(609,a,581,a)]. 1.52/1.72 Derived: hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | ti(fun(A,B),D) != hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D) | -lattice(B). [resolve(609,a,586,b)]. 1.52/1.72 610 -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(472)]. 1.52/1.72 611 -bounded_lattice(A) | bounded_lattice_bot(fun(B,A)) # label(arity_fun___Lattices_Obounded__lattice__bot) # label(axiom). [clausify(197)]. 1.52/1.72 612 -bounded_lattice_bot(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),bot_bot(A)) # label(fact_225_sup__bot__right) # label(axiom). [clausify(9)]. 1.52/1.72 613 -bounded_lattice_bot(A) | bot_bot(A) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),bot_bot(A)),B) # label(fact_364_inf__bot__left) # label(axiom). [clausify(78)]. 1.52/1.72 Derived: -bounded_lattice(A) | ti(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),bot_bot(fun(B,A))). [resolve(611,b,612,a)]. 1.52/1.72 Derived: -bounded_lattice(A) | bot_bot(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)),bot_bot(fun(B,A))),C). [resolve(611,b,613,a)]. 1.52/1.72 614 -bounded_lattice_bot(A) | bot_bot(A) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),bot_bot(A)) # label(fact_363_inf__bot__right) # label(axiom). [clausify(200)]. 1.52/1.72 Derived: bot_bot(fun(A,B)) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),bot_bot(fun(A,B))) | -bounded_lattice(B). [resolve(614,a,611,b)]. 1.52/1.72 615 -bounded_lattice_bot(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),bot_bot(A)),B) # label(fact_226_sup__bot__left) # label(axiom). [clausify(434)]. 1.52/1.72 Derived: ti(fun(A,B),C) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),bot_bot(fun(A,B))),C) | -bounded_lattice(B). [resolve(615,a,611,b)]. 1.52/1.72 616 bounded_lattice_bot(bool) # label(arity_HOL_Obool___Lattices_Obounded__lattice__bot) # label(axiom). [assumption]. 1.52/1.72 Derived: ti(bool,A) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),bot_bot(bool)). [resolve(616,a,612,a)]. 1.52/1.72 Derived: bot_bot(bool) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),bot_bot(bool)),A). [resolve(616,a,613,a)]. 1.52/1.72 Derived: bot_bot(bool) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),bot_bot(bool)). [resolve(616,a,614,a)]. 1.52/1.72 Derived: ti(bool,A) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),bot_bot(bool)),A). [resolve(616,a,615,a)]. 1.52/1.72 617 -bounded_lattice_bot(A) | bot_bot(A) != ti(A,B) | bot_bot(A) != ti(A,C) | bot_bot(A) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_224_sup__eq__bot__iff) # label(axiom). [clausify(492)]. 1.52/1.74 Derived: bot_bot(fun(A,B)) != ti(fun(A,B),C) | bot_bot(fun(A,B)) != ti(fun(A,B),D) | bot_bot(fun(A,B)) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D) | -bounded_lattice(B). [resolve(617,a,611,b)]. 1.52/1.74 Derived: bot_bot(bool) != ti(bool,A) | bot_bot(bool) != ti(bool,B) | bot_bot(bool) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B). [resolve(617,a,616,a)]. 1.52/1.74 618 -bounded_lattice_bot(A) | bot_bot(A) = ti(A,B) | bot_bot(A) != hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_224_sup__eq__bot__iff) # label(axiom). [clausify(492)]. 1.52/1.74 Derived: bot_bot(fun(A,B)) = ti(fun(A,B),C) | bot_bot(fun(A,B)) != hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),C),D) | -bounded_lattice(B). [resolve(618,a,611,b)]. 1.52/1.74 Derived: bot_bot(bool) = ti(bool,A) | bot_bot(bool) != hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B). [resolve(618,a,616,a)]. 