TSTP Solution File: SWW474+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW474+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:10 EDT 2022
% Result : Theorem 13.97s 14.21s
% Output : Refutation 13.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW474+2 : TPTP v8.1.0. Released v5.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 5 12:41:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.42/1.79 ============================== Prover9 ===============================
% 1.42/1.79 Prover9 (32) version 2009-11A, November 2009.
% 1.42/1.79 Process 17540 was started by sandbox2 on n028.cluster.edu,
% 1.42/1.79 Sun Jun 5 12:41:43 2022
% 1.42/1.79 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17387_n028.cluster.edu".
% 1.42/1.79 ============================== end of head ===========================
% 1.42/1.79
% 1.42/1.79 ============================== INPUT =================================
% 1.42/1.79
% 1.42/1.79 % Reading from file /tmp/Prover9_17387_n028.cluster.edu
% 1.42/1.79
% 1.42/1.79 set(prolog_style_variables).
% 1.42/1.79 set(auto2).
% 1.42/1.79 % set(auto2) -> set(auto).
% 1.42/1.79 % set(auto) -> set(auto_inference).
% 1.42/1.79 % set(auto) -> set(auto_setup).
% 1.42/1.79 % set(auto_setup) -> set(predicate_elim).
% 1.42/1.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.42/1.79 % set(auto) -> set(auto_limits).
% 1.42/1.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.42/1.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.42/1.79 % set(auto) -> set(auto_denials).
% 1.42/1.79 % set(auto) -> set(auto_process).
% 1.42/1.79 % set(auto2) -> assign(new_constants, 1).
% 1.42/1.79 % set(auto2) -> assign(fold_denial_max, 3).
% 1.42/1.79 % set(auto2) -> assign(max_weight, "200.000").
% 1.42/1.79 % set(auto2) -> assign(max_hours, 1).
% 1.42/1.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.42/1.79 % set(auto2) -> assign(max_seconds, 0).
% 1.42/1.79 % set(auto2) -> assign(max_minutes, 5).
% 1.42/1.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.42/1.79 % set(auto2) -> set(sort_initial_sos).
% 1.42/1.79 % set(auto2) -> assign(sos_limit, -1).
% 1.42/1.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.42/1.79 % set(auto2) -> assign(max_megs, 400).
% 1.42/1.79 % set(auto2) -> assign(stats, some).
% 1.42/1.79 % set(auto2) -> clear(echo_input).
% 1.42/1.79 % set(auto2) -> set(quiet).
% 1.42/1.79 % set(auto2) -> clear(print_initial_clauses).
% 1.42/1.79 % set(auto2) -> clear(print_given).
% 1.42/1.79 assign(lrs_ticks,-1).
% 1.42/1.79 assign(sos_limit,10000).
% 1.42/1.79 assign(order,kbo).
% 1.42/1.79 set(lex_order_vars).
% 1.42/1.79 clear(print_given).
% 1.42/1.79
% 1.42/1.79 % formulas(sos). % not echoed (868 formulas)
% 1.42/1.79
% 1.42/1.79 ============================== end of input ==========================
% 1.42/1.79
% 1.42/1.79 % From the command line: assign(max_seconds, 300).
% 1.42/1.79
% 1.42/1.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.42/1.79
% 1.42/1.79 % Formulas that are not ordinary clauses:
% 1.42/1.79 1 (all B_1_1 (is_bool(B_1_1) -> is_fun_pname_bool(cOMBK_bool_pname(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 2 (all B_1_1 (is_bool(B_1_1) -> is_fun1661590463l_bool(cOMBK_1857069011e_bool(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 3 (all B_1_1 all B_2_1 is_bool(finite1282449217_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 4 (all B_1_1 all B_2_1 is_bool(finite774711482_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 5 (all B_1_1 all B_2_1 is_bool(finite1626890877e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 6 (all B_1_1 all B_2_1 is_bool(finite132673334e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 7 (all B_1_1 all B_2_1 is_bool(finite89670078_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 8 (all B_1_1 all B_2_1 is_bool(finite506823037_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 9 (all B_1_1 all B_2_1 is_bool(finite1268145088e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 10 (all B_1_1 all B_2_1 is_bool(finite959343283e_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Hoare____Mirabelle____ddpg) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 11 (all B_1_1 is_fun_pname_bool(dom_pname_com(B_1_1))) # label(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom) # label(hypothesis) # label(non_clause). [assumption].
% 1.42/1.79 12 (all B_1_1 (is_pname(B_1_1) -> is_option_pname(some_pname(B_1_1)))) # label(gsy_c_Option_Ooption_OSome_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 13 (all B_1_1 (is_option_pname(B_1_1) -> is_fun_pname_bool(set_pname(B_1_1)))) # label(gsy_c_Option_Oset_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 14 (all B_1_1 all B_2_1 is_bool(hAPP_com_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ocom_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 15 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_pname(hAPP_pname_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 16 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_1_1) & is_pname(B_2_1) -> is_bool(hAPP_pname_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 17 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 18 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 19 (all B_1_1 all B_2_1 is_bool(hAPP_state_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 20 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 21 (all B_1_1 all B_2_1 is_pname(hAPP_H1344248906_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 22 (all B_1_1 all B_2_1 is_bool(hAPP_H513860823e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_001) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 23 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H1632039476e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_002) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 24 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_H737849090l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_003) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 25 (all B_1_1 all B_2_1 is_bool(hAPP_f990396704l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 26 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 27 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_1_1) & is_fun_pname_bool(B_2_1) -> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 28 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 29 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 30 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f42430548e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__fun_Itc__Com__Opname_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 31 (all B_1_1 all B_2_1 is_bool(hAPP_f327114704l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 32 (all B_1_1 all B_2_1 is_pname(hAPP_f1008690464_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 33 (all B_1_1 all B_2_1 is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_004) # label(hypothesis) # label(non_clause). [assumption].
% 1.42/1.79 34 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f1745235422e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_005) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 35 (all B_1_1 all B_2_1 is_fun1661590463l_bool(hAPP_f748867288l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_006) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 36 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 37 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun_pname_bool(hAPP_f674760225e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_007) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 38 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_008) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 39 (all B_1_1 all B_2_1 is_bool(hAPP_f239102607l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 40 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f280588268e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It_009) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 41 (all B_1_1 all B_2_1 is_bool(hAPP_f389811538l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 42 (all B_1_1 all B_2_1 is_bool(hAPP_f1904669497l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 43 (all G_1 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 44 (all Ts all G_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)))) # label(fact_1_asm) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 45 (all Ts all G_1 all Ts_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),Ts_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_2_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 46 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G_2),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 47 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 48 (all Ts all G_1 all T (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts)))))) # label(fact_5_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 49 (all G_1 all T all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))) & hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)))) # label(fact_6_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 50 (all Pn_1 all G_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),G_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1)))),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),bot_bo1055319631e_bool))))) # label(fact_7_MGT__BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 51 (all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,hAPP_f783502055l_bool(collec1613912337l_bool,hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,ord_le675606854l_bool),A_1)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 52 (all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> hBOOL(hAPP_f1904669497l_bool(finite1586217244l_bool,hAPP_f1987093l_bool(collec1277803610l_bool,hAPP_f1269496639l_bool(hAPP_f1508257257l_bool(cOMBC_1084925030l_bool,ord_le1076702565l_bool),A_1)))))) # label(fact_9_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 53 (all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,ord_le1720872323e_bool),A_1)))))) # label(fact_10_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 54 (all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,ord_le313189616e_bool),A_1)))))) # label(fact_11_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 55 (all H all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f748867288l_bool(image_1259634916e_bool(H),Fa))))) # label(fact_12_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 56 (all H all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f854625363l_bool(image_277167759e_bool(H),Fa))))) # label(fact_13_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 57 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(H),Fa))))) # label(fact_14_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 58 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1874607724l_bool(image_505480954e_bool(H),Fa))))) # label(fact_15_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 59 (all H all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f780887186e_bool(image_936554724_state(H),Fa))))) # label(fact_16_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 60 (all H all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f772567431e_bool(image_774712299_state(H),Fa))))) # label(fact_17_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 61 (all H all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(H),Fa))))) # label(fact_18_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 62 (all H all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f280588268e_bool(image_636285904_pname(H),Fa))))) # label(fact_19_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 63 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(H),Fa))))) # label(fact_20_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 64 (all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1))) # label(fact_21_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 65 (all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A_1))) # label(fact_22_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 66 (all A all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1))))) # label(fact_23_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 67 (all A all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),A_1))))) # label(fact_24_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 68 (all A all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1))))) # label(fact_25_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 69 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))))) # label(fact_26_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 70 (all Q_1 all P_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1))) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)))))) # label(fact_31_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 71 (all Q_1 all P_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1))) | hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),P_1)),Q_1)))))) # label(fact_32_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 72 (all Q_1 all P_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,P_1))) | hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,Q_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),P_1)),Q_1)))))) # label(fact_33_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 73 (all Q_1 all P_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1))) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)))))) # label(fact_34_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 74 (all C all A_1 ((A_1 = bot_bo1055319631e_bool -> hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1) = bot_bo844097828e_bool) & (A_1 != bot_bo1055319631e_bool -> hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool)))) # label(fact_35_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 75 (all C all A_1 (is_fun_pname_bool(A_1) -> (A_1 = bot_bo844097828e_bool -> hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1) = bot_bo1055319631e_bool) & (A_1 != bot_bo844097828e_bool -> hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool)))) # label(fact_36_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 76 (all C all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool))) # label(fact_37_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 77 (all C all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool))) # label(fact_38_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 78 (all F all X_1 all Y_1 (hAPP_p799580910on_com(F,X_1) = some_com(Y_1) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) = dom_pname_com(F))) # label(fact_39_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 79 (all B all F all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_40_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 80 (all B all F all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f854625363l_bool(image_277167759e_bool(F),A_1))) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))))) # label(fact_41_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.79 81 (all B all F all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_42_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 82 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_43_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 83 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1))) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))))) # label(fact_44_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 84 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_45_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 85 (all B all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f780887186e_bool(image_936554724_state(F),A_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))))) # label(fact_46_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 86 (all B all F all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f772567431e_bool(image_774712299_state(F),A_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))))) # label(fact_47_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 87 (all B all F all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_48_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 88 (all B all F all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f280588268e_bool(image_636285904_pname(F),A_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_49_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 89 (all B all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))))) # label(fact_50_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 90 (all A_1 all X_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) -> A_1 = bot_bo844097828e_bool | A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) # label(fact_51_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 91 (all A_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))) -> A_1 = bot_bo1055319631e_bool | A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))) # label(fact_52_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 92 (all C (hBOOL(hoare_298929751gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))))))) # label(fact_53_MGF) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 93 (all A -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),bot_bo844097828e_bool))) # label(fact_54_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 94 (all A -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),bot_bo1055319631e_bool))) # label(fact_55_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 95 (all B_1 all A all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B)) -> A = B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_56_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 96 (all B_1 all A all B ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B)) -> A = B_1) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))))) # label(fact_57_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 97 (all A all B_1 all A_1 (is_pname(A) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1))) -> (A != B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)))))) # label(fact_58_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 98 (all A all B_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),A_1))) -> (A != B_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))))) # label(fact_59_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 99 (all A_1 all B (is_fun_pname_bool(A_1) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> A_1 = B)))) # label(fact_60_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 100 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> A_1 = B))) # label(fact_61_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 101 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_62_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 102 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_63_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 103 (all A_1 all B_1 all F all X_1 (B_1 = hAPP_H1344248906_pname(F,X_1) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))))) # label(fact_64_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 104 (all A_1 all B_1 all F all X_1 (B_1 = hAPP_p1842370726_state(F,X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))))) # label(fact_65_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 105 (all A all A_1 (A_1 = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)))) # label(fact_66_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 106 (all A all A_1 (A_1 = bot_bo1055319631e_bool -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)))) # label(fact_67_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 107 (all P_1 (hAPP_f759274231e_bool(collect_pname,P_1) = bot_bo844097828e_bool <-> (all X_2 (is_pname(X_2) -> -hBOOL(hAPP_pname_bool(P_1,X_2)))))) # label(fact_68_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 108 (all P_1 (hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = bot_bo1649642514l_bool <-> (all X_2 (is_fun_pname_bool(X_2) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_2)))))) # label(fact_69_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 109 (all P_1 (hAPP_f1970439265l_bool(collec111528142e_bool,P_1) = bot_bo1325454745l_bool <-> (all X_2 -hBOOL(hAPP_f1760790145l_bool(P_1,X_2))))) # label(fact_70_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 110 (all P_1 (hAPP_f921536533e_bool(collec727977250_state,P_1) = bot_bo1055319631e_bool <-> (all X_2 -hBOOL(hAPP_H513860823e_bool(P_1,X_2))))) # label(fact_71_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 111 (all C -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool))) # label(fact_72_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 112 (all C -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),bot_bo1055319631e_bool))) # label(fact_73_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 113 (all P_1 (bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,P_1) <-> (all X_2 (is_pname(X_2) -> -hBOOL(hAPP_pname_bool(P_1,X_2)))))) # label(fact_74_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 114 (all P_1 (bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,P_1) <-> (all X_2 (is_fun_pname_bool(X_2) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_2)))))) # label(fact_75_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 115 (all P_1 (bot_bo1325454745l_bool = hAPP_f1970439265l_bool(collec111528142e_bool,P_1) <-> (all X_2 -hBOOL(hAPP_f1760790145l_bool(P_1,X_2))))) # label(fact_76_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 116 (all P_1 (bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,P_1) <-> (all X_2 -hBOOL(hAPP_H513860823e_bool(P_1,X_2))))) # label(fact_77_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 117 (all A_1 (is_fun_pname_bool(A_1) -> ((exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)))) <-> A_1 != bot_bo844097828e_bool))) # label(fact_78_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 118 (all A_1 ((exists X_2 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))) <-> A_1 != bot_bo1055319631e_bool)) # label(fact_79_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 119 (all A_1 (is_fun_pname_bool(A_1) -> ((all X_2 (is_pname(X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)))) <-> A_1 = bot_bo844097828e_bool))) # label(fact_80_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 120 (all A_1 ((all X_2 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))) <-> A_1 = bot_bo1055319631e_bool)) # label(fact_81_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 121 (all A all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) = A_1))) # label(fact_86_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 122 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = A_1)) # label(fact_87_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 123 (all B_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_88_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 124 (all B_1 