TSTP Solution File: SWW474+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW474+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 15.96s 16.28s
% Output : Refutation 15.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW474+1 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 03:00:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.96/1.25 ============================== Prover9 ===============================
% 0.96/1.25 Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.25 Process 23115 was started by sandbox2 on n018.cluster.edu,
% 0.96/1.25 Mon Jun 6 03:00:05 2022
% 0.96/1.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22959_n018.cluster.edu".
% 0.96/1.25 ============================== end of head ===========================
% 0.96/1.25
% 0.96/1.25 ============================== INPUT =================================
% 0.96/1.25
% 0.96/1.25 % Reading from file /tmp/Prover9_22959_n018.cluster.edu
% 0.96/1.25
% 0.96/1.25 set(prolog_style_variables).
% 0.96/1.25 set(auto2).
% 0.96/1.25 % set(auto2) -> set(auto).
% 0.96/1.25 % set(auto) -> set(auto_inference).
% 0.96/1.25 % set(auto) -> set(auto_setup).
% 0.96/1.25 % set(auto_setup) -> set(predicate_elim).
% 0.96/1.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.25 % set(auto) -> set(auto_limits).
% 0.96/1.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.25 % set(auto) -> set(auto_denials).
% 0.96/1.25 % set(auto) -> set(auto_process).
% 0.96/1.25 % set(auto2) -> assign(new_constants, 1).
% 0.96/1.25 % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.25 % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.25 % set(auto2) -> assign(max_hours, 1).
% 0.96/1.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.25 % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.25 % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.25 % set(auto2) -> set(sort_initial_sos).
% 0.96/1.25 % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.25 % set(auto2) -> assign(max_megs, 400).
% 0.96/1.25 % set(auto2) -> assign(stats, some).
% 0.96/1.25 % set(auto2) -> clear(echo_input).
% 0.96/1.25 % set(auto2) -> set(quiet).
% 0.96/1.25 % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.25 % set(auto2) -> clear(print_given).
% 0.96/1.25 assign(lrs_ticks,-1).
% 0.96/1.25 assign(sos_limit,10000).
% 0.96/1.25 assign(order,kbo).
% 0.96/1.25 set(lex_order_vars).
% 0.96/1.25 clear(print_given).
% 0.96/1.25
% 0.96/1.25 % formulas(sos). % not echoed (428 formulas)
% 0.96/1.25
% 0.96/1.25 ============================== end of input ==========================
% 0.96/1.25
% 0.96/1.25 % From the command line: assign(max_seconds, 300).
% 0.96/1.25
% 0.96/1.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.25
% 0.96/1.25 % Formulas that are not ordinary clauses:
% 0.96/1.25 1 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2_1)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 2 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 3 (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].
% 0.96/1.25 4 (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].
% 0.96/1.25 5 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 6 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2_1)))) # label(gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 7 (all B_1_1 is_bool(wt(B_1_1))) # label(gsy_c_Com_OWT) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 8 (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].
% 0.96/1.25 9 (all B_1_1 is_fun1661590463l_bool(dom_fu2081503504ol_com(B_1_1))) # label(gsy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 10 (all B_1_1 (is_fun_pname_bool(B_1_1) -> is_fun_pname_bool(collect_pname(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 11 (all B_1_1 (is_fun1661590463l_bool(B_1_1) -> is_fun1661590463l_bool(collec1974731493e_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 12 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(image_pname_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 13 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_2_1) -> is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 14 (all B_1_1 all B_2_1 is_fun_pname_bool(image_54689091_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 15 (all B_1_1 all B_2_1 is_fun1661590463l_bool(image_2131964411e_bool(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta_001) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 16 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 17 (all B_1_1 all B_2_1 is_fun_pname_bool(image_187965177_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 18 (all B_1_1 all B_2_1 is_fun_pname_bool(image_1705983821_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 19 (all B_1_1 all B_2_1 is_fun_pname_bool(image_1619336331_pname(B_1_1,B_2_1))) # label(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otri) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 20 (all B_1_1 all B_2_1 (is_pname(B_1_1) & is_fun_pname_bool(B_2_1) -> is_fun_pname_bool(insert_pname(B_1_1,B_2_1)))) # label(gsy_c_Set_Oinsert_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 21 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_1_1) & is_fun1661590463l_bool(B_2_1) -> is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2_1)))) # label(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 22 (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].