1.52/1.74 619 -bounded_lattice_bot(A) | bot_bot(A) = ti(A,B) | bot_bot(A) != hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) # label(fact_224_sup__eq__bot__iff) # label(axiom). [clausify(492)]. 1.52/1.74 Derived: bot_bot(fun(A,B)) = ti(fun(A,B),C) | bot_bot(fun(A,B)) != hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_sup_sup(fun(A,B)),D),C) | -bounded_lattice(B). [resolve(619,a,611,b)]. 1.52/1.74 Derived: bot_bot(bool) = ti(bool,A) | bot_bot(bool) != hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A). [resolve(619,a,616,a)]. 1.52/1.74 620 -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(19)]. 1.52/1.74 621 -lattice(A) | semilattice_inf(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__inf) # label(axiom). [clausify(12)]. 1.52/1.74 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D)) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D) | -lattice(B). [resolve(620,a,621,b)]. 1.52/1.74 622 -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(25)]. 1.52/1.74 Derived: semilattice_inf_inf(fun(A,B)) = ti(fun(fun(A,B),fun(fun(A,B),fun(A,B))),semilattice_inf_inf(fun(A,B))) | -lattice(B). [resolve(622,a,621,b)]. 1.52/1.74 623 -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(85)]. 1.52/1.74 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),E))) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | -lattice(B). [resolve(623,a,621,b)]. 1.52/1.74 624 -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(85)]. 1.52/1.74 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),E))) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),E)) | -lattice(B). [resolve(624,a,621,b)]. 1.52/1.74 625 semilattice_inf(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__inf) # label(axiom). [assumption]. 1.52/1.74 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(625,a,620,a)]. 1.52/1.74 Derived: semilattice_inf_inf(bool) = ti(fun(bool,fun(bool,bool)),semilattice_inf_inf(bool)). [resolve(625,a,622,a)]. 1.52/1.74 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(625,a,623,a)]. 1.52/1.74 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(625,a,624,a)]. 1.52/1.74 626 -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(106)]. 1.52/1.74 Derived: hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D)),C)) | -lattice(B). [resolve(626,a,621,b)]. 1.52/1.74 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(626,a,625,a)]. 1.52/1.74 627 -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(161)]. 1.52/1.74 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),E)) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),E)) | -lattice(B). [resolve(627,a,621,b)]. 1.52/1.74 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(627,a,625,a)]. 1.52/1.74 628 -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(186)]. 1.52/1.74 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),E)),D)) | -lattice(B). [resolve(628,a,621,b)]. 1.52/1.74 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(628,a,625,a)]. 1.52/1.74 629 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) # label(fact_351_inf__absorb1) # label(axiom). [clausify(234)]. 1.52/1.74 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | ti(fun(A,B),C) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D) | -lattice(B). [resolve(629,a,621,b)]. 1.52/1.74 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | ti(bool,A) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B). [resolve(629,a,625,a)]. 1.52/1.74 630 -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(264)]. 1.52/1.74 Derived: hBOOL(hAPP(fun(fun(A,B),fun(fun(A,B),fun(A,B))),bool,finite_comp_fun_idem(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)))) | -lattice(B). [resolve(630,a,621,b)]. 