all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))))) # label(fact_89_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 125 (all B all X_1 all A_1 (is_fun_pname_bool(B) & is_fun_pname_bool(A_1) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B) <-> A_1 = B))))) # label(fact_90_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 126 (all B all X_1 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) -> (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B) <-> A_1 = B)))) # label(fact_91_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 127 (all Y_1 all A_1 all X_1 (is_pname(Y_1) & is_pname(X_1) -> (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_pname_bool(A_1,X_1))))) # label(fact_92_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 128 (all Y_1 all A_1 all X_1 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A_1),X_1)) <-> Y_1 = X_1 | hBOOL(hAPP_H513860823e_bool(A_1,X_1)))) # label(fact_93_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 129 (all A all B_1 all A_1 (is_pname(A) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1))) <-> A = B_1 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))))) # label(fact_94_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 130 (all A all B_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),A_1))) <-> A = B_1 | hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)))) # label(fact_95_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 131 (all X_1 all Y_1 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1))) # label(fact_96_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 132 (all X_1 all Y_1 all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1))) # label(fact_97_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 133 (all X_1 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) # label(fact_98_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 134 (all X_1 all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) # label(fact_99_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 135 (all A all P_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(collect_pname,P_1)) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fimplies),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A)))),P_1))) # label(fact_100_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 136 (all A all P_1 hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fimplies),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A)))),P_1))) # label(fact_101_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 137 (all A all P_1 hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),hAPP_f1970439265l_bool(collec111528142e_bool,P_1)) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fimplies),hAPP_f1970439265l_bool(cOMBB_1957242197e_bool(fNot),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A)))),P_1))) # label(fact_102_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 138 (all A all P_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,P_1)) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fimplies),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A)))),P_1))) # label(fact_103_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 139 (all A all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_104_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 140 (all A all B hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_105_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 141 (all A all B hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B)))) # label(fact_106_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 142 (all A all B hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B)))) # label(fact_107_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 143 (all A all B hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)))) # label(fact_108_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 144 (all A all B hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)))) # label(fact_109_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 145 (all A_1 all B (A_1 = B -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))))) # label(fact_110_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 146 (all A_1 all B (A_1 = B -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1))))) # label(fact_111_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 147 (all C_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1))))) # label(fact_112_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 148 (all C_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),C_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1))))) # label(fact_113_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 149 (all X_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_114_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 150 (all X_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))))) # label(fact_115_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 151 (all B all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_116_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 152 (all B all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))))) # label(fact_117_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 153 (all X_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) # label(fact_118_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 154 (all X_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))))) # label(fact_119_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 155 (all A_1 all B (A_1 = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)))) # label(fact_120_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 156 (all A_1 all B (A_1 = B -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)))) # label(fact_121_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 157 (all A_1 all B (A_1 = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)))) # label(fact_122_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 158 (all A_1 all B (A_1 = B -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)))) # label(fact_123_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 159 (all A_1 all B (is_fun_pname_bool(A_1) & is_fun_pname_bool(B) -> (A_1 = B <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))))) # label(fact_124_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 160 (all A_1 all B (A_1 = B <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)))) # label(fact_125_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 161 (all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1))) # label(fact_126_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 162 (all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),A_1))) # label(fact_127_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 163 (all B_1 all F all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (B_1 = hAPP_H1344248906_pname(F,X_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))))) # label(fact_128_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 164 (all B_1 all F all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (B_1 = hAPP_p1842370726_state(F,X_1) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))))) # label(fact_129_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 165 (all F all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1344248906_pname(F,X_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))))) # label(fact_130_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 166 (all F all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F,X_1)),hAPP_f631639356e_bool(image_275883510_state(F),A_1))))) # label(fact_131_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 167 (all Z all F all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Z),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) <-> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & Z = hAPP_p1842370726_state(F,X_2))))) # label(fact_132_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 168 (all P_1 all Q_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1))) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))) # label(fact_133_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 169 (all P_1 all Q_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1))) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))))) # label(fact_134_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 170 (all P_1 all Q_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,P_1))) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,Q_1))))) # label(fact_135_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 171 (all P_1 all Q_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1))) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))))) # label(fact_136_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 172 (all X_2 all Xa hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),Xa) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),X_2))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),Xa)))) # label(fact_137_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 173 (all X_2 all Xa hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),Xa) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),X_2))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),Xa)))) # label(fact_138_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 174 (all X_2 all Xa hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),Xa) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),X_2))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),Xa)))) # label(fact_139_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 175 (all X_2 all Xa hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),Xa) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),X_2))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),Xa)))) # label(fact_140_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 176 (all A all B_1 (is_pname(A) & is_pname(B_1) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool) -> A = B_1))) # label(fact_141_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 177 (all A all B_1 (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),bot_bo1055319631e_bool) -> A = B_1)) # label(fact_142_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 178 (all B_1 all A (is_pname(B_1) & is_pname(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) -> B_1 = A))) # label(fact_143_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 179 (all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) -> B_1 = A)) # label(fact_144_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 180 (all A all B_1 all C all D (is_pname(A) & is_pname(B_1) & is_pname(C) & is_pname(D) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D),bot_bo844097828e_bool)) <-> A = C & B_1 = D | A = D & B_1 = C))) # label(fact_145_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 181 (all A all B_1 all C all D (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D),bot_bo1055319631e_bool)) <-> A = C & B_1 = D | A = D & B_1 = C)) # label(fact_146_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 182 (all B_1 all A (is_pname(B_1) & is_pname(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) <-> B_1 = A))) # label(fact_147_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 183 (all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) <-> B_1 = A)) # label(fact_148_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 184 (all A all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) != bot_bo844097828e_bool) # label(fact_149_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 185 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) != bot_bo1055319631e_bool) # label(fact_150_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 186 (all A all A_1 bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)) # label(fact_151_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 187 (all A all A_1 bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)) # label(fact_152_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 188 (all A all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)))) # label(fact_153_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 189 (all A all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),A_1))) <-> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)))) # label(fact_154_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 190 (all A all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)))) # label(fact_155_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 191 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)))) # label(fact_156_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 192 (all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool)) <-> A_1 = bot_bo844097828e_bool))) # label(fact_157_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 193 (all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),bot_bo1055319631e_bool)) <-> A_1 = bot_bo1055319631e_bool)) # label(fact_158_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 194 (all F all A_1 (hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1) = bot_bo844097828e_bool <-> A_1 = bot_bo1055319631e_bool)) # label(fact_159_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 195 (all F all A_1 (is_fun_pname_bool(A_1) -> (hAPP_f631639356e_bool(image_275883510_state(F),A_1) = bot_bo1055319631e_bool <-> A_1 = bot_bo844097828e_bool))) # label(fact_160_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 196 (all F hAPP_f1745235422e_bool(image_1925245338_pname(F),bot_bo1055319631e_bool) = bot_bo844097828e_bool) # label(fact_161_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 197 (all F hAPP_f631639356e_bool(image_275883510_state(F),bot_bo844097828e_bool) = bot_bo1055319631e_bool) # label(fact_162_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 198 (all F all A_1 (bot_bo844097828e_bool = hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1) <-> A_1 = bot_bo1055319631e_bool)) # label(fact_163_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 199 (all F all A_1 (is_fun_pname_bool(A_1) -> (bot_bo1055319631e_bool = hAPP_f631639356e_bool(image_275883510_state(F),A_1) <-> A_1 = bot_bo844097828e_bool))) # label(fact_164_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 200 (all A_1 all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))))) # label(fact_165_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 201 (all A_1 all B (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))))) # label(fact_166_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 202 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))))) # label(fact_167_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 203 (all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))))) # label(fact_168_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 204 (all A_1 all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))))) # label(fact_169_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 205 (all A_1 all B (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))))) # label(fact_170_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 206 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))))) # label(fact_171_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 207 (all A_1 all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))))) # label(fact_172_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 208 (all A all C_1 all D_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),C_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),D_1))))) # label(fact_173_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 209 (all A all C_1 all D_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),D_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),C_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),D_1))))) # label(fact_174_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 210 (all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) <-> hBOOL(hAPP_pname_bool(A_1,X_1)))) # label(fact_175_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 211 (all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) <-> hBOOL(hAPP_H513860823e_bool(A_1,X_1)))) # label(fact_176_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 212 (all P_1 hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1) # label(fact_177_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 213 (all P_1 (is_fun_pname_bool(P_1) -> hAPP_f759274231e_bool(collect_pname,P_1) = P_1)) # label(fact_178_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 214 (all P_1 (is_fun1661590463l_bool(P_1) -> hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = P_1)) # label(fact_179_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 215 (all P_1 hAPP_f1970439265l_bool(collec111528142e_bool,P_1) = P_1) # label(fact_180_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 216 (all B_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))))) # label(fact_181_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 217 (all B_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))))) # label(fact_182_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 218 (all B all X_1 all A_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))))) # label(fact_183_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 219 (all B all X_1 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))))) # label(fact_184_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 220 (all X_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),B)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)))) # label(fact_185_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 221 (all X_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)),B)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)))) # label(fact_186_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 222 (all B all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)))) # label(fact_187_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 223 (all B all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)))) # label(fact_188_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 224 (all F all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1344248906_pname(F,X_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)) = hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) # label(fact_189_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 225 (all F all X_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F,X_1)),hAPP_f631639356e_bool(image_275883510_state(F),A_1)) = hAPP_f631639356e_bool(image_275883510_state(F),A_1))) # label(fact_190_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 226 (all F all A all B hAPP_f1745235422e_bool(image_1925245338_pname(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1344248906_pname(F,A)),hAPP_f1745235422e_bool(image_1925245338_pname(F),B))) # label(fact_191_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 227 (all F all A all B hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F,A)),hAPP_f631639356e_bool(image_275883510_state(F),B))) # label(fact_192_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 228 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),B))))) # label(fact_193_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 229 (all F all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B))))) # label(fact_194_image__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 230 (all B all F all A_1 (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) <-> (exists AA (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,AA),A_1)) & B = hAPP_f1745235422e_bool(image_1925245338_pname(F),AA)))))) # label(fact_195_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 231 (all B all F all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) <-> (exists AA (is_fun_pname_bool(AA) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1)) & B = hAPP_f631639356e_bool(image_275883510_state(F),AA))))) # label(fact_196_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 232 (all M_1 all A all B_1 (hAPP_p799580910on_com(M_1,A) = some_com(B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1))))) # label(fact_197_domI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 233 (all P_1 all A ((hBOOL(hAPP_pname_bool(P_1,A)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(P_1,A)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),P_1)) = bot_bo844097828e_bool))) # label(fact_198_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 234 (all P_1 all A ((hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),P_1)) = bot_bo1649642514l_bool))) # label(fact_199_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 235 (all P_1 all A ((hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),P_1)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool)) & (-hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),P_1)) = bot_bo1325454745l_bool))) # label(fact_200_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 236 (all P_1 all A ((hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),P_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) & (-hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),P_1)) = bot_bo1055319631e_bool))) # label(fact_201_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 237 (all P_1 all A ((hBOOL(hAPP_pname_bool(P_1,A)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(P_1,A)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A))),P_1)) = bot_bo844097828e_bool))) # label(fact_202_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 238 (all P_1 all A ((hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(P_1,A)) -> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A))),P_1)) = bot_bo1649642514l_bool))) # label(fact_203_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 239 (all P_1 all A ((hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(fequal1746921144e_bool,A))),P_1)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool)) & (-hBOOL(hAPP_f1760790145l_bool(P_1,A)) -> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(fequal1746921144e_bool,A))),P_1)) = bot_bo1325454745l_bool))) # label(fact_204_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 240 (all P_1 all A ((hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A))),P_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) & (-hBOOL(hAPP_H513860823e_bool(P_1,A)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A))),P_1)) = bot_bo1055319631e_bool))) # label(fact_205_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 241 (all A hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)) # label(fact_206_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 242 (all A hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool)) # label(fact_207_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 243 (all A hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool)) # label(fact_208_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 244 (all A hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) # label(fact_209_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 245 (all A hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)) # label(fact_210_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 246 (all A hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(fequal533582459e_bool,A)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool)) # label(fact_211_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 247 (all A hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(fequal1746921144e_bool,A)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool)) # label(fact_212_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 248 (all A hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) # label(fact_213_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 249 (all C all G_1 (hBOOL(hoare_298929751gleton) -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),dom_pname_com(body))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_2))),bot_bo1055319631e_bool)))))) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))))))) # label(fact_214_MGF__lemma1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 250 (all Pn all B_4 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = some_com(B_4) -> hBOOL(hAPP_com_bool(wt,B_4))))) # label(fact_215_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 251 (all B_1 all F all A_1 (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> -(all X_2 (B_1 = hAPP_H1344248906_pname(F,X_2) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))))))) # label(fact_216_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 252 (all B_1 all F all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> -(all X_2 (is_pname(X_2) -> (B_1 = hAPP_p1842370726_state(F,X_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))))))) # label(fact_217_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 253 (all P_1 all A_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) -> ((all A_3 all F_1 (is_fun_pname_bool(A_3) & is_fun1661590463l_bool(F_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),A_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),F_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_1)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),F_1))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa))))))) # label(fact_218_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 254 (all P_1 all A_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,Fa),A_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,bot_bo1325454745l_bool)) -> ((all A_3 all F_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_3),A_1)) -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_3),F_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,F_1)) -> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A_3),F_1)))))))) -> hBOOL(hAPP_f239102607l_bool(P_1,Fa))))))) # label(fact_219_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 255 (all P_1 all A_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) -> ((all A_3 all F_1 (is_pname(A_3) & is_fun_pname_bool(F_1) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),F_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_1)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),F_1))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa))))))) # label(fact_220_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 256 (all P_1 all A_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Fa),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,bot_bo1055319631e_bool)) -> ((all A_3 all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),F_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,F_1)) -> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),F_1)))))))) -> hBOOL(hAPP_f1760790145l_bool(P_1,Fa))))))) # label(fact_221_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 257 (all P (hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,P))) -> -(all Y_2 hAPP_p799580910on_com(body,P) != some_com(Y_2)))) # label(fact_222_WTs__elim__cases_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 258 (all B all A_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)))) # label(fact_223_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 259 (all B all A_1 ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)))) # label(fact_224_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 260 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f780887186e_bool(image_936554724_state(F),A_1))) -> (exists C_3 (is_fun1661590463l_bool(C_3) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3)) & B = hAPP_f780887186e_bool(image_936554724_state(F),C_3)))))) # label(fact_225_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 261 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f772567431e_bool(image_774712299_state(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,C_3),A_1)) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,C_3)) & B = hAPP_f772567431e_bool(image_774712299_state(F),C_3)))))) # label(fact_226_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 262 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A_1))) -> (exists C_3 (is_fun1661590463l_bool(C_3) & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3)) & B = hAPP_f674760225e_bool(image_1283814551_pname(F),C_3))))))) # label(fact_227_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 263 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f280588268e_bool(image_636285904_pname(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,C_3),A_1)) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,C_3)) & B = hAPP_f280588268e_bool(image_636285904_pname(F),C_3))))))) # label(fact_228_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 264 (all F all A_1 all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1)) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3)) & B = hAPP_f748867288l_bool(image_1259634916e_bool(F),C_3))))))) # label(fact_229_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 265 (all F all A_1 all B (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f854625363l_bool(image_277167759e_bool(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1)) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3)) & B = hAPP_f854625363l_bool(image_277167759e_bool(F),C_3)))))) # label(fact_230_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 266 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> (exists C_3 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1)) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3)) & B = hAPP_f1745235422e_bool(image_1925245338_pname(F),C_3))))))) # label(fact_231_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 267 (all F all A_1 all B (is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A_1))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f434788991l_bool(image_47868345e_bool(F),C_3))))))) # label(fact_232_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 268 (all F all A_1 all B (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f1874607724l_bool(image_505480954e_bool(F),C_3)))))) # label(fact_233_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.80 269 (all F all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A_1))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f759274231e_bool(image_pname_pname(F),C_3))))))) # label(fact_234_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 270 (all F all A_1 all B (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> (exists C_3 (is_fun_pname_bool(C_3) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3)) & B = hAPP_f631639356e_bool(image_275883510_state(F),C_3)))))) # label(fact_235_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 271 (all P_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) -> ((all X_2 all F_1 (is_fun_pname_bool(X_2) & is_fun1661590463l_bool(F_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_1)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1)))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)))))) # label(fact_237_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 272 (all P_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (hBOOL(hAPP_f239102607l_bool(P_1,bot_bo1325454745l_bool)) -> ((all X_2 all F_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1)) -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),F_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,F_1)) -> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),F_1))))))) -> hBOOL(hAPP_f239102607l_bool(P_1,Fa)))))) # label(fact_238_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 273 (all P_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) -> ((all X_2 all F_1 (is_pname(X_2) & is_fun_pname_bool(F_1) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_1)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1)))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)))))) # label(fact_239_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 274 (all P_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,bot_bo1055319631e_bool)) -> ((all X_2 all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,F_1)) -> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_1))))))) -> hBOOL(hAPP_f1760790145l_bool(P_1,Fa)))))) # label(fact_240_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 275 (all A (is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) <-> A = bot_bo1649642514l_bool | (exists A_4 exists A_3 (is_fun1661590463l_bool(A_4) & is_fun_pname_bool(A_3) & A = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),A_4) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_4))))))) # label(fact_241_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 276 (all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) <-> A = bot_bo1325454745l_bool | (exists A_4 exists A_3 (A = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A_3),A_4) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_4)))))) # label(fact_242_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 277 (all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) <-> A = bot_bo844097828e_bool | (exists A_4 exists A_3 (is_fun_pname_bool(A_4) & is_pname(A_3) & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),A_4) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_4))))))) # label(fact_243_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 278 (all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) <-> A = bot_bo1055319631e_bool | (exists A_4 exists A_3 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_4) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_4)))))) # label(fact_244_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 279 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(F),A_1))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,hAPP_f567934427l_bool(cOMBB_408569982_pname(fequal533582459e_bool),F)),hAPP_p61793385e_bool(F,X_2))))))))))) # label(fact_245_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 280 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f1745235422e_bool(hAPP_f1558052123e_bool(cOMBC_2140141647l_bool,hAPP_f2081555625l_bool(cOMBB_44445098_pname(fequal1746921144e_bool),F)),hAPP_p877885514e_bool(F,X_2))))))))))) # label(fact_246_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 281 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(image_650584225_state(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & -hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,hAPP_f1844318385e_bool(cOMBB_291471741_state(fequal1531560888_state),F)),hAPP_H563960305_state(F,X_2))))))))))) # label(fact_247_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 282 (all F all A_1 (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f780887186e_bool(image_936554724_state(F),A_1))) -> (exists X_2 (is_fun_pname_bool(X_2) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1)) & -hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_H737849090l_bool(hAPP_f261382953l_bool(cOMBC_2107548985e_bool,hAPP_f547518321e_bool(cOMBB_1170234304e_bool(fequal1531560888_state),F)),hAPP_f1308959284_state(F,X_2))))))))))) # label(fact_248_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 283 (all F all A_1 (-hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f772567431e_bool(image_774712299_state(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1)) & -hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_H248360617l_bool(hAPP_f492098723l_bool(cOMBC_1305755390e_bool,hAPP_f481659057e_bool(cOMBB_1099197107e_bool(fequal1531560888_state),F)),hAPP_f2143211163_state(F,X_2))))))))))) # label(fact_249_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 284 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A_1))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X_2))))))))))) # label(fact_250_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 285 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & -hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_p877885514e_bool(hAPP_f294904177e_bool(cOMBC_725526061e_bool,hAPP_f833390165e_bool(cOMBB_1456120487_state(fequal_pname),F)),hAPP_H1344248906_pname(F,X_2))))))))))) # label(fact_251_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 286 (all F all A_1 (-hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(F),A_1))) -> (exists X_2 (is_fun_pname_bool(X_2) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1)) & -hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,hAPP_f1385420507e_bool(cOMBB_598082538e_bool(fequal_pname),F)),hAPP_f1297739591_pname(F,X_2))))))))))) # label(fact_252_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 287 (all F all A_1 (-hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f280588268e_bool(image_636285904_pname(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1)) & -hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_p1617973726l_bool(hAPP_f2070658331l_bool(cOMBC_367297061e_bool,hAPP_f1973135743e_bool(cOMBB_1671808265e_bool(fequal_pname),F)),hAPP_f1008690464_pname(F,X_2))))))))))) # label(fact_253_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 288 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & -hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f631639356e_bool(hAPP_f1721106985e_bool(cOMBC_498627897l_bool,hAPP_f376825399l_bool(cOMBB_1722165949_state(fequal533582459e_bool),F)),hAPP_H1632039476e_bool(F,X_2))))))))))) # label(fact_254_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 289 (all F all A_1 (-hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f854625363l_bool(image_277167759e_bool(F),A_1))) -> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & -hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,hAPP_f1862834069l_bool(cOMBB_1239130257_state(fequal1746921144e_bool),F)),hAPP_H1645666623e_bool(F,X_2))))))))))) # label(fact_255_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 290 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(F),A_1))) -> (exists X_2 (is_pname(X_2) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,hAPP_f998786331e_bool(cOMBB_799949246_pname(fequal1531560888_state),F)),hAPP_p1842370726_state(F,X_2))))))))))) # label(fact_256_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 291 (all Pname_2 all Pname_1 (is_pname(Pname_2) & is_pname(Pname_1) -> (hAPP_pname_com(body_1,Pname_2) = hAPP_pname_com(body_1,Pname_1) <-> Pname_2 = Pname_1))) # label(fact_257_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 292 (all G_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Procs))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Procs)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),Procs)))))) # label(fact_258_MGT__Body) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 293 (all A all M_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1))) -> (exists B_3 hAPP_p799580910on_com(M_1,A) = some_com(B_3)))) # label(fact_259_domD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 294 (all X_1 (is_pname(X_1) -> hAPP_f1297739591_pname(the_elem_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1)) # label(fact_260_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 295 (all X_1 hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = X_1) # label(fact_261_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 296 (all F all B all A_1 ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1344248906_pname(F,X_2)),B)))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)),B)))) # label(fact_262_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 297 (all F all B all A_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F,X_2)),B))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),B)))) # label(fact_263_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 298 (all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),X_1))) # label(fact_264_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 299 (all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),X_1))) # label(fact_265_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 300 (all A_1 (is_fun_pname_bool(A_1) -> (A_1 != bot_bo844097828e_bool <-> (exists X_2 exists B_2 (is_pname(X_2) & is_fun_pname_bool(B_2) & A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2))))))) # label(fact_266_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 301 (all A_1 (A_1 != bot_bo1055319631e_bool <-> (exists X_2 exists B_2 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_2) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_2)))))) # label(fact_267_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 302 (all X_4 hAPP_option_com_com(the_com,some_com(X_4)) = X_4) # label(fact_268_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 303 (all G_1 all P_1 all Pn_1 all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1055319631e_bool))))) # label(fact_269_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 304 (all A_1 all C all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))) # label(fact_270_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 305 (all A_1 all C all B ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) # label(fact_271_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 306 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_272_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 307 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_273_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 308 (all P_1 all Q_1 hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))) # label(fact_274_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 309 (all P_1 all Q_1 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) # label(fact_275_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 310 (all P_1 all Q_1 hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),P_1)),Q_1)) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) # label(fact_276_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 311 (all P_1 all Q_1 hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),P_1)),Q_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1))) # label(fact_277_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 312 (all Fun1_2 all Com_2 all Fun2_2 all Fun1_1 all Com_1 all Fun2_1 (hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_2),Com_2),Fun2_2) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_1),Com_1),Fun2_1) <-> Fun1_2 = Fun1_1 & Com_2 = Com_1 & Fun2_2 = Fun2_1)) # label(fact_278_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 313 (all A_1 all C all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))) # label(fact_279_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 314 (all A_1 all C all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) # label(fact_280_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 315 (all B all C all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))))) # label(fact_281_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 316 (all B all C all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))))) # label(fact_282_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 317 (all P_1 all A_1 all B ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) -> hBOOL(hAPP_H513860823e_bool(P_1,X_2)))) <-> (all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_H513860823e_bool(P_1,X_2)))) & (all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B)) -> hBOOL(hAPP_H513860823e_bool(P_1,X_2)))))) # label(fact_283_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 318 (all P_1 all A_1 all B ((exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) & hBOOL(hAPP_H513860823e_bool(P_1,X_2)))) <-> (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) & hBOOL(hAPP_H513860823e_bool(P_1,X_2)))) | (exists X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B)) & hBOOL(hAPP_H513860823e_bool(P_1,X_2)))))) # label(fact_284_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 319 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1))) # label(fact_285_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 320 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_286_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 321 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) | hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)))) # label(fact_287_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 322 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C_1))) # label(fact_288_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 323 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) # label(fact_289_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 324 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1)) # label(fact_290_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 325 (all A_1 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_291_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 326 (all A_1 all B hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_292_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 327 (all A_1 all B hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B)))) # label(fact_293_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 328 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B)))) # label(fact_294_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 329 (all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),A_1) = A_1) # label(fact_295_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 330 (all A_1 all B (is_fun_pname_bool(A_1) & is_fun_pname_bool(B) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = bot_bo844097828e_bool <-> A_1 = bot_bo844097828e_bool & B = bot_bo844097828e_bool))) # label(fact_296_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 331 (all A_1 all B (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = bot_bo1055319631e_bool <-> A_1 = bot_bo1055319631e_bool & B = bot_bo1055319631e_bool)) # label(fact_297_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 332 (all A_1 (is_fun_pname_bool(A_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),bot_bo844097828e_bool) = A_1)) # label(fact_298_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 333 (all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),bot_bo1055319631e_bool) = A_1) # label(fact_299_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 334 (all B (is_fun_pname_bool(B) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B) = B)) # label(fact_300_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 335 (all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),B) = B) # label(fact_301_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 336 (all G_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1)))))) # label(fact_302_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 337 (all G_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,Fa),G_1)))))) # label(fact_303_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 338 (all G_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1)))))) # label(fact_304_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 339 (all G_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Fa),G_1)))))) # label(fact_305_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 340 (all Fa all G_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)))) # label(fact_306_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 341 (all Fa all G_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,Fa),G_1))) <-> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) & hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)))) # label(fact_307_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 342 (all Fa all G_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)))) # label(fact_308_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 343 (all Fa all G_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Fa),G_1))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)))) # label(fact_309_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 344 (all A all B all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))) # label(fact_310_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 345 (all A all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1))) # label(fact_311_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 346 (all A_1 all A all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) # label(fact_312_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 347 (all A_1 all A all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) # label(fact_313_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 348 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),D_1)))))) # label(fact_314_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 349 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),D_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),D_1)))))) # label(fact_315_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 350 (all B all A_1 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),C_1))))) # label(fact_316_Un__least) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 351 (all B all A_1 all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),C_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C_1))))) # label(fact_317_Un__least) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 352 (all B all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = A_1))) # label(fact_318_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 353 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = A_1)) # label(fact_319_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 354 (all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B))) # label(fact_320_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 355 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = B)) # label(fact_321_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 356 (all A_1 all B (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) <-> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B))) # label(fact_322_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 357 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) <-> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = B)) # label(fact_323_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 358 (all B all A_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))) # label(fact_324_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 359 (all B all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))) # label(fact_325_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 360 (all A_1 all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))) # label(fact_326_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 361 (all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))) # label(fact_327_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 362 (all F all A_1 all B hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B))) # label(fact_328_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 363 (all A all B hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),B)) # label(fact_329_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 364 (all A all B hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),B)) # label(fact_330_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 365 (all A all B hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),B)) # label(fact_331_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 366 (all A all B hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),B) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),B)) # label(fact_332_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 367 (all A all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)),A_1)) # label(fact_333_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 368 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1)) # label(fact_334_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 369 (all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))))) # label(fact_335_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 370 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),Y_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1))))) # label(fact_336_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 371 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),Y_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_1))))) # label(fact_337_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 372 (all Y_1 all X_1 (is_fun_pname_bool(Y_1) & is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> X_1 = Y_1)))) # label(fact_338_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 373 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> X_1 = Y_1))) # label(fact_339_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 374 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),Z)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z))))) # label(fact_340_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 375 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),Z)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z))))) # label(fact_341_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 376 (all X_1 all Y_1 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> X_1 = Y_1)))) # label(fact_342_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 377 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> X_1 = Y_1))) # label(fact_343_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 378 (all C all B_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A)) -> (B_1 = C -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A))))) # label(fact_344_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 379 (all C all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A)) -> (B_1 = C -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),A))))) # label(fact_345_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 380 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B_1)) -> (B_1 = C -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))))) # label(fact_346_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 381 (all C all A all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B_1)) -> (B_1 = C -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C))))) # label(fact_347_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 382 (all C all A all B_1 (A = B_1 -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A))))) # label(fact_348_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 383 (all C all A all B_1 (A = B_1 -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),A))))) # label(fact_349_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 384 (all C all A all B_1 (A = B_1 -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))))) # label(fact_350_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 385 (all C all A all B_1 (A = B_1 -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C))))) # label(fact_351_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 386 (all Y_1 all X_1 (is_fun_pname_bool(Y_1) & is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) <-> X_1 = Y_1)))) # label(fact_352_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 387 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) <-> X_1 = Y_1))) # label(fact_353_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 388 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)))) # label(fact_354_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 389 (all X_1 all Y_1 (X_1 = Y_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)))) # label(fact_355_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 390 (all X_1 all Y_1 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_1) -> (X_1 = Y_1 <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))))) # label(fact_356_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 391 (all X_1 all Y_1 (X_1 = Y_1 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)))) # label(fact_357_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 392 (all A all A_2 (some_com(A) = some_com(A_2) <-> A = A_2)) # label(fact_358_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 393 (all G_1 all P_1 all C all Q_1 all C_1 ((hBOOL(C_1) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(cOMBB_1757942702_state(cOMBC_231445413l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),C_1)),C),Q_1)),bot_bo1055319631e_bool))))) # label(fact_359_constant) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 394 (all Pn_1 all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procs)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,Pn_1)),hAPP_pname_com(body_1,Pn_1)),hAPP_p1637813682e_bool(Q_1,Pn_1))),bot_bo1055319631e_bool)))))) # label(fact_360_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 395 (all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool)) -> A = bot_bo844097828e_bool))) # label(fact_361_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 396 (all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool)) -> A = bot_bo1055319631e_bool)) # label(fact_362_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 397 (all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool)) <-> A = bot_bo844097828e_bool))) # label(fact_363_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 398 (all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool)) <-> A = bot_bo1055319631e_bool)) # label(fact_364_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 399 (all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A))) # label(fact_365_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 400 (all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A))) # label(fact_366_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 401 (all X_1 all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))))) # label(fact_367_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 402 (all X_1 all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))))) # label(fact_368_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 403 (all X_1 all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))))) # label(fact_369_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 404 (all X_1 all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))))) # label(fact_370_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 405 (all F all G (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) <-> (all X_2 (is_pname(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))))) # label(fact_371_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 406 (all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) <-> (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2)))))) # label(fact_372_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 407 (all X_1 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_373_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 408 (all X_1 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_374_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 409 (all X_2 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_375_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 410 (all X_2 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_376_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 411 (all P_1 all Pn_1 all Q_1 all G_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),G_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1055319631e_bool))))) # label(fact_377_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 412 (all P_1 all Q_1 all G_1 all P_2 all C0_1 all Q_2 all U_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1)) -> ((all P_3 (is_pname(P_3) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_2,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_2,P_3))),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_1,P_3))),bot_bo1055319631e_bool)))))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_2)),C0_1)),Q_2)),U_1))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),C0_1)),Q_1)),U_1))))))) # label(fact_378_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 413 (all G_1 all C all Q_1 all P_1 ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,cOMBK_631994958_state(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),cOMBK_631994958_state(hAPP_s1806633685e_bool(Q_1,Z_2)))),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))))) # label(fact_379_escape) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 414 (all G_1 all P_1 all Q_1 all Procs (hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs))) -> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))))) # label(fact_380_Body__sound__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 415 (all P_1 all G_1 all P_2 all C all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_2),C),Q_1)),bot_bo1055319631e_bool))) -> ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_2),S_3)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_381_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 416 (all Q_1 all G_1 all P_1 all C all Q_2 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_2)),bot_bo1055319631e_bool))) -> ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_2),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_3)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_382_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 417 (all P_1 all Q_1 all C (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_383_MGF__complete) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 418 (all A_1 all B all X_1 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)) -> (-hBOOL(hAPP_H513860823e_bool(A_1,X_1)) -> hBOOL(hAPP_H513860823e_bool(B,X_1))))) # label(fact_384_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 419 (all A_1 all B all X_1 ((-hBOOL(hAPP_H513860823e_bool(B,X_1)) -> hBOOL(hAPP_H513860823e_bool(A_1,X_1))) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)))) # label(fact_385_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 420 (all G_1 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_1),Ts)))) # label(fact_386_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 421 (all X_2 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),bot_bo844097828e_bool)))) # label(fact_387_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 422 (all X_2 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),bot_bo1055319631e_bool)))) # label(fact_388_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 423 (all Q_1 all P_1 all X_1 (hBOOL(hAPP_pname_bool(P_1,X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) -> hBOOL(hAPP_pname_bool(Q_1,X_1))))) # label(fact_389_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 424 (all Q_1 all P_1 all X_1 (hBOOL(hAPP_H513860823e_bool(P_1,X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_1))))) # label(fact_390_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 425 (all X_1 all P_1 all Q_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) -> (hBOOL(hAPP_pname_bool(P_1,X_1)) -> hBOOL(hAPP_pname_bool(Q_1,X_1))))) # label(fact_391_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 426 (all X_1 all P_1 all Q_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1)) -> (hBOOL(hAPP_H513860823e_bool(P_1,X_1)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_1))))) # label(fact_392_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 427 (all A_1 all B all X_1 (hBOOL(hAPP_H513860823e_bool(B,X_1)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)))) # label(fact_393_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 428 (all B all A_1 all X_1 (hBOOL(hAPP_H513860823e_bool(A_1,X_1)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)))) # label(fact_394_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 429 (all R_1 all S (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,R_1),S)))) # label(fact_395_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 430 (all R_1 all S (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,R_1),S)))) # label(fact_396_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 431 (all R_1 all S all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S))))) # label(fact_397_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 432 (all R_1 all S all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S)),X_2)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,R_1),S))))) # label(fact_398_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 433 (all Q_1 all P_1 all G_1 all P_2 all C all Q_2 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_2),C),Q_2)),bot_bo1055319631e_bool))) -> ((all Z_2 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3)) -> (all S_4 ((all Z_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_3),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_3),S_4)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_4)))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))))) # label(fact_399_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 434 (all F all G ((all X_2 (is_pname(X_2) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)))) # label(fact_400_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 435 (all F all G ((all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)))) # label(fact_401_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 436 (all X_1 set_pname(some_pname(X_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) # label(fact_402_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 437 (all X_1 set_Ho1831989999_state(some_H1133819688_state(X_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) # label(fact_403_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 438 (all X_1 set_com(some_com(X_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) # label(fact_404_Option_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 439 (all X_1 all Xo (is_option_pname(Xo) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),set_pname(Xo))) <-> Xo = some_pname(X_1)))) # label(fact_405_elem__set) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 440 (all X_1 all Xo (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),set_Ho1831989999_state(Xo))) <-> Xo = some_H1133819688_state(X_1))) # label(fact_406_elem__set) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 441 (all X_1 all Xo (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),set_com(Xo))) <-> Xo = some_com(X_1))) # label(fact_407_elem__set) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 442 (all X_1 all P_1 all A_1 ((all X_2 (hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),set_com(A_1))) -> hBOOL(hAPP_com_bool(P_1,X_2)))) -> (A_1 = some_com(X_1) -> hBOOL(hAPP_com_bool(P_1,X_1))))) # label(fact_408_ospec) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 443 (all F all G all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2))))) # label(fact_409_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 444 (all F all G all X_1 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),G),X_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))))) # label(fact_410_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 445 hBOOL(hoare_298929751gleton) -> (all T_2 -(all S_3 S_3 = T_2)) # label(fact_411_single__stateE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 446 hBOOL(hoare_298929751gleton) <-> (exists S_3 exists T_2 S_3 != T_2) # label(fact_412_state__not__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 447 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z))) # label(fact_413_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 448 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z))) # label(fact_414_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 449 (all A all B_1 all C hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),C) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C))) # label(fact_415_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 450 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z))) # label(fact_416_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 451 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z))) # label(fact_417_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 452 (all B_1 all A all C hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),C)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C))) # label(fact_418_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 453 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) # label(fact_419_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 454 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) # label(fact_420_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.81 455 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) # label(fact_421_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 456 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1)) # label(fact_422_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 457 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1)) # label(fact_423_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 458 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A)) # label(fact_424_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 459 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),X_1) = X_1) # label(fact_425_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 460 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),A) = A) # label(fact_426_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 461 (all A all B_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),X_1)) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1))))) # label(fact_427_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 