% 0.96/1.25 23 (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].
% 0.96/1.25 24 (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].
% 0.96/1.25 25 (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].
% 0.96/1.25 26 (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].
% 0.96/1.25 27 (all B_1_1 all B_2_1 is_pname(hAPP_H1621176307_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 28 (all B_1_1 all B_2_1 is_bool(hAPP_H78829294e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_002) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 29 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H356885323e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_003) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 30 (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].
% 0.96/1.26 31 (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].
% 0.96/1.26 32 (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].
% 0.96/1.26 33 (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].
% 0.96/1.26 34 (all B_1_1 all B_2_1 is_pname(hAPP_f560369737_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 35 (all B_1_1 all B_2_1 is_bool(hAPP_f971112728l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004) # label(hypothesis) # label(non_clause). [assumption].
% 0.96/1.26 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].
% 0.96/1.26 37 (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_005) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 38 (all B_1_1 all B_2_1 is_bool(hAPP_f166538662l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 39 (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].
% 0.96/1.26 40 (all B_1_1 all B_2_1 is_bool(hAPP_f468958928l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__O) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 41 (all B_1_1 all B_2_1 is_bool(hAPP_f595608956l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 42 (all B_1_1 all B_2_1 is_bool(hAPP_f1022807134l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfeh) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 43 (all G hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),bot_bo620288102e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 44 (all Ts all G (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Ts),G)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)))) # label(fact_1_asm) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 45 (all Ts all G all Ts_1 (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts_1)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Ts),Ts_1)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))))) # label(fact_2_weaken) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 46 (all G all G_1 all Ts (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,G_1),G)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 47 (all G all G_1 all Ts (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts)) -> (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),G_1)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))))) # label(fact_4_cut) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 48 (all Ts all G all T (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,bot_bo620288102e_bool))) -> (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,Ts)))))) # label(fact_5_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 49 (all G all T all Ts (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,Ts))) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,bot_bo620288102e_bool))) & hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)))) # label(fact_6_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 50 (all Pn_1 all G (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),G)),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),bot_bo620288102e_bool))) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),bot_bo620288102e_bool))))) # label(fact_7_MGT__BodyN) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 51 (all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A)))))) # label(fact_8_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 52 (all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(ord_le1285840794e_bool),A)))))) # label(fact_9_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 53 (all A (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) -> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A)))))) # label(fact_10_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 54 (all A (hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) -> hBOOL(hAPP_f1022807134l_bool(finite34021339l_bool,collec256567069l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(ord_le889598034l_bool),A)))))) # label(fact_11_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 55 (all A (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) -> hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(ord_le287025148l_bool),A)))))) # label(fact_12_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 56 (all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A)))))) # label(fact_13_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 57 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_2003357581_state(H,Fa))))) # label(fact_14_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 58 (all H all Fa (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,Fa))))) # label(fact_15_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 59 (all H all Fa (hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1619336331_pname(H,Fa))))) # label(fact_16_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 60 (all H all Fa (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_187965177_pname(H,Fa))))) # label(fact_17_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 61 (all H all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,Fa))))) # label(fact_18_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 62 (all H all Fa (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_677922117_state(H,Fa))))) # label(fact_19_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 63 (all H all Fa (hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,Fa)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_892968839_state(H,Fa))))) # label(fact_20_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 64 (all H all Fa (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_18964633_state(H,Fa))))) # label(fact_21_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 65 (all H all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_516545147_state(H,Fa))))) # label(fact_22_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 66 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,Fa))))) # label(fact_23_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 67 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_288317893l_bool(H,Fa))))) # label(fact_24_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 68 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_70449425e_bool(H,Fa))))) # label(fact_25_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 69 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,Fa))))) # label(fact_26_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 70 (all H all Fa (hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1210605179l_bool(H,Fa))))) # label(fact_27_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 71 (all H all Fa (hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) -> hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_1761575943l_bool(H,Fa))))) # label(fact_28_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 72 (all H all Fa (hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_1828608335e_bool(H,Fa))))) # label(fact_29_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 