1.52/1.75 Derived: hBOOL(hAPP(fun(bool,fun(bool,bool)),bool,finite_comp_fun_idem(bool,bool),semilattice_inf_inf(bool))). [resolve(630,a,625,a)]. 1.52/1.75 631 -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(273)]. 1.52/1.75 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D)),E) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),E)) | -lattice(B). [resolve(631,a,621,b)]. 1.52/1.75 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(631,a,625,a)]. 1.52/1.75 632 -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(281)]. 1.52/1.75 633 -semilattice_inf(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) # label(fact_365_inf_Oidem) # label(axiom). [clausify(293)]. 1.52/1.75 Derived: ti(fun(A,B),C) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),C) | -lattice(B). [resolve(633,a,621,b)]. 1.52/1.75 Derived: ti(bool,A) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),A). [resolve(633,a,625,a)]. 1.52/1.75 634 -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(297)]. 1.52/1.75 635 -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(304)]. 1.52/1.75 Derived: hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),C) | -lattice(B). [resolve(635,a,621,b)]. 1.52/1.75 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(635,a,625,a)]. 1.52/1.75 636 -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(318)]. 1.52/1.75 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),E)) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),E))) | -lattice(B). [resolve(636,a,621,b)]. 1.52/1.75 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),C)) | 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))). [resolve(636,a,625,a)]. 1.52/1.75 637 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),C),B) # label(fact_352_inf__absorb2) # label(axiom). [clausify(322)]. 1.52/1.76 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | ti(fun(A,B),C) = hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),C) | -lattice(B). [resolve(637,a,621,b)]. 1.52/1.76 Derived: -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | ti(bool,A) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),B),A). [resolve(637,a,625,a)]. 1.52/1.76 638 -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(404)]. 1.52/1.76 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),E),C)),D)) | -lattice(B). [resolve(638,a,621,b)]. 1.52/1.76 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(638,a,625,a)]. 1.52/1.76 639 -semilattice_inf(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) # label(fact_347_le__iff__inf) # label(axiom). [clausify(436)]. 1.52/1.76 640 -semilattice_inf(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),C) # label(fact_347_le__iff__inf) # label(axiom). [clausify(436)]. 1.52/1.76 Derived: hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | ti(fun(A,B),C) != hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D) | -lattice(B). [resolve(640,a,621,b)]. 1.52/1.76 Derived: hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),A),B)) | ti(bool,A) != hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_inf_inf(bool),A),B). [resolve(640,a,625,a)]. 1.52/1.76 641 -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(451)]. 1.52/1.76 642 -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(453)]. 1.52/1.76 Derived: hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),D)),D)) | -lattice(B). [resolve(642,a,621,b)]. 1.52/1.76 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(642,a,625,a)]. 1.52/1.76 643 -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(517)]. 