462 (all A all B_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),X_1)) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1))))) # label(fact_428_le__supE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 463 (all B_1 all D all A all C (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C),D)))))) # label(fact_429_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 464 (all B_1 all D all A all C (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),D)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C),D)))))) # label(fact_430_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 465 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z)),X_1))))) # label(fact_431_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 466 (all Z all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)),X_1))))) # label(fact_432_sup__least) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 467 (all B_1 all A all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),X_1))))) # label(fact_433_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 468 (all B_1 all A all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),X_1))))) # label(fact_434_le__supI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 469 (all Y_1 all X_1 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = X_1))) # label(fact_435_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 470 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = X_1)) # label(fact_436_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 471 (all X_1 all Y_1 (is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = Y_1))) # label(fact_437_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 472 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = Y_1)) # label(fact_438_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 473 (all A all X_1 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))))) # label(fact_439_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 474 (all A all X_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))))) # label(fact_440_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 475 (all B_1 all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))))) # label(fact_441_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 476 (all B_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))))) # label(fact_442_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 477 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),Z)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),Z)))) # label(fact_443_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 478 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),Z)))) # label(fact_444_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 479 (all X_1 all Y_1 (is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) <-> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = Y_1))) # label(fact_445_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 480 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) <-> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = Y_1)) # label(fact_446_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 481 (all Y_1 all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_447_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 482 (all Y_1 all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_448_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 483 (all Y_1 all X_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_449_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 484 (all Y_1 all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_450_inf__sup__ord_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 485 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_451_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 486 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_452_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 487 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)))) # label(fact_453_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 488 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)))) # label(fact_454_inf__sup__ord_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 489 (all X_1 all Y_1 (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y_1) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = bot_bo844097828e_bool <-> X_1 = bot_bo844097828e_bool & Y_1 = bot_bo844097828e_bool))) # label(fact_455_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 490 (all X_1 all Y_1 (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = bot_bo1055319631e_bool <-> X_1 = bot_bo1055319631e_bool & Y_1 = bot_bo1055319631e_bool)) # label(fact_456_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 491 (all X_1 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),bot_bo844097828e_bool) = X_1)) # label(fact_457_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 492 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),bot_bo1055319631e_bool) = X_1) # label(fact_458_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 493 (all X_1 (is_fun_pname_bool(X_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),X_1) = X_1)) # label(fact_459_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 494 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),X_1) = X_1) # label(fact_460_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 495 (all B all A_1 all F all Fa (is_fun1661590463l_bool(B) & is_fun1661590463l_bool(A_1) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (B != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B))))))))) # label(fact_461_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 496 (all B all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (A_1 != bot_bo1325454745l_bool -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (B != bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B)))))))) # label(fact_462_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 497 (all B all A_1 all F all Fa (is_fun_pname_bool(B) & is_fun_pname_bool(A_1) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (B != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B))))))))) # label(fact_463_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 498 (all B all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (B != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B)))))))) # label(fact_464_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 499 (all B all A_1 all F all Fa (is_fun1661590463l_bool(B) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (B != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,B)),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,A_1))))))) # label(fact_465_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 500 (all B all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (B != bot_bo1325454745l_bool -> (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,B)),hAPP_f772567431e_bool(Fa,A_1)) = hAPP_f772567431e_bool(Fa,A_1)))))) # label(fact_466_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 501 (all B all A_1 all F all Fa (is_fun_pname_bool(B) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (B != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,B)),hAPP_f1297739591_pname(Fa,A_1)) = hAPP_f1297739591_pname(Fa,A_1))))))) # label(fact_467_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 502 (all B all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (B != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,B)),hAPP_f2143211163_state(Fa,A_1)) = hAPP_f2143211163_state(Fa,A_1)))))) # label(fact_468_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 503 (all G_1 all P_1 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),skip),P_1)),bot_bo1055319631e_bool)))) # label(fact_469_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 504 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(A_1) -> (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1))))))) # label(fact_470_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 505 (all X_1 all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)))))) # label(fact_471_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 506 (all X_1 all A_1 all F all Fa (is_fun1661590463l_bool(A_1) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1))))))) # label(fact_472_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 507 (all X_1 all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (A_1 != bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)))))) # label(fact_473_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 508 (all P_1 all Fa (is_fun_pname_bool(Fa) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (Fa != bot_bo844097828e_bool -> ((all X_2 (is_pname(X_2) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool))))) -> ((all X_2 all F_1 (is_pname(X_2) & is_fun_pname_bool(F_1) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (F_1 != bot_bo844097828e_bool -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_1)) -> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)))))))) # label(fact_474_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 509 (all P_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) -> (Fa != bot_bo1055319631e_bool -> ((all X_2 hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) -> ((all X_2 all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (F_1 != bot_bo1055319631e_bool -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,F_1)) -> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_1)))))))) -> hBOOL(hAPP_f1760790145l_bool(P_1,Fa))))))) # label(fact_475_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 510 (all P_1 all Fa (is_fun1661590463l_bool(Fa) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (Fa != bot_bo1649642514l_bool -> ((all X_2 (is_fun_pname_bool(X_2) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),bot_bo1649642514l_bool))))) -> ((all X_2 all F_1 (is_fun_pname_bool(X_2) & is_fun1661590463l_bool(F_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (F_1 != bot_bo1649642514l_bool -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_1)) -> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)))))))) # label(fact_476_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 511 (all P_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) -> (Fa != bot_bo1325454745l_bool -> ((all X_2 hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),bot_bo1325454745l_bool)))) -> ((all X_2 all F_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1)) -> (F_1 != bot_bo1325454745l_bool -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),F_1)) -> (hBOOL(hAPP_f239102607l_bool(P_1,F_1)) -> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),F_1)))))))) -> hBOOL(hAPP_f239102607l_bool(P_1,Fa))))))) # label(fact_477_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 512 (all Pname hAPP_pname_com(body_1,Pname) != skip) # label(fact_478_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 513 (all Pname skip != hAPP_pname_com(body_1,Pname)) # label(fact_479_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 514 (all X_1 all A_1 all F all Fa (hBOOL(finite89670078_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) = hAPP_f1297739591_pname(Fa,A_1))))) # label(fact_481_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 515 (all X_1 all A_1 all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)) = hAPP_f2143211163_state(Fa,A_1))))) # label(fact_482_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 516 (all X_1 all A_1 all F all Fa (hBOOL(finite1268145088e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,A_1))))) # label(fact_483_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 517 (all X_1 all A_1 all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)) = hAPP_f772567431e_bool(Fa,A_1))))) # label(fact_484_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 518 (all N all H all F all Fa (is_fun1661590463l_bool(N) -> (hBOOL(finite1268145088e_bool(F,Fa)) -> ((all X_2 all Y_2 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_2) -> hAPP_f759274231e_bool(H,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f759274231e_bool(H,X_2)),hAPP_f759274231e_bool(H,Y_2)))) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N)) -> (N != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(H,hAPP_f674760225e_bool(Fa,N)) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(image_2063528359e_bool(H),N)))))))) # label(fact_485_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 519 (all N all H all F all Fa (hBOOL(finite959343283e_bool(F,Fa)) -> ((all X_2 all Y_2 hAPP_f921536533e_bool(H,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_2),Y_2)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f921536533e_bool(H,X_2)),hAPP_f921536533e_bool(H,Y_2))) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,N)) -> (N != bot_bo1325454745l_bool -> hAPP_f921536533e_bool(H,hAPP_f772567431e_bool(Fa,N)) = hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(image_505022149e_bool(H),N))))))) # label(fact_486_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 520 (all N all H all F all Fa (is_fun_pname_bool(N) -> (hBOOL(finite89670078_pname(F,Fa)) -> ((all X_2 all Y_2 (is_pname(X_2) & is_pname(Y_2) -> hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H,X_2)),hAPP_pname_pname(H,Y_2)))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N)) -> (N != bot_bo844097828e_bool -> hAPP_pname_pname(H,hAPP_f1297739591_pname(Fa,N)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(image_pname_pname(H),N)))))))) # label(fact_487_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 521 (all N all H all F all Fa (hBOOL(finite506823037_state(F,Fa)) -> ((all X_2 all Y_2 hAPP_H563960305_state(H,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_H563960305_state(H,X_2)),hAPP_H563960305_state(H,Y_2))) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,N)) -> (N != bot_bo1055319631e_bool -> hAPP_H563960305_state(H,hAPP_f2143211163_state(Fa,N)) = hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(image_650584225_state(H),N))))))) # label(fact_488_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 522 (all G_1 all P_1 all B_1 all C hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B_1))),while(B_1,C)),P_1)),bot_bo1055319631e_bool)))) # label(fact_489_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 523 (all D all R_1 all G_1 all P_1 all C all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Q_1),D),R_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),semi(C,D)),R_1)),bot_bo1055319631e_bool)))))) # label(fact_490_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 524 (all X_3 hAPP_f1297739591_pname(the_elem_pname,X_3) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_3)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool)))) # label(fact_491_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 525 (all X_3 hAPP_f2143211163_state(the_el23965208_state,X_3) = hAPP_f2143211163_state(the_Ho10452358_state,hAPP_f1456107715e_bool(cOMBB_1653402815_state(hAPP_f854625363l_bool(fequal1746921144e_bool,X_3)),hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,insert1835143293_state),bot_bo1055319631e_bool)))) # label(fact_492_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 526 (all B_1 all C (hBOOL(hAPP_com_bool(wt,while(B_1,C))) -> hBOOL(hAPP_com_bool(wt,C)))) # label(fact_493_WTs__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 527 (all C1 all C2 (hBOOL(hAPP_com_bool(wt,semi(C1,C2))) -> -(hBOOL(hAPP_com_bool(wt,C1)) -> -hBOOL(hAPP_com_bool(wt,C2))))) # label(fact_494_WTs__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 528 (all Com1_3 all Com2_3 all Fun all Com_1 semi(Com1_3,Com2_3) != while(Fun,Com_1)) # label(fact_495_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 529 (all Fun all Com_1 all Com1_3 all Com2_3 while(Fun,Com_1) != semi(Com1_3,Com2_3)) # label(fact_496_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 530 (all Com1_3 all Com2_3 all Com1_2 all Com2_2 (semi(Com1_3,Com2_3) = semi(Com1_2,Com2_2) <-> Com1_3 = Com1_2 & Com2_3 = Com2_2)) # label(fact_497_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 531 (all Fun_1 all Com_2 all Fun all Com_1 (while(Fun_1,Com_2) = while(Fun,Com_1) <-> Fun_1 = Fun & Com_2 = Com_1)) # label(fact_498_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 532 (all Pname_1 all Fun_1 all Com_2 hAPP_pname_com(body_1,Pname_1) != while(Fun_1,Com_2)) # label(fact_499_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 533 (all Fun_1 all Com_2 all Pname_1 while(Fun_1,Com_2) != hAPP_pname_com(body_1,Pname_1)) # label(fact_500_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 534 (all B_1 all C (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_com_bool(wt,while(B_1,C))))) # label(fact_501_While) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 535 (all Fun all Com_1 skip != while(Fun,Com_1)) # label(fact_502_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 536 (all Fun all Com_1 while(Fun,Com_1) != skip) # label(fact_503_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 537 (all Pname all Com1_1 all Com2_1 hAPP_pname_com(body_1,Pname) != semi(Com1_1,Com2_1)) # label(fact_504_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 538 (all Com1_1 all Com2_1 all Pname semi(Com1_1,Com2_1) != hAPP_pname_com(body_1,Pname)) # label(fact_505_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 539 (all C1 all C0 (hBOOL(hAPP_com_bool(wt,C0)) -> (hBOOL(hAPP_com_bool(wt,C1)) -> hBOOL(hAPP_com_bool(wt,semi(C0,C1)))))) # label(fact_506_WT_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 540 (all Com1 all Com2 skip != semi(Com1,Com2)) # label(fact_507_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 541 (all Com1 all Com2 semi(Com1,Com2) != skip) # label(fact_508_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 542 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (A_1 != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)))))))) # label(fact_509_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 543 (all X_1 all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (A_1 != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1))))))) # label(fact_510_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 544 (all X_1 all A_1 all F all Fa (is_fun1661590463l_bool(A_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) -> (A_1 != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)))))))) # label(fact_511_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 545 (all X_1 all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) -> (A_1 != bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1))))))) # label(fact_512_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 546 (all X_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1))) # label(fact_513_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 547 (all X_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = X_1)) # label(fact_514_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 548 (all A_1 all F all Fa (is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> ((all X_2 all Y_2 (is_pname(X_2) & is_pname(Y_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(Fa,A_1)),A_1)))))))) # label(fact_515_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 549 (all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> ((all X_2 all Y_2 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(Fa,A_1)),A_1))))))) # label(fact_516_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 550 (all A_1 all F all Fa (is_fun1661590463l_bool(A_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> ((all X_2 all Y_2 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_2) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_2),bot_bo1649642514l_bool)))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f674760225e_bool(Fa,A_1)),A_1)))))))) # label(fact_517_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 551 (all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (A_1 != bot_bo1325454745l_bool -> ((all X_2 all Y_2 hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_2),Y_2)),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,Y_2),bot_bo1325454745l_bool))))) -> hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f772567431e_bool(Fa,A_1)),A_1))))))) # label(fact_518_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 552 (all Y_1 -(all Fun1 all Com all Fun2 Y_1 != hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2))) # label(fact_519_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 553 (all F all G all M all N (M = N -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),N)) -> hAPP_p1842370726_state(F,X_2) = hAPP_p1842370726_state(G,X_2)))) -> hAPP_f631639356e_bool(image_275883510_state(F),M) = hAPP_f631639356e_bool(image_275883510_state(G),N)))) # label(fact_520_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 554 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1))))) # label(fact_521_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 555 (all Q_1 all P_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))))) # label(fact_522_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 556 (all Q_1 all P_1 ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) -> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))) # label(fact_523_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 557 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_f1760790145l_bool(P_1,X_2)) -> hBOOL(hAPP_f1760790145l_bool(Q_1,X_2)))) -> hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))))) # label(fact_524_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 558 (all Q_1 all P_1 ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)))) # label(fact_525_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 559 (all Q_1 all P_1 ((all X_2 (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_2)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1)))) # label(fact_526_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 560 (all A all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> (exists B_2 (is_fun_pname_bool(B_2) & A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B_2))))))) # label(fact_527_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 561 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> (exists B_2 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_2) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_2)))))) # label(fact_528_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 562 (all X_1 all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> -(all B_2 (is_fun_pname_bool(B_2) -> (A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_2)))))))) # label(fact_529_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 563 (all X_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> -(all B_2 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B_2) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_2)))))) # label(fact_530_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 564 (all A_1 (is_fun_pname_bool(A_1) -> ((all Y_2 (is_pname(Y_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_2),A_1)))) -> A_1 = bot_bo844097828e_bool))) # label(fact_531_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 565 (all A_1 ((all Y_2 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_2),A_1))) -> A_1 = bot_bo1055319631e_bool)) # label(fact_532_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 566 (all G_1 all C (hBOOL(hoare_298929751gleton) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))))) # label(fact_533_MGT__alternD) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 567 (all G_1 all C (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo1055319631e_bool))))) # label(fact_534_MGT__alternI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 568 (all C hAPP_c1546227244_state(hoare_Mirabelle_MGT,C) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,fequal_state),C),evalc(C))) # label(fact_535_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 569 (all Pn all S0 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn))),S0),S1_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,Pn)),S0),S1_1)))) # label(fact_536_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 570 (all P all S_2 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,P)),S_2),S1_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,P))),S_2),S1_1)))) # label(fact_537_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 571 (all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),T_1)) -> T_1 = S_2)) # label(fact_538_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 572 (all C all B_1 all S_1 (-hBOOL(hAPP_state_bool(B_1,S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),S_1)))) # label(fact_539_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 573 (all S2_1 all C all S1_2 all B_1 all S0_1 (hBOOL(hAPP_state_bool(B_1,S0_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0_1),S1_2)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1_2),S2_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S0_1),S2_1)))))) # label(fact_540_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 574 (all C1 all S2 all C0 all S0 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0),S1_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1_1),S2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0,C1)),S0),S2))))) # label(fact_541_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 575 (all S_2 hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),S_2))) # label(fact_542_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 576 (all U all C_2 all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),U)) -> U = T_1))) # label(fact_543_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 577 (all C1 all C2 all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1,C2)),S_2),T_1)) -> -(all S1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_2),S1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1),T_1)))))) # label(fact_544_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 578 (all B_1 all C all S_1 all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),T)) -> ((T = S_1 -> hBOOL(hAPP_state_bool(B_1,S_1))) -> -(hBOOL(hAPP_state_bool(B_1,S_1)) -> (all S1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S_1),S1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1),T)))))))) # label(fact_545_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 579 (all C all A all F all B_1 (A = hAPP_f759274231e_bool(F,B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1)) -> ((all X_2 all Y_2 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,C)),A)))))) # label(fact_546_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 580 (all C all A all F all B_1 (A = hAPP_f921536533e_bool(F,B_1) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_2)),hAPP_f921536533e_bool(F,X_2))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,C)),A)))))) # label(fact_547_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 581 (all F all C all B_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A)) -> (hAPP_f759274231e_bool(F,B_1) = C -> ((all X_2 all Y_2 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),hAPP_f759274231e_bool(F,A))))))) # label(fact_548_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 582 (all F all C all B_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A)) -> (hAPP_f921536533e_bool(F,B_1) = C -> ((all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_2)),hAPP_f921536533e_bool(F,X_2))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),hAPP_f921536533e_bool(F,A))))))) # label(fact_549_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 583 (all B all A_1 all F all Fa (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B))),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B))))))) # label(fact_550_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 584 (all B all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) != bot_bo1325454745l_bool -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B))),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B))) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B))))))) # label(fact_551_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 585 (all B all A_1 all F all Fa (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) != bot_bo844097828e_bool -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B))))))) # label(fact_552_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 586 (all B all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) != bot_bo1055319631e_bool -> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B))))))) # label(fact_553_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 587 (all B all A_1 all F all Fa (is_fun1661590463l_bool(B) & is_fun1661590463l_bool(A_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (B != bot_bo1649642514l_bool -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)))))))))) # label(fact_554_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 588 (all B all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (A_1 != bot_bo1325454745l_bool -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) -> (B != bot_bo1325454745l_bool -> (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) = bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B))))))))) # label(fact_555_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 589 (all B all A_1 all F all Fa (is_fun_pname_bool(B) & is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (B != bot_bo844097828e_bool -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)))))))))) # label(fact_556_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 590 (all B all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) -> (B != bot_bo1055319631e_bool -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B))))))))) # label(fact_557_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 591 (all B all C all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))))) # label(fact_558_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 592 (all B all C all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))))) # label(fact_559_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 593 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_560_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 594 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_561_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 595 (all G_1 all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,Fa),G_1))))) # label(fact_562_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 596 (all G_1 all Fa (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa)) | hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,Fa),G_1))))) # label(fact_563_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 597 (all G_1 all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Fa),G_1))))) # label(fact_564_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 598 (all G_1 all Fa (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa)) | hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Fa),G_1))))) # label(fact_565_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 599 (all A_1 all B (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = bot_bo844097828e_bool <-> (all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (all Xa (is_pname(Xa) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B)) -> X_2 != Xa)))))))) # label(fact_566_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 600 (all A_1 all B (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = bot_bo1055319631e_bool <-> (all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (all Xa (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Xa),B)) -> X_2 != Xa)))))) # label(fact_567_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 601 (all A_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),bot_bo844097828e_bool) = bot_bo844097828e_bool) # label(fact_568_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 602 (all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),bot_bo1055319631e_bool) = bot_bo1055319631e_bool) # label(fact_569_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 603 (all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),B) = bot_bo844097828e_bool) # label(fact_570_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 604 (all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),B) = bot_bo1055319631e_bool) # label(fact_571_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 605 (all A_1 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) # label(fact_572_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 606 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B)))) # label(fact_573_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 607 (all A_1 all B hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) # label(fact_574_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 608 (all A_1 all B hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B)))) # label(fact_575_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 609 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_576_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 610 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) & hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)))) # label(fact_577_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 611 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)))) # label(fact_578_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 612 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)))) # label(fact_579_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 613 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)))) # label(fact_580_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 614 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)))) # label(fact_581_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 615 (all P_1 all Q_1 hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),P_1)),Q_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1))) # label(fact_582_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 616 (all P_1 all Q_1 hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))) # label(fact_583_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 617 (all P_1 all Q_1 hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) # label(fact_584_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 618 (all P_1 all Q_1 hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),P_1)),Q_1)) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) # label(fact_585_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 619 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,P_1)))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) & hBOOL(hAPP_pname_bool(P_1,X_1)))) # label(fact_586_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 620 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(collec727977250_state,P_1)))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) & hBOOL(hAPP_H513860823e_bool(P_1,X_1)))) # label(fact_587_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 621 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)))) <-> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) & hBOOL(hAPP_f1664156314l_bool(P_1,X_1)))) # label(fact_588_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 622 (all X_1 all A_1 all P_1 (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),hAPP_f1970439265l_bool(collec111528142e_bool,P_1)))) <-> hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) & hBOOL(hAPP_f1760790145l_bool(P_1,X_1)))) # label(fact_589_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 623 (all R_1 all S all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,R_1),S))))) # label(fact_590_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.82 624 (all R_1 all S all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S)),X_2)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,R_1),S))))) # label(fact_591_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 625 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A_1))) # label(fact_592_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 626 (all B all C_1 all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A_1))) # label(fact_593_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 627 (all B all C_1 all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),A_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),A_1))) # label(fact_594_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 628 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C_1))) # label(fact_595_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 629 (all A_1 all B all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),C_1))) # label(fact_596_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 630 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),D_1)))))) # label(fact_597_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 631 (all B all D_1 all A_1 all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),D_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),D_1)))))) # label(fact_598_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 632 (all B all C_1 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))))) # label(fact_599_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 633 (all B all C_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))))) # label(fact_600_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 634 (all B all A_1 (is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = B))) # label(fact_601_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 635 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = B)) # label(fact_602_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 636 (all A_1 all B (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = A_1))) # label(fact_603_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 637 (all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = A_1)) # label(fact_604_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 638 (all A_1 all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),B))) # label(fact_605_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 639 (all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),B))) # label(fact_606_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 640 (all A_1 all B hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),A_1))) # label(fact_607_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 641 (all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),A_1))) # label(fact_608_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 642 (all B all A all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)))) # label(fact_609_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 643 (all B all A all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)))) # label(fact_610_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 644 (all B all A all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))) # label(fact_611_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 645 (all B all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))) # label(fact_612_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 646 (all B all A all C_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))) # label(fact_613_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 647 (all B all A all C_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1))) # label(fact_614_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 648 (all B all A all A_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) # label(fact_615_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 649 (all B all A all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) # label(fact_616_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 650 (all A all A_1 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) # label(fact_617_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 651 (all A all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) # label(fact_618_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 652 (all B all A all C_1 ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)))) # label(fact_619_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 653 (all B all A all C_1 ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)))) # label(fact_620_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 654 (all B all A all A_1 ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))) # label(fact_621_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 655 (all B all A all A_1 ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))) # label(fact_622_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 656 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1))) # label(fact_623_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 657 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),X_1))) # label(fact_624_inf__sup__ord_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 658 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1))) # label(fact_625_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 659 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),X_1))) # label(fact_626_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 660 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1))) # label(fact_627_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 661 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),Y_1))) # label(fact_628_inf__sup__ord_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 662 (all X_1 all Y_1 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1))) # label(fact_629_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 663 (all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),Y_1))) # label(fact_630_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 664 (all X_1 all Y_1 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) <-> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = X_1))) # label(fact_631_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 665 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) <-> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = X_1)) # label(fact_632_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 666 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)))) # label(fact_633_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 667 (all X_1 all Y_1 all Z (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)))) # label(fact_634_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 668 (all B_1 all A all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),X_1)))) # label(fact_635_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 669 (all B_1 all A all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),X_1)))) # label(fact_636_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 670 (all A all B_1 all X_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),X_1)))) # label(fact_637_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 671 (all A all B_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),X_1)))) # label(fact_638_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 672 (all X_1 all Y_1 (is_fun_pname_bool(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = X_1))) # label(fact_639_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 673 (all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = X_1)) # label(fact_640_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 674 (all Y_1 all X_1 (is_fun_pname_bool(Y_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = Y_1))) # label(fact_641_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 675 (all Y_1 all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = Y_1)) # label(fact_642_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 676 (all B_1 all X_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)))))) # label(fact_643_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 677 (all B_1 all X_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)))))) # label(fact_644_le__infI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 678 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z)))))) # label(fact_645_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 679 (all Z all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)))))) # label(fact_646_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 680 (all B_1 all D all A all C (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C),D)))))) # label(fact_647_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 681 (all B_1 all D all A all C (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),D)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C),D)))))) # label(fact_648_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 682 (all X_1 all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1))))) # label(fact_649_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 683 (all X_1 all A all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1))) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1))))) # label(fact_650_le__infE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 684 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = X_1) # label(fact_651_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 685 (all X_1 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)) = X_1) # label(fact_652_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 686 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z))) # label(fact_653_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 687 (all X_1 all Y_1 all Z hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z))) # label(fact_654_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 688 (all Y_1 all Z all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)),X_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),X_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Z),X_1))) # label(fact_655_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 689 (all Y_1 all Z all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)),X_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Z),X_1))) # label(fact_656_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 