73 (all H all Fa (hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_2131964411e_bool(H,Fa))))) # label(fact_30_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 74 (all H all Fa (hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_54689091_pname(H,Fa))))) # label(fact_31_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 75 (all H all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,Fa))))) # label(fact_32_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 76 (all A hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),A))) # label(fact_33_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 77 (all A hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,bot_bo1649642514l_bool),A))) # label(fact_34_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 78 (all A hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,bot_bo535777328l_bool),A))) # label(fact_35_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 79 (all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A))) # label(fact_36_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 80 (all A_2 all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(A_2,A))))) # label(fact_37_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 81 (all A_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A))))) # label(fact_38_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 82 (all A_2 all A (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_2,A))))) # label(fact_39_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 83 (all A_2 all A (hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) -> hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,insert203537868l_bool(A_2,A))))) # label(fact_40_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 84 (all A_2 all A (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(A_2,A))))) # label(fact_41_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 85 (all A_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A))))) # label(fact_42_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 86 (all Q_1 all P_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1))) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,P_1),Q_1)))))) # label(fact_49_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 87 (all Q_1 all P_1 (hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(P_1))) | hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(Q_1))) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,P_1),Q_1)))))) # label(fact_50_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 88 (all Q_1 all P_1 (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(P_1))) | hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(Q_1))) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(cOMBS_811933079l_bool(cOMBB_689948150l_bool(fconj,P_1),Q_1)))))) # label(fact_51_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 89 (all Q_1 all P_1 (hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(P_1))) | hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(Q_1))) -> hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(cOMBS_1358309691l_bool(cOMBB_404111180l_bool(fconj,P_1),Q_1)))))) # label(fact_52_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 90 (all Q_1 all P_1 (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(P_1))) | hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(Q_1))) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,P_1),Q_1)))))) # label(fact_53_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 91 (all Q_1 all P_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1))) | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,P_1),Q_1)))))) # label(fact_54_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 92 (all C_1 all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> image_2003357581_state(cOMBK_367030522_pname(C_1),A) = bot_bo620288102e_bool) & (A != bot_bo844097828e_bool -> image_2003357581_state(cOMBK_367030522_pname(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)))) # label(fact_55_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 93 (all C_1 all A ((A = bot_bo620288102e_bool -> image_54689091_pname(cOMBK_168215364_state(C_1),A) = bot_bo844097828e_bool) & (A != bot_bo620288102e_bool -> image_54689091_pname(cOMBK_168215364_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)))) # label(fact_56_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 94 (all C_1 all A ((A = bot_bo620288102e_bool -> image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = bot_bo1649642514l_bool) & (A != bot_bo620288102e_bool -> image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool)))) # label(fact_57_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 95 (all C_1 all A ((A = bot_bo620288102e_bool -> image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = bot_bo535777328l_bool) & (A != bot_bo620288102e_bool -> image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool)))) # label(fact_58_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 96 (all C_1 all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = bot_bo1649642514l_bool) & (A != bot_bo844097828e_bool -> image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool)))) # label(fact_59_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 97 (all C_1 all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = bot_bo535777328l_bool) & (A != bot_bo844097828e_bool -> image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool)))) # label(fact_60_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 98 (all C_1 all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> image_pname_pname(cOMBK_pname_pname(C_1),A) = bot_bo844097828e_bool) & (A != bot_bo844097828e_bool -> image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)))) # label(fact_61_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 99 (all C_1 all A (is_fun1661590463l_bool(A) -> (A = bot_bo1649642514l_bool -> image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = bot_bo620288102e_bool) & (A != bot_bo1649642514l_bool -> image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)))) # label(fact_62_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 100 (all C_1 all A ((A = bot_bo535777328l_bool -> image_18964633_state(cOMBK_701929478e_bool(C_1),A) = bot_bo620288102e_bool) & (A != bot_bo535777328l_bool -> image_18964633_state(cOMBK_701929478e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)))) # label(fact_63_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 101 (all C_1 all A (is_fun1661590463l_bool(A) -> (A = bot_bo1649642514l_bool -> image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = bot_bo844097828e_bool) & (A != bot_bo1649642514l_bool -> image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)))) # label(fact_64_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 102 (all C_1 all A ((A = bot_bo535777328l_bool -> image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = bot_bo844097828e_bool) & (A != bot_bo535777328l_bool -> image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)))) # label(fact_65_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 103 (all C_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> image_2003357581_state(cOMBK_367030522_pname(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool))) # label(fact_66_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 104 (all C_1 all X_2 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> image_54689091_pname(cOMBK_168215364_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool))) # label(fact_67_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 105 (all C_1 all X_2 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool))) # label(fact_68_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 