1.52/1.76 644 -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(517)]. 1.52/1.76 645 -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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_348_le__inf__iff) # label(axiom). [clausify(517)]. 1.52/1.76 646 -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(540)]. 3.53/3.73 647 -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(547)]. 3.53/3.73 Derived: -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),C),D)) | -hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),E),F)) | hBOOL(hAPP(fun(A,B),bool,hAPP(fun(A,B),fun(fun(A,B),bool),ord_less_eq(fun(A,B)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),C),E)),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,B),fun(fun(A,B),fun(A,B)),semilattice_inf_inf(fun(A,B)),D),F))) | -lattice(B). [resolve(647,a,621,b)]. 3.53/3.73 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(647,a,625,a)]. 3.53/3.73 648 -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(561)]. 3.53/3.73 649 -semilattice_inf(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_inf_inf(A),B),B) # label(fact_366_inf__idem) # label(axiom). [clausify(575)]. 3.53/3.73 3.53/3.73 ============================== end predicate elimination ============= 3.53/3.73 3.53/3.73 Auto_denials: (non-Horn, no changes). 3.53/3.73 3.53/3.73 Term ordering decisions: 3.53/3.73 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. f17=1. f26=1. f41=1. f45=1. f46=1. f47=1. f49=1. f70=1. f71=1. f88=1. f93=1. f97=1. f98=1. f100=1. f101=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. f61=1. f72=1. combb=1. combs=1. combc=1. f8=1. f16=1. f22=1. f27=1. f32=1. f33=1. f35=1. f38=1. f39=1. f40=1. f73=1. f74=1. f77=1. f78=1. f79=1. f85=1. f89=1. f95=1. hAPP=1. f1=1. f2=1. f12=1. f14=1. f15=1. f25=1. f28=1. f29=1. f30=1. f31=1. f36=1. f37=1. f42=1. f52=1. f53=1. f54=1. f67=1. f68=1. f69=1. f76=1. f80=1. f81=1. f82=1. f84=1. f91=1. f92=1. f94=1. f96=1. f7=1. f20=1. f21=1. f48=1. f50=1. f51=1. f56=1. f59=1. f60=1. f62=1. f75=1. f86=1. f87=1. f90=1. f99=1. f3=1. f4=1. f5=1. f6=1. f13=1. f18=1. f19=1. f23=1. f24=1. f43=1. f44=1. f57=1. f58=1. f63=1. f64=1. f65=1. f66=1. f9=1. f10=1. f11=1. f83=1. f34=1. f55=1. 3.53/3.73 3.53/3.73 ============================== end of process initial clauses ======== 3.53/3.73 3.53/3.73 ============================== CLAUSES FOR SEARCH ==================== 3.53/3.73 3.53/3.73 ============================== end of clauses for search ============= 3.53/3.73 3.53/3.73 ============================== SEARCH ================================ 3.53/3.73 3.53/3.73 % Starting search at 0.69 seconds. 3.53/3.73 3.53/3.73 Low Water (keep): wt=177.000, iters=3508 3.53/3.73 3.53/3.73 Low Water (keep): wt=175.000, iters=3475 3.53/3.73 3.53/3.73 Low Water (keep): wt=172.000, iters=3438 7.71/7.92 7.71/7.92 Low Water (keep): wt=167.000, iters=3375 7.71/7.92 7.71/7.92 Low Water (keep): wt=166.000, iters=3406 7.71/7.92 7.71/7.92 Low Water (keep): wt=165.000, iters=3471 7.71/7.92 7.71/7.92 Low Water (keep): wt=160.000, iters=3484 7.71/7.92 7.71/7.92 Low Water (keep): wt=154.000, iters=3433 7.71/7.92 7.71/7.92 Low Water (keep): wt=148.000, iters=3358 7.71/7.92 7.71/7.92 Low Water (keep): wt=146.000, iters=3341 7.71/7.92 7.71/7.92 Low Water (keep): wt=144.000, iters=3418 7.71/7.92 7.71/7.92 Low Water (keep): wt=139.000, iters=3357 7.71/7.92 7.71/7.92 Low Water (keep): wt=137.000, iters=3336 7.71/7.92 7.71/7.92 Low Water (keep): wt=136.000, iters=3373 7.71/7.92 7.71/7.92 Low Water (keep): wt=134.000, iters=3468 7.71/7.92 7.71/7.92 Low Water (keep): wt=130.000, iters=3369 7.71/7.92 7.71/7.92 Low Water (keep): wt=129.000, iters=3397 7.71/7.92 7.71/7.92 Low Water (keep): wt=128.000, iters=3362 7.71/7.92 7.71/7.92 Low Water (keep): wt=127.000, iters=3372 7.71/7.92 7.71/7.92 Low Water (keep): wt=123.000, iters=3388 7.71/7.92 7.71/7.92 Low Water (keep): wt=121.000, iters=3335 7.71/7.92 7.71/7.92 Low Water (keep): wt=120.000, iters=3363 7.71/7.92 7.71/7.92 Low Water (keep): wt=119.000, iters=3338 7.71/7.92 7.71/7.92 Low Water (keep): wt=118.000, iters=3503 7.71/7.92 7.71/7.92 Low Water (keep): wt=117.000, iters=3419 7.71/7.92 7.71/7.92 Low Water (keep): wt=116.000, iters=3396 7.71/7.92 7.71/7.92 Low Water (keep): wt=113.000, iters=3366 7.71/7.92 7.71/7.92 Low Water (keep): wt=112.000, iters=3381 7.71/7.92 7.71/7.92 Low Water (keep): wt=111.000, iters=3371 7.71/7.92 7.71/7.92 Low Water (keep): wt=110.000, iters=3432 7.71/7.92 7.71/7.92 Low Water (keep): wt=109.000, iters=3374 7.71/7.92 7.71/7.92 Low Water (keep): wt=106.000, iters=3344 7.71/7.92 7.71/7.92 Low Water (keep): wt=105.000, iters=3361 7.71/7.92 7.71/7.92 Low Water (keep): wt=103.000, iters=3359 7.71/7.92 7.71/7.92 Low Water (keep): wt=102.000, iters=3346 7.71/7.92 7.71/7.92 Low Water (keep): wt=101.000, iters=3346 7.71/7.92 7.71/7.92 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 63 (0.00 of 3.40 sec). 7.71/7.92 7.71/7.92 Low Water (keep): wt=98.000, iters=3358 7.71/7.92 7.71/7.92 Low Water (keep): wt=97.000, iters=3377 7.71/7.92 7.71/7.92 Low Water (keep): wt=95.000, iters=3354 7.71/7.92 7.71/7.92 Low Water (keep): wt=94.000, iters=3374 7.71/7.92 7.71/7.92 Low Water (keep): wt=92.000, iters=3373 7.71/7.92 7.71/7.92 Low Water (keep): wt=91.000, iters=3382 7.71/7.92 7.71/7.92 Low Water (keep): wt=90.000, iters=3356 7.71/7.92 7.71/7.92 Low Water (keep): wt=87.000, iters=3369 7.71/7.92 7.71/7.92 Low Water (keep): wt=86.000, iters=3378 7.71/7.92 7.71/7.92 Low Water (keep): wt=85.000, iters=3346 7.71/7.92 7.71/7.92 Low Water (keep): wt=84.000, iters=3402 7.71/7.92 7.71/7.92 Low Water (keep): wt=82.000, iters=3340 7.71/7.92 7.71/7.92 Low Water (keep): wt=80.000, iters=3371 7.71/7.92 7.71/7.92 Low Water (keep): wt=79.000, iters=3450 7.71/7.92 7.71/7.92 Low Water (keep): wt=78.000, iters=3396 7.71/7.92 7.71/7.92 Low Water (keep): wt=77.000, iters=3431 7.71/7.92 7.71/7.92 Low Water (keep): wt=76.000, iters=3460 7.71/7.92 7.71/7.92 Low Water (keep): wt=75.000, iters=3383 7.71/7.92 7.71/7.92 Low Water (keep): wt=74.000, iters=3354 7.71/7.92 7.71/7.92 Low Water (keep): wt=73.000, iters=3362 7.71/7.92 7.71/7.92 Low Water (keep): wt=72.000, iters=3364 7.71/7.92 7.71/7.92 Low Water (keep): wt=71.000, iters=3359 7.71/7.92 7.71/7.92 Low Water (keep): wt=70.000, iters=3362 7.71/7.92 7.71/7.92 Low Water (keep): wt=69.000, iters=3390 7.71/7.92 7.71/7.92 Low Water (keep): wt=68.000, iters=3338 7.71/7.92 7.71/7.92 Low Water (keep): wt=66.000, iters=3355 7.71/7.92 7.71/7.92 Low Water (keep): wt=63.000, iters=3346 7.71/7.92 7.71/7.92 Low Water (keep): wt=61.000, iters=3445 7.71/7.92 7.71/7.92 Low Water (keep): wt=60.000, iters=3493 7.71/7.92 7.71/7.92 Low Water (keep): wt=59.000, iters=3409 7.71/7.92 7.71/7.92 Low Water (keep): wt=58.000, iters=3353 7.71/7.92 7.71/7.92 Low Water (keep): wt=57.000, iters=3360 7.71/7.92 7.71/7.92 Low Water (keep): wt=54.000, iters=3476 7.71/7.92 7.71/7.92 Low Water (keep): wt=53.000, iters=3380 7.71/7.92 7.71/7.92 Low Water (keep): wt=44.000, iters=3629 7.71/7.92 7.71/7.92 Low Water (keep): wt=40.000, iters=3344 7.71/7.92 7.71/7.92 Low Water (keep): wt=39.000, iters=3447 7.71/7.92 7.71/7.92 