690 (all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),bot_bo844097828e_bool) = bot_bo844097828e_bool) # label(fact_657_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 691 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),bot_bo1055319631e_bool) = bot_bo1055319631e_bool) # label(fact_658_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 692 (all X_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),X_1) = bot_bo844097828e_bool) # label(fact_659_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 693 (all X_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),X_1) = bot_bo1055319631e_bool) # label(fact_660_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 694 (all X_1 all Y_1 all Z hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z))))) # label(fact_661_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 695 (all X_1 all Y_1 all Z hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z))))) # label(fact_662_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 696 (all X_1 all Y_1 all Z hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z))))) # label(fact_663_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 697 (all X_1 all Y_1 all Z hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z))))) # label(fact_664_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 698 (all F all A_1 all B hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B))))) # label(fact_665_image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 699 (all A_1 all B all C_1 (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1)))) # label(fact_666_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 700 (all A_1 all B all C_1 (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),A_1)))) # label(fact_667_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 701 (all P_1 all F all G all S hAPP_f631639356e_bool(image_275883510_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,hAPP_f1405979047_state(cOMBB_707293872_pname(if_Hoa533980679_state),P_1)),F)),G)),S) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,P_1)))),hAPP_f631639356e_bool(image_275883510_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1)))))) # label(fact_668_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 702 (all P_1 all F all G dom_pname_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,hAPP_f755519727on_com(cOMBB_1394247784_pname(if_option_com),P_1)),F)),G)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(G)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1))))) # label(fact_669_dom__if) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 703 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) -> ((all X_2 (is_pname(X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (hBOOL(hAPP_pname_bool(P_1,X_2)) -> hBOOL(hAPP_pname_bool(Q_1,X_2)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),hAPP_f759274231e_bool(collect_pname,Q_1))))))) # label(fact_670_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 704 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) -> ((all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (hBOOL(hAPP_H513860823e_bool(P_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(Q_1,X_2))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(collec727977250_state,P_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),hAPP_f921536533e_bool(collec727977250_state,Q_1))))))) # label(fact_671_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 705 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B)) -> ((all X_2 (is_fun_pname_bool(X_2) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) -> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2)))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,B),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))))))) # label(fact_672_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 706 (all Q_1 all P_1 all A_1 all B (hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B)) -> ((all X_2 (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(P_1,X_2)) -> hBOOL(hAPP_f1760790145l_bool(Q_1,X_2))))) -> hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),hAPP_f1970439265l_bool(collec111528142e_bool,P_1))),hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,B),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))))))) # label(fact_673_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 707 (all X_1 all Y_1 all Z ((all X_2 all Y_2 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_2),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),Z_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)))) # label(fact_674_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 708 (all X_1 all Y_1 all Z ((all X_2 all Y_2 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_2),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z)))) # label(fact_675_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 709 (all X_1 all A_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,A_1) = X_1) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,A_1) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))))))))) # label(fact_676_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 710 (all X_1 all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,A_1) = X_1) & (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool))))))))) # label(fact_677_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 711 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(X_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1)) -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,A_1) = X_1) & (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))))))))) # label(fact_678_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 712 (all X_1 all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1)) -> (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) = bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,A_1) = X_1) & (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) != bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool))))))))) # label(fact_679_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 713 (all X_1 all A_1 all F all Fa (is_pname(X_1) -> (hBOOL(finite1282449217_pname(F,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = X_1) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))))))) # label(fact_680_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 714 (all X_1 all A_1 all F all Fa (hBOOL(finite774711482_state(F,Fa)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = X_1) & (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool -> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))))))) # label(fact_681_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 715 (all X_1 all A_1 all F all Fa (is_fun_pname_bool(X_1) -> (hBOOL(finite1626890877e_bool(F,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = X_1) & (hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool))))))))) # label(fact_682_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 716 (all X_1 all A_1 all F all Fa (hBOOL(finite132673334e_bool(F,Fa)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) = bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = X_1) & (hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) != bot_bo1325454745l_bool -> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)))))))) # label(fact_683_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 717 (all B all C all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B)))))) # label(fact_684_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 718 (all B all C all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B)))))) # label(fact_685_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 719 (all C all A_1 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))))) # label(fact_686_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 720 (all C all A_1 all B (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B))) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))))) # label(fact_687_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 721 (all B all A_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),B))))) # label(fact_688_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 722 (all B all A_1 (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) -> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),B))))) # label(fact_689_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 723 (all B all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B))))) # label(fact_690_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 724 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B))))) # label(fact_691_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 725 (all A all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) = A_1))) # label(fact_692_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 726 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = A_1)) # label(fact_693_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 727 (all X_1 all A_1 (is_fun_pname_bool(A_1) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A_1))) # label(fact_694_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 728 (all X_1 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = A_1)) # label(fact_695_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 729 (all A all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)) # label(fact_696_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 730 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)) # label(fact_697_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 731 (all A_1 all A all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))),B)) # label(fact_698_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 732 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 733 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 734 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 735 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 736 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 737 (all Q all P (-hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 738 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 739 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 740 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 741 (all Q all P (hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 742 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 743 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 744 (all X all P (-hBOOL(hAPP_f327114704l_bool(fAll_state,P)) | hBOOL(hAPP_state_bool(P,X)))) # label(help_fAll_1_1_fAll_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 745 (all X all Y (is_pname(X) & is_pname(Y) -> -hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 746 (all X all Y (X != Y | hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 747 (all X all Y (-hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 748 (all X all Y (X != Y | hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 749 (all P all Q (is_bool(P) -> hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 750 (all X all Y hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 751 (all X all Y hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 752 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 753 (all X all Y (is_fun_pname_bool(X) & is_fun_pname_bool(Y) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 754 (all X all Y (X != Y | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 755 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(cOMBB_647938656_pname(P),Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 756 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 757 (all P all Q all R hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 758 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,P),Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 759 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 760 (all P all Q all R hAPP_pname_bool(hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 761 (all P all Q all R hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 762 (all P all Q (is_bool(P) -> hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 763 (all P all Q hAPP_s1806633685e_bool(cOMBK_631994958_state(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 764 (all X all Y hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fTrue),X),Y) = X) # label(help_If_1_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 765 (all X all Y hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fFalse),X),Y) = Y) # label(help_If_2_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 766 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 767 (all X all Y (-hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 768 (all X all Y (X != Y | hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 769 (all P all Q all R hAPP_pname_com(hAPP_f96342628me_com(cOMBB_923936821_pname(P),Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 770 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBB_307249310e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 771 (all P all Q all R hAPP_p393069232l_bool(hAPP_f1402196763l_bool(cOMBB_675860798_pname(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 772 (all P all Q all R hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 773 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 774 (all P all Q all R hAPP_pname_bool(hAPP_f42430548e_bool(cOMBB_530759491_pname(P),Q),R) = hAPP_f1664156314l_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 775 (all P all Q all R hAPP_state_bool(hAPP_f1012183542e_bool(cOMBB_1911358915_state(P),Q),R) = hAPP_f327114704l_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 776 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 777 (all P all Q all R hAPP_s1806633685e_bool(hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_s1874344717e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__fun_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 778 (all P all Q all R hAPP_f1664156314l_bool(hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 779 (all P all Q all R hAPP_p61793385e_bool(hAPP_f1336811455e_bool(cOMBB_542850580_pname(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 780 (all P all Q (is_bool(P) -> hAPP_H513860823e_bool(cOMBK_1079618832_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 781 (all P all Q (is_pname(P) -> hAPP_H1344248906_pname(cOMBK_588224941_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 782 (all P all Q hAPP_p1842370726_state(cOMBK_90103121_pname(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 783 (all X all Y (-hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 784 (all X all Y (X != Y | hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 785 (all P all Q all R hAPP_p799580910on_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,P),Q),R) = hAPP_o356497025on_com(hAPP_p1086945780on_com(P,R),hAPP_p799580910on_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 786 (all P all Q all R hAPP_p1842370726_state(hAPP_f1758910594_state(cOMBB_422605457_pname(P),Q),R) = hAPP_c1546227244_state(P,hAPP_pname_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 787 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBB_416661851_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 788 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 789 (all P all Q all R hAPP_pname_bool(hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_p877885514e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 790 (all P all Q all R hAPP_H513860823e_bool(hAPP_p877885514e_bool(hAPP_f294904177e_bool(cOMBC_725526061e_bool,P),Q),R) = hAPP_pname_bool(hAPP_H1632039476e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 791 (all P all Q all R hAPP_f1476298914l_bool(hAPP_f143162813l_bool(cOMBB_2095475776e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 792 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 793 (all P all Q all R hAPP_f759274231e_bool(hAPP_f1385420507e_bool(cOMBB_598082538e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_012) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 794 (all P all Q all R hAPP_p61793385e_bool(hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_013) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 795 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_s1226857760e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 796 (all P all Q (is_bool(P) -> hAPP_f1760790145l_bool(cOMBK_564432736e_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 797 (all P all Q all R hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(cOMBB_1957242197e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1760790145l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 798 (all P all Q all R hAPP_H226398757l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_014) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 799 (all P all Q all R hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1508101115l_bool(P,R),hAPP_f1760790145l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 800 (all P all Q all R hAPP_pname_bool(hAPP_f1745235422e_bool(hAPP_f1558052123e_bool(cOMBC_2140141647l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_p1617973726l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____dd) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 801 (all P all Q all R hAPP_H513860823e_bool(hAPP_f631639356e_bool(hAPP_f1721106985e_bool(cOMBC_498627897l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_H737849090l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___015) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 802 (all P all Q all R hAPP_f1664156314l_bool(hAPP_H737849090l_bool(hAPP_f261382953l_bool(cOMBC_2107548985e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_f631639356e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 803 (all P all Q all R hAPP_f1760790145l_bool(hAPP_p1617973726l_bool(hAPP_f2070658331l_bool(cOMBC_367297061e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f1745235422e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 804 (all P all Q all R hAPP_H1632039476e_bool(hAPP_f833390165e_bool(cOMBB_1456120487_state(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_H1344248906_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_016) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 805 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_017) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 806 (all P all Q all R hAPP_p338031245l_bool(hAPP_f567934427l_bool(cOMBB_408569982_pname(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 807 (all P all Q all R hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(cOMBB_1759179140_state(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 808 (all P all Q all R hAPP_s336103912e_bool(hAPP_f249262236e_bool(cOMBB_1476898461_state(P),Q),R) = hAPP_f1863945078e_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_018) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 809 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f1935169308e_bool(cOMBB_1036740637_state(P),Q),R) = hAPP_f1012183542e_bool(P,hAPP_s336103912e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 810 (all P all Q all R hAPP_p1086945780on_com(hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,P),Q),R) = hAPP_o334540577on_com(hAPP_p1164893188on_com(P,R),hAPP_p799580910on_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J__019) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 811 (all P all Q all R hAPP_H513860823e_bool(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___020) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 812 (all P all Q all R hAPP_p1842370726_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,P),Q),R) = hAPP_H563960305_state(hAPP_p80247908_state(P,R),hAPP_p1842370726_state(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 813 (all P all Q all R hAPP_f1508101115l_bool(hAPP_f482022705l_bool(cOMBB_2020112947e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1760790145l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_021) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 814 (all P all Q all R hAPP_f1745235422e_bool(hAPP_f1973135743e_bool(cOMBB_1671808265e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1008690464_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_022) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 815 (all P all Q all R hAPP_p1842370726_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,P),Q),R) = hAPP_f588507005_state(hAPP_p1712839024_state(P,R),hAPP_p1637813682e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 816 (all P all Q all R hAPP_f1935102916l_bool(hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 817 (all P all Q all R hAPP_s1874344717e_bool(hAPP_f873506917e_bool(cOMBB_1757942702_state(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_s2001034685l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 818 (all P all Q all R hAPP_p1164893188on_com(hAPP_f755519727on_com(cOMBB_1394247784_pname(P),Q),R) = hAPP_b1679505845on_com(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Option__Ooption_Itc__Com_) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 819 (all P all Q all R hAPP_H513860823e_bool(hAPP_f1456107715e_bool(cOMBB_1653402815_state(P),Q),R) = hAPP_f1760790145l_bool(P,hAPP_H1645666623e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 820 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___023) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 821 (all P all Q all R hAPP_f1760790145l_bool(hAPP_H248360617l_bool(hAPP_f492098723l_bool(cOMBC_1305755390e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_f921536533e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_024) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 822 (all P all Q all R hAPP_p877885514e_bool(hAPP_f998786331e_bool(cOMBB_799949246_pname(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_p1842370726_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 823 (all P all Q all R hAPP_H737849090l_bool(hAPP_f376825399l_bool(cOMBB_1722165949_state(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_H1632039476e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 824 (all P all Q all R hAPP_p1712839024_state(hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,P),Q),R) = hAPP_c408625258_state(hAPP_p2032835427_state(P,R),hAPP_pname_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 825 (all P all Q all R hAPP_s1226857760e_bool(hAPP_f1138284024e_bool(cOMBB_20296667_state(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_s2001034685l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_026) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.83 826 (all P all Q all R hAPP_f1760790145l_bool(hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_f854625363l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_027) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 827 (all P all Q all R hAPP_f631639356e_bool(hAPP_f547518321e_bool(cOMBB_1170234304e_bool(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_f1308959284_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___028) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 828 (all P all Q all R hAPP_H1645666623e_bool(hAPP_f1844318385e_bool(cOMBB_291471741_state(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_H563960305_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___029) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 829 (all P all Q all R hAPP_p80247908_state(hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,P),Q),R) = hAPP_H521649881_state(hAPP_p964374716_state(P,R),hAPP_p1842370726_state(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__030) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 830 (all P all Q all R hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,P),Q),R) = hAPP_f239102607l_bool(hAPP_f105100493l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_031) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 831 (all P all Q all R hAPP_p1617973726l_bool(hAPP_f2081555625l_bool(cOMBB_44445098_pname(P),Q),R) = hAPP_f854625363l_bool(P,hAPP_p877885514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_032) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 832 (all P all Q all R hAPP_f921536533e_bool(hAPP_f481659057e_bool(cOMBB_1099197107e_bool(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_f2143211163_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___033) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 833 (all P all Q all R hAPP_H1645666623e_bool(hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___034) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 834 (all P all Q all R hAPP_p964374716_state(hAPP_f1405979047_state(cOMBB_707293872_pname(P),Q),R) = hAPP_b798484845_state(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 835 (all P all Q all R hAPP_f239102607l_bool(hAPP_f1269496639l_bool(hAPP_f1508257257l_bool(cOMBC_1084925030l_bool,P),Q),R) = hAPP_f239102607l_bool(hAPP_f1269496639l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 836 (all P all Q all R hAPP_p2032835427_state(hAPP_f950918952_state(cOMBB_2123334001_pname(P),Q),R) = hAPP_f1949912908_state(P,hAPP_p1637813682e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___035) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86 837 (all P all Q all R hAPP_H248360617l_bool(hAPP_f1862834069l_bool(cOMBB_1239130257_state(P),Q),R) = hAPP_f854625363l_bool(P,hAPP_H1645666623e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_036) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.86