Low Water (keep): wt=36.000, iters=3481 7.71/7.92 7.71/7.92 Low Water (keep): wt=35.000, iters=3936 7.71/7.92 7.71/7.92 Low Water (keep): wt=23.000, iters=3354 7.71/7.92 7.71/7.92 Low Water (displace): id=5091, wt=200.000 7.71/7.92 7.71/7.92 Low Water (displace): id=3004, wt=199.000 7.71/7.92 7.71/7.92 Low Water (displace): id=4610, wt=198.000 7.71/7.92 7.71/7.92 Low Water (displace): id=4362, wt=197.000 7.71/7.92 7.71/7.92 Low Water (displace): id=4364, wt=196.000 7.71/7.92 7.71/7.92 Low Water (displace): id=3204, wt=195.000 7.71/7.92 7.71/7.92 Low Water (displace): id=4735, wt=194.000 7.71/7.92 7.71/7.92 Low Water (displace): id=14228, wt=177.000 7.71/7.92 7.71/7.92 Low Water (displace): id=11363, wt=169.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13665, wt=164.000 7.71/7.92 7.71/7.92 Low Water (displace): id=10761, wt=162.000 7.71/7.92 7.71/7.92 Low Water (displace): id=10010, wt=161.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13722, wt=159.000 7.71/7.92 7.71/7.92 Low Water (displace): id=11348, wt=152.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13746, wt=146.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13699, wt=145.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13657, wt=144.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13654, wt=143.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13745, wt=141.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13687, wt=139.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13892, wt=138.000 7.71/7.92 7.71/7.92 Low Water (displace): id=11364, wt=136.000 7.71/7.92 7.71/7.92 Low Water (displace): id=13701, wt=133.000 207.32/207.59 207.32/207.59 Low Water (keep): wt=18.000, iters=3352 207.32/207.59 207.32/207.59 Low Water (displace): id=14284, wt=14.000 207.32/207.59 207.32/207.59 Low Water (displace): id=14292, wt=13.000 207.32/207.59 207.32/207.59 Low Water (displace): id=14296, wt=12.000 207.32/207.59 207.32/207.59 Low Water (displace): id=14298, wt=11.000 207.32/207.59 207.32/207.59 Low Water (keep): wt=17.000, iters=3361 207.32/207.59 207.32/207.59 Low Water (keep): wt=16.000, iters=3342 207.32/207.59 207.32/207.59 Low Water (keep): wt=15.000, iters=3333 207.32/207.59 207.32/207.59 Low Water (keep): wt=14.000, iters=3335 207.32/207.59 207.32/207.59 ============================== STATISTICS ============================ 207.32/207.59 207.32/207.59 Given=15718. Generated=5031356. Kept=140217. proofs=0. 207.32/207.59 Usable=15076. Sos=10000. Demods=485. Limbo=7346, Disabled=108709. Hints=0. 207.32/207.59 Kept_by_rule=0, Deleted_by_rule=294915. 207.32/207.59 Forward_subsumed=158415. Back_subsumed=102. 207.32/207.59 Sos_limit_deleted=4437809. Sos_displaced=104934. Sos_removed=0. 207.32/207.59 New_demodulators=811 (0 lex), Back_demodulated=2517. Back_unit_deleted=242. 207.32/207.59 Demod_attempts=212181982. Demod_rewrites=385311. 207.32/207.59 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 207.32/207.59 Nonunit_fsub_feature_tests=3003092. Nonunit_bsub_feature_tests=18273. 207.32/207.59 Megabytes=419.43. 207.32/207.59 User_CPU=203.29, System_CPU=2.76, Wall_clock=206. 207.32/207.59 207.32/207.59 Megs malloced by palloc(): 400. 