% 1.42/1.86 ============================== end of process non-clausal formulas ===
% 1.42/1.86
% 1.42/1.86 ============================== PROCESS INITIAL CLAUSES ===============
% 1.42/1.86
% 1.42/1.86 ============================== PREDICATE ELIMINATION =================
% 1.42/1.86 838 -is_option_pname(A) | is_fun_pname_bool(set_pname(A)) # label(gsy_c_Option_Oset_000tc__Com__Opname) # label(axiom). [clausify(13)].
% 1.42/1.86 839 -is_pname(A) | is_option_pname(some_pname(A)) # label(gsy_c_Option_Ooption_OSome_000tc__Com__Opname) # label(axiom). [clausify(12)].
% 1.42/1.86 Derived: is_fun_pname_bool(set_pname(some_pname(A))) | -is_pname(A). [resolve(838,a,839,b)].
% 1.42/1.86 840 -is_option_pname(A) | -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(A))) | some_pname(B) = A # label(fact_405_elem__set) # label(axiom). [clausify(439)].
% 2.20/2.50 Derived: -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),set_pname(some_pname(B)))) | some_pname(A) = some_pname(B) | -is_pname(B). [resolve(840,a,839,b)].
% 2.20/2.50 841 -is_option_pname(A) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),set_pname(A))) | some_pname(B) != A # label(fact_405_elem__set) # label(axiom). [clausify(439)].
% 2.20/2.50 Derived: hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),set_pname(some_pname(B)))) | some_pname(A) != some_pname(B) | -is_pname(B). [resolve(841,a,839,b)].
% 2.20/2.50
% 2.20/2.50 ============================== end predicate elimination =============
% 2.20/2.50
% 2.20/2.50 Auto_denials: (non-Horn, no changes).
% 2.20/2.50
% 2.20/2.50 Term ordering decisions:
% 2.20/2.50 Function symbol KB weights: ord_le313189616e_bool=1. ord_le1720872323e_bool=1. bot_bo1055319631e_bool=1. member1758697444_state=1. semila447562797e_bool=1. insert1835143293_state=1. bot_bo844097828e_bool=1. member_pname=1. finite_finite_pname=1. insert_pname=1. finite595471783e_bool=1. finite784854244_state=1. semila2145357127e_bool=1. finite899049100e_bool=1. semila1635148844e_bool=1. bot_bo1649642514l_bool=1. semila278973382e_bool=1. collect_pname=1. hoare_1575745797_state=1. collec1974731493e_bool=1. bot_bo1325454745l_bool=1. collec727977250_state=1. collec111528142e_bool=1. fconj=1. insert1325755072e_bool=1. insert1991711667e_bool=1. ord_le675606854l_bool=1. fdisj=1. member799430823e_bool=1. ord_le1076702565l_bool=1. member402455436e_bool=1. cOMBC_1058051404l_bool=1. cOMBC_764456866l_bool=1. body_1=1. cOMBS_1248383340l_bool=1. cOMBS_568398431l_bool=1. cOMBS_2138645332l_bool=1. cOMBS_350070575l_bool=1. semila1130628874l_bool=1. wt=1. body=1. hoare_Mirabelle_MGT=1. fequal1531560888_state=1. fequal_pname=1. semila1410775201l_bool=1. cOMBS_1401555724_state=1. cOMBS_1615712031_state=1. fequal1746921144e_bool=1. fequal533582459e_bool=1. minus_2076558538e_bool=1. minus_1015773161e_bool=1. the_com=1. fFalse=1. ord_less_eq_bool=1. semila1782091504l_bool=1. semila2055205435l_bool=1. bot_bot_bool=1. cOMBC_1018307482l_bool=1. cOMBC_1149511130e_bool=1. cOMBC_1166591542l_bool=1. cOMBC_1284144636l_bool=1. cOMBC_1424981238e_bool=1. cOMBC_1988546018l_bool=1. fimplies=1. fNot=1. fequal_state=1. hoare_298929751gleton=1. minus_1290075917l_bool=1. minus_164259166l_bool=1. fTrue=1. cOMBC_952831051e_bool=1. cOMBS_1378840469l_bool=1. semila1168014441p_bool=1. skip=1. wT_bodies=1. bool=1. cOMBC_231445413l_bool=1. cOMBC_471052088e_bool=1. fAll_state=1. fa=1. if_Hoa533980679_state=1. if_option_com=1. member_com=1. pname=1. cOMBC_1004116266e_bool=1. cOMBC_1084925030l_bool=1. cOMBC_1123258281e_bool=1. cOMBC_1305755390e_bool=1. cOMBC_2027030106e_bool=1. cOMBC_2107548985e_bool=1. cOMBC_2140141647l_bool=1. cOMBC_290948233e_bool=1. cOMBC_367297061e_bool=1. cOMBC_488258100e_bool=1. cOMBC_498627897l_bool=1. cOMBC_725526061e_bool=1. cOMBC_7971162l_bool=1. cOMBS_1529518335on_com=1. cOMBS_381334199_state=1. cOMBS_843273363_state=1. cOMBS_904531235on_com=1. pn=1. the_el23965208_state=1. the_elem_pname=1. bot_bot_fun_com_bool=1. collec1277803610l_bool=1. collec1613912337l_bool=1. finite1586217244l_bool=1. finite786885583l_bool=1. insert_com=1. the_Ho10452358_state=1. the_pname=1. y=1. c1=1. c2=1. hAPP_f1760790145l_bool=1. hAPP_f921536533e_bool=1. hAPP_f1664156314l_bool=1. hAPP_f759274231e_bool=1. hAPP_f1583986009e_bool=1. hAPP_f434788991l_bool=1. hAPP_f854625363l_bool=1. hAPP_f1935102916l_bool=1. hAPP_f1388330588e_bool=1. hAPP_H727730819e_bool=1. hAPP_f239102607l_bool=1. hAPP_H248360617l_bool=1. hAPP_f559147733l_bool=1. hAPP_p338031245l_bool=1. hAPP_f1970439265l_bool=1. hAPP_p905327722e_bool=1. hAPP_H513860823e_bool=1. hAPP_f631639356e_bool=1. hAPP_pname_bool=1. hAPP_state_bool=1. hAPP_s1806633685e_bool=1. hAPP_c408625258_state=1. hAPP_f1949912908_state=1. hAPP_f588507005_state=1. hAPP_f674760225e_bool=1. hAPP_f1297739591_pname=1. hAPP_f1745235422e_bool=1. hAPP_bool_bool=1. hAPP_f1320879424l_bool=1. hAPP_f772567431e_bool=1. hAPP_f230953622l_bool=1. hAPP_f510955609l_bool=1. hAPP_f2143211163_state=1. hAPP_f1587382801l_bool=1. hAPP_f601642911l_bool=1. hAPP_f1269496639l_bool=1. hAPP_b589554111l_bool=1. hAPP_p61793385e_bool=1. hAPP_H1645666623e_bool=1. hAPP_f1262649863e_bool=1. hAPP_f661147897e_bool=1. hAPP_H563960305_state=1. hAPP_com_bool=1. hAPP_f556039215l_bool=1. hAPP_pname_pname=1. hAPP_f1402196763l_bool=1. hAPP_f1558728829l_bool=1. hAPP_f649174806e_bool=1. hAPP_f760664097e_bool=1. hAPP_f105100493l_bool=1. hAPP_f143162813l_bool=1. hAPP_f1850463605l_bool=1. hAPP_f482022705l_bool=1. hAPP_f624840228l_bool=1. hAPP_p1842370726_state=1. hAPP_pname_com=1. while=1. hAPP_H521649881_state=1. hAPP_f1296386871_state=1. hAPP_f1777033564_state=1. hAPP_f2136041130_state=1. hAPP_f358330902_state=1. hAPP_f950918952_state=1. hAPP_p799580910on_com=1. hAPP_c1546227244_state=1. hAPP_p1170154830_pname=1. semi=1. finite1282449217_pname=1. finite1626890877e_bool=1. hAPP_H1344248906_pname=1. finite774711482_state=1. hAPP_f1874607724l_bool=1. hAPP_f780887186e_bool=1. finite132673334e_bool=1. hAPP_f1145991873l_bool=1. hAPP_f1297925993l_bool=1. hAPP_f2119687429l_bool=1. hAPP_f22061361e_bool=1. hAPP_f262880489e_bool=1. hAPP_f280588268e_bool=1. hAPP_f517001763l_bool=1. hAPP_f748867288l_bool=1. finite1268145088e_bool=1. finite89670078_pname=1. hAPP_p1637813682e_bool=1. hAPP_H1632039476e_bool=1. hAPP_option_com_com=1. finite506823037_state=1. finite959343283e_bool=1. hAPP_f1283379615l_bool=1. hAPP_f1758910594_state=1. hAPP_f96342628me_com=1. hAPP_p877885514e_bool=1. hAPP_H737849090l_bool=1. hAPP_f1138284024e_bool=1. hAPP_f1759915619e_bool=1. hAPP_f915354021e_bool=1. hAPP_f990396704l_bool=1. hAPP_p1617973726l_bool=1. fun=1. hAPP_b1095269219e_bool=1. hAPP_b1679505845on_com=1. hAPP_b798484845_state=1. hAPP_c667411853l_bool=1. hAPP_f1008690464_pname=1. hAPP_f1863945078e_bool=1. hAPP_f1935169308e_bool=1. hAPP_f249262236e_bool=1. hAPP_f327114704l_bool=1. hAPP_f42430548e_bool=1. hAPP_f701449317e_bool=1. hAPP_f873506917e_bool=1. hAPP_o334540577on_com=1. hAPP_o356497025on_com=1. hAPP_s2001034685l_bool=1. hAPP_s58564346l_bool=1. hAPP_H226398757l_bool=1. hAPP_b2019457360e_bool=1. hAPP_f1012183542e_bool=1. hAPP_f1259673775l_bool=1. hAPP_f1308959284_state=1. hAPP_f1336811455e_bool=1. hAPP_f137248406_state=1. hAPP_f1385420507e_bool=1. hAPP_f1405979047_state=1. hAPP_f1456107715e_bool=1. hAPP_f1476298914l_bool=1. hAPP_f1508101115l_bool=1. hAPP_f1508257257l_bool=1. hAPP_f1558052123e_bool=1. hAPP_f1661207211_state=1. hAPP_f167292325e_bool=1. hAPP_f1673966486on_com=1. hAPP_f167506745e_bool=1. hAPP_f1721106985e_bool=1. hAPP_f180827860e_bool=1. hAPP_f1844318385e_bool=1. hAPP_f1862834069l_bool=1. hAPP_f1879335953l_bool=1. hAPP_f1904669497l_bool=1. hAPP_f1973135743e_bool=1. hAPP_f2070658331l_bool=1. hAPP_f2081555625l_bool=1. hAPP_f2082757169l_bool=1. hAPP_f2093196134on_com=1. hAPP_f2101567797_state=1. hAPP_f2123220539on_com=1. hAPP_f261382953l_bool=1. hAPP_f294904177e_bool=1. hAPP_f376825399l_bool=1. hAPP_f389811538l_bool=1. hAPP_f481659057e_bool=1. hAPP_f492098723l_bool=1. hAPP_f547518321e_bool=1. hAPP_f567934427l_bool=1. hAPP_f644196280e_bool=1. hAPP_f648377725on_com=1. hAPP_f698292281e_bool=1. hAPP_f755519727on_com=1. hAPP_f762269719e_bool=1. hAPP_f817621513e_bool=1. hAPP_f833390165e_bool=1. hAPP_f939130838_state=1. hAPP_f964290431e_bool=1. hAPP_f998786331e_bool=1. hAPP_p1086945780on_com=1. hAPP_p1164893188on_com=1. hAPP_p1712839024_state=1. hAPP_p2032835427_state=1. hAPP_p393069232l_bool=1. hAPP_p80247908_state=1. hAPP_p964374716_state=1. hAPP_s1226857760e_bool=1. hAPP_s1874344717e_bool=1. hAPP_s336103912e_bool=1. hAPP_c566651504m_bool=1. hAPP_f1682609283m_bool=1. hAPP_f1987093l_bool=1. hAPP_f783502055l_bool=1. f16=1. f28=1. f29=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f82=1. f83=1. f94=1. f95=1. f98=1. f99=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f130=1. f131=1. f132=1. f133=1. f134=1. f135=1. f136=1. f137=1. f138=1. f139=1. f152=1. f153=1. f154=1. f155=1. image_275883510_state=1. hoare_659004819_state=1. image_1925245338_pname=1. evalc=1. cOMBB_1382207997_state=1. cOMBB_675860798_pname=1. cOMBB_2020112947e_bool=1. cOMBB_2095475776e_bool=1. some_com=1. cOMBB_2123334001_pname=1. dom_pname_com=1. image_pname_pname=1. image_1283814551_pname=1. image_47868345e_bool=1. image_505480954e_bool=1. image_936554724_state=1. image_1259634916e_bool=1. image_277167759e_bool=1. image_636285904_pname=1. image_774712299_state=1. some_pname=1. cOMBB_1759179140_state=1. cOMBB_188601460_state=1. cOMBB_422605457_pname=1. cOMBB_923936821_pname=1. cOMBB_20296667_state=1. cOMBB_647938656_pname=1. cOMBK_588224941_state=1. cOMBK_90103121_pname=1. hoare_1065416081_state=1. set_com=1. set_pname=1. cOMBB_1036740637_state=1. cOMBB_1476898461_state=1. cOMBB_1757942702_state=1. cOMBB_1911358915_state=1. cOMBK_1857069011e_bool=1. cOMBK_631994958_state=1. cOMBK_bool_pname=1. image_2063528359e_bool=1. image_650584225_state=1. set_Ho1831989999_state=1. some_H1133819688_state=1. cOMBB_1099197107e_bool=1. cOMBB_1170234304e_bool=1. cOMBB_1239130257_state=1. cOMBB_1394247784_pname=1. cOMBB_1456120487_state=1. cOMBB_160679318_state=1. cOMBB_1653402815_state=1. cOMBB_1671808265e_bool=1. cOMBB_1722165949_state=1. cOMBB_1957242197e_bool=1. cOMBB_291471741_state=1. cOMBB_307249310e_bool=1. cOMBB_408569982_pname=1. cOMBB_416661851_state=1. cOMBB_44445098_pname=1. cOMBB_530759491_pname=1. cOMBB_542850580_pname=1. cOMBB_598082538e_bool=1. cOMBB_707293872_pname=1. cOMBB_799949246_pname=1. cOMBK_1079618832_state=1. cOMBK_564432736e_bool=1. image_505022149e_bool=1. undefi17486888e_bool=1. undefi64961550l_bool=1. undefined_pname=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f27=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f72=1. f73=1. f74=1. f75=1. f97=1. f126=1. f127=1. f128=1. f140=1. f141=1. f13=1. f14=1. f15=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f39=1. f40=1. f70=1. f71=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f96=1. f118=1. f119=1. f120=1. f121=1. f122=1. f123=1. f124=1. f125=1. f160=1. f161=1. f162=1. f163=1. f164=1. f165=1. f85=1. f86=1. f110=1. f111=1. f112=1. f113=1. f114=1. f115=1. f116=1. f117=1. f129=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f148=1. f149=1. f150=1. f151=1. f156=1. f157=1. f158=1. f159=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f84=1.
% 5.68/5.92
% 5.68/5.92 ============================== end of process initial clauses ========
% 5.68/5.92
% 5.68/5.92 ============================== CLAUSES FOR SEARCH ====================
% 5.68/5.92
% 5.68/5.92 ============================== end of clauses for search =============
% 5.68/5.92
% 5.68/5.92 ============================== SEARCH ================================
% 5.68/5.92
% 5.68/5.92 % Starting search at 0.85 seconds.
% 5.68/5.92
% 5.68/5.92 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 1.58 sec).
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=39.000, iters=3472
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=38.000, iters=3424
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=37.000, iters=3409
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=35.000, iters=3357
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=34.000, iters=3346
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=32.000, iters=3366
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=31.000, iters=3352
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=30.000, iters=3517
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=29.000, iters=3376
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=28.000, iters=3390
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=27.000, iters=3333
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=26.000, iters=3553
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=25.000, iters=3385
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=24.000, iters=3360
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=23.000, iters=3337
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=22.000, iters=3343
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=21.000, iters=3341
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=20.000, iters=3338
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=19.000, iters=3362
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=18.000, iters=3335
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=17.000, iters=3344
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=16.000, iters=3361
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=15.000, iters=3354
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=14.000, iters=3344
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=13.000, iters=3334
% 5.68/5.92
% 5.68/5.92 Low Water (keep): wt=12.000, iters=3335
% 5.68/5.92
% 5.68/5.92 Low Water (displace): id=4656, wt=96.000
% 5.68/5.92
% 5.68/5.92 Low Water (displace): id=4839, wt=89.000
% 5.68/5.92
% 5.68/5.92 Low Water (displace): id=5015, wt=82.000
% 5.68/5.92
% 5.68/5.92 Low Water (displace): id=4682, wt=81.000
% 5.68/5.92
% 5.68/5.92 Low Water (displace): id=4681, wt=80.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=5098, wt=79.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4685, wt=77.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4319, wt=75.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=5011, wt=73.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=5156, wt=72.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4828, wt=71.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4675, wt=69.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4282, wt=67.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4838, wt=65.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4680, wt=64.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4826, wt=63.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4626, wt=61.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4822, wt=60.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4877, wt=59.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4402, wt=58.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=4793, wt=57.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=5035, wt=55.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=8422, wt=43.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=8419, wt=39.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=14098, wt=10.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=14118, wt=9.000
% 13.97/14.21
% 13.97/14.21 Low Water (displace): id=14209, wt=8.000
% 13.97/14.21
% 13.97/14.21 Low Water (keep): wt=11.000, iters=3336
% 13.97/14.21
% 13.97/14.21 Low Water (keep): wt=10.000, iters=3333
% 13.97/14.21
% 13.97/14.21 ============================== PROOF =================================
% 13.97/14.21 % SZS status Theorem
% 13.97/14.21 % SZS output start Refutation
% 13.97/14.21
% 13.97/14.21 % Proof 1 at 12.38 (+ 0.20) seconds.
% 13.97/14.21 % Length of proof is 25.
% 13.97/14.21 % Level of proof is 6.
% 13.97/14.21 % Maximum clause weight is 19.000.
% 13.97/14.21 % Given clauses 6725.
% 13.97/14.21
% 13.97/14.21 43 (all G_1 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 13.97/14.21 47 (all G_1 all G_2 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 13.97/14.21 92 (all C (hBOOL(hoare_298929751gleton) -> (hBOOL(wT_bodies) -> (hBOOL(hAPP_com_bool(wt,C)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))))))) # label(fact_53_MGF) # label(axiom) # label(non_clause). [assumption].
% 13.97/14.21 212 (all P_1 hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1) # label(fact_177_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 13.97/14.21 248 (all A hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) # label(fact_213_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 13.97/14.21 250 (all Pn all B_4 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = some_com(B_4) -> hBOOL(hAPP_com_bool(wt,B_4))))) # label(fact_215_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 13.97/14.21 894 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(A),bot_bo1055319631e_bool)) # label(fact_0_empty) # label(axiom). [clausify(43)].
% 13.97/14.21 898 -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(A),B)) | -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(C),A)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(C),B)) # label(fact_4_cut) # label(axiom). [clausify(47)].
% 13.97/14.21 960 -hBOOL(hoare_298929751gleton) | -hBOOL(wT_bodies) | -hBOOL(hAPP_com_bool(wt,A)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,A)),bot_bo1055319631e_bool))) # label(fact_53_MGF) # label(axiom). [clausify(92)].
% 13.97/14.21 1136 hAPP_f921536533e_bool(collec727977250_state,A) = A # label(fact_177_Collect__def) # label(axiom). [clausify(212)].
% 13.97/14.21 1210 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A)) # label(fact_213_singleton__conv2) # label(axiom). [clausify(248)].
% 13.97/14.21 1211 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_H1645666623e_bool(fequal1531560888_state,A). [copy(1210),rewrite([1136(8)])].
% 13.97/14.22 1218 -hBOOL(wT_bodies) | some_com(A) != hAPP_p799580910on_com(body,B) | hBOOL(hAPP_com_bool(wt,A)) # label(fact_215_WT__bodiesD) # label(axiom). [clausify(250)].
% 13.97/14.22 2237 hBOOL(hoare_298929751gleton) # label(conj_0) # label(hypothesis). [assumption].
% 13.97/14.22 2238 hBOOL(wT_bodies) # label(conj_1) # label(hypothesis). [assumption].
% 13.97/14.22 2242 hAPP_p799580910on_com(body,pn) = some_com(y) # label(conj_5) # label(hypothesis). [assumption].
% 13.97/14.22 2244 -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool))) # label(conj_7) # label(negated_conjecture). [assumption].
% 13.97/14.22 2245 -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)))). [copy(2244),rewrite([1211(16)])].
% 13.97/14.22 2326 -hBOOL(hAPP_com_bool(wt,A)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,A)))). [back_rewrite(960),rewrite([1211(15)]),unit_del(a,2237),unit_del(b,2238)].
% 13.97/14.22 2416 some_com(A) != hAPP_p799580910on_com(body,B) | hBOOL(hAPP_com_bool(wt,A)). [back_unit_del(1218),unit_del(a,2238)].
% 13.97/14.22 2554 -hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),A)) | hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(B),A)). [resolve(898,b,894,a)].
% 13.97/14.22 8490 hBOOL(hAPP_com_bool(wt,y)). [resolve(2416,a,2242,a(flip))].
% 13.97/14.22 9334 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)))). [resolve(8490,a,2326,a)].
% 13.97/14.22 32357 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(A),hAPP_H1645666623e_bool(fequal1531560888_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)))). [resolve(9334,a,2554,a)].
% 13.97/14.22 32358 $F. [resolve(32357,a,2245,a)].
% 13.97/14.22
% 13.97/14.22 % SZS output end Refutation
% 13.97/14.22 ============================== end of proof ==========================
% 13.97/14.22
% 13.97/14.22 ============================== STATISTICS ============================
% 13.97/14.22
% 13.97/14.22 Given=6725. Generated=271607. Kept=31168. proofs=1.
% 13.97/14.22 Usable=5893. Sos=9999. Demods=838. Limbo=0, Disabled=16587. Hints=0.
% 13.97/14.22 Megabytes=172.95.
% 13.97/14.22 User_CPU=12.38, System_CPU=0.20, Wall_clock=13.
% 13.97/14.22
% 13.97/14.22 ============================== end of statistics =====================
% 13.97/14.22
% 13.97/14.22 ============================== end of search =========================
% 13.97/14.22
% 13.97/14.22 THEOREM PROVED
% 13.97/14.22 % SZS status Theorem
% 13.97/14.22
% 13.97/14.22 Exiting with 1 proof.
% 13.97/14.22
% 13.97/14.22 Process 17540 exit (max_proofs) Sun Jun 5 12:41:56 2022
% 13.97/14.22 Prover9 interrupted
%------------------------------------------------------------------------------