207.32/207.59 type (bytes each) gets frees in use bytes 207.32/207.59 chunk ( 104) 56560 56560 0 0.0 K 207.32/207.59 string_buf ( 8) 50838 50838 0 0.0 K 207.32/207.59 token ( 20) 129070 129070 0 0.0 K 207.32/207.59 pterm ( 16) 91898 91898 0 0.0 K 207.32/207.59 hashtab ( 8) 580 580 0 0.0 K 207.32/207.59 hashnode ( 8) 2169 2169 0 0.0 K 207.32/207.59 term ( 20) 273921162 263388859 10532303 205709.0 K 207.32/207.59 term arg arrays: 49710.0 K 207.32/207.59 attribute ( 12) 4186 100 4086 47.9 K 207.32/207.59 ilist ( 8) 549713090 549007776 705314 5510.3 K 207.32/207.59 plist ( 8) 6301073 6115336 185737 1451.1 K 207.32/207.59 i2list ( 12) 13342230 13342230 0 0.0 K 207.32/207.59 just ( 12) 5338571 5185375 153196 1795.3 K 207.32/207.59 parajust ( 16) 532076 439482 92594 1446.8 K 207.32/207.59 instancejust ( 8) 0 0 0 0.0 K 207.32/207.59 ivyjust ( 24) 0 0 0 0.0 K 207.32/207.59 formula ( 28) 23580 14692 8888 243.0 K 207.32/207.59 formula arg arrays: 30.2 K 207.32/207.59 topform ( 52) 5032890 4891139 141751 7198.3 K 207.32/207.59 clist_pos ( 20) 399993 258377 141616 2765.9 K 207.32/207.59 clist ( 16) 8 1 7 0.1 K 207.32/207.59 context ( 808) 18826637 18826637 0 0.0 K 207.32/207.59 trail ( 12) 26061720 26061720 0 0.0 K 207.32/207.59 ac_match_pos (70044) 0 0 0 0.0 K 207.32/207.59 ac_match_free_vars_pos (20020) 207.32/207.59 0 0 0 0.0 K 207.32/207.59 btm_state ( 60) 0 0 0 0.0 K 207.32/207.59 btu_state ( 60) 0 0 0 0.0 K 207.32/207.59 ac_position (285432) 0 0 0 0.0 K 207.32/207.59 fpa_trie ( 20) 2924637 2642359 282278 5513.2 K 207.32/207.59 fpa_state ( 28) 8709579 8709579 0 0.0 K 207.32/207.59 fpa_index ( 12) 10 0 10 0.1 K 207.32/207.59 fpa_chunk ( 20) 4397351 4217358 179993 3515.5 K 207.32/207.59 fpa_list ( 16) 2719568 0 2719568 42493.2 K 207.32/207.59 fpa_list chunks: 19172.8 K 207.32/207.59 discrim ( 12) 2987772 2560531 427241 5006.7 K 207.32/207.59 discrim_pos ( 16) 499558 499558 0 0.0 K 207.32/207.59 flat2 ( 32) 64587033 64587033 0 0.0 K 207.32/207.59 flat ( 48) 0 0 0 0.0 K 207.32/207.59 flatterm ( 32) 264765391 264765391 0 0.0 K 207.32/207.59 mindex ( 28) 13 0 13 0.4 K 207.32/207.59 mindex_pos ( 56) 7729514 7729514 0 0.0 K 207.32/207.59 lindex ( 12) 5 0 5 0.1 K 207.32/207.59 clash ( 40) 0 0 0 0.0 K 207.32/207.59 di_tree ( 12) 28387642 24002505 4385137 51388.3 K 207.32/207.59 avl_node ( 20) 264618 244618 20000 390.6 K 207.32/207.59 207.32/207.59 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 207.32/207.59 List 1, length 8, 0.0 K 207.32/207.59 List 2, length 4205, 32.9 K 207.32/207.59 List 3, length 500419, 5864.3 K 207.32/207.59 List 5, length 8331, 162.7 K 207.32/207.59 List 7, length 348, 9.5 K 207.32/207.59 List 8, length 1987, 62.1 K 207.32/207.59 List 9, length 57, 2.0 K 207.32/207.59 List 10, length 2, 0.1 K 207.32/207.59 List 11, length 8, 0.3 K 207.32/207.59 List 12, length 4, 0.2 K 207.32/207.59 List 13, length 1, 0.1 K 207.32/207.59 List 14, length 9, 0.5 K 207.32/207.59 List 16, length 2005, 125.3 K 207.32/207.59 List 26, length 768, 78.0 K 207.32/207.59 List 32, length 1975, 246.9 K 207.32/207.59 List 64, length 754, 188.5 K 207.32/207.59 List 128, length 292, 146.0 K 207.32/207.59 List 202, length 4, 3.2 K 207.32/207.59 List 256, length 20, 20.0 K 207.32/207.59 207.32/207.59 ============================== SELECTOR REPORT ======================= 207.32/207.59 Sos_deleted=4437809, Sos_displaced=104934, Sos_size=10000 207.32/207.59 SELECTOR PART PRIORITY ORDER SIZE SELECTED 207.32/207.59 I 2147483647 high age 0 777 207.32/207.60 H 1 high weight 0 0 207.32/207.60 A 1 low age 10000 1661 207.32/207.60 F 4 low weight 1983 6640 207.32/207.60 T 4 low weight 8017 6640 207.32/207.60 ============================== end of selector report ================ 207.32/207.60 207.32/207.60 ============================== end of statistics ===================== 207.32/207.60 207.32/207.60 Exiting with failure. 207.32/207.60 207.32/207.60 Process 64561 exit (max_megs) Sat Jul 14 05:49:07 2018 207.32/207.60 Prover9 interrupted 207.32/207.60 EOF