106 (all C_1 all X_2 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool))) # label(fact_69_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 107 (all C_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool))) # label(fact_70_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 108 (all C_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool))) # label(fact_71_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 109 (all C_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool))) # label(fact_72_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 110 (all C_1 all X_2 all A (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool))) # label(fact_73_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 111 (all C_1 all X_2 all A (hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A)) -> image_18964633_state(cOMBK_701929478e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool))) # label(fact_74_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 112 (all C_1 all X_2 all A (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool))) # label(fact_75_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 113 (all C_1 all X_2 all A (hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A)) -> image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool))) # label(fact_76_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 114 (all F all X_2 all Y_2 (hAPP_p799580910on_com(F,X_2) = some_com(Y_2) -> insert_pname(X_2,dom_pname_com(F)) = dom_pname_com(F))) # label(fact_77_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 115 (all F all X_2 all Y_2 (hAPP_f2138803836on_com(F,X_2) = some_com(Y_2) -> insert1325755072e_bool(X_2,dom_fu2081503504ol_com(F)) = dom_fu2081503504ol_com(F))) # label(fact_78_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 116 (all F all X_2 all Y_2 (hAPP_f2134636538on_com(F,X_2) = some_com(Y_2) -> insert1556680138e_bool(X_2,dom_fu1342267980ol_com(F)) = dom_fu1342267980ol_com(F))) # label(fact_79_insert__dom) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 117 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A))) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))))) # label(fact_80_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 118 (all B all F all A (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1705983821_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_81_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 119 (all B all F all A (hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1619336331_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_82_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 120 (all B all F all A (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_187965177_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_83_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 121 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_84_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 122 (all B all F all A (hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_677922117_state(F,A))) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))))) # label(fact_85_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 123 (all B all F all A (hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_892968839_state(F,A))) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))))) # label(fact_86_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 124 (all B all F all A (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_18964633_state(F,A))) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))))) # label(fact_87_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 125 (all B all F all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_516545147_state(F,A))) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))))) # label(fact_88_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 126 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_1642285373l_bool(F,A))) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B))))) # label(fact_89_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 127 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,B),image_288317893l_bool(F,A))) -> hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,B))))) # label(fact_90_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 128 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_91_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 129 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),image_70449425e_bool(F,A))) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B))))) # label(fact_92_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 130 (all B all F all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_93_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 131 (all B all F all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) -> (hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_1210605179l_bool(F,A))) -> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B))))) # label(fact_94_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 132 (all B all F all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) -> (hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,B),image_1761575943l_bool(F,A))) -> hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,B))))) # label(fact_95_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 133 (all B all F all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_54689091_pname(F,A))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))))) # label(fact_96_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 134 (all B all F all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),image_1828608335e_bool(F,A))) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B))))) # label(fact_97_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 135 (all B all F all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_2131964411e_bool(F,A))) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))))) # label(fact_98_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 136 (all A all X_2 (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(X_2,bot_bo620288102e_bool))) -> A = bot_bo620288102e_bool | A = insert1415133716_state(X_2,bot_bo620288102e_bool))) # label(fact_99_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 137 (all A all X_2 (is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),insert1325755072e_bool(X_2,bot_bo1649642514l_bool))) -> A = bot_bo1649642514l_bool | A = insert1325755072e_bool(X_2,bot_bo1649642514l_bool)))) # label(fact_100_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 138 (all A all X_2 (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),insert1556680138e_bool(X_2,bot_bo535777328l_bool))) -> A = bot_bo535777328l_bool | A = insert1556680138e_bool(X_2,bot_bo535777328l_bool))) # label(fact_101_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 139 (all A all X_2 (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,bot_bo844097828e_bool))) -> A = bot_bo844097828e_bool | A = insert_pname(X_2,bot_bo844097828e_bool)))) # label(fact_102_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 140 (all C_1 (hBOOL(hoare_165779456gleton) -> (hBOOL(wT_bodies) -> (hBOOL(wt(C_1)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool))))))) # label(fact_103_MGF) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 141 (all A_2 -hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),bot_bo620288102e_bool))) # label(fact_104_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 142 (all A_2 -hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),bot_bo1649642514l_bool))) # label(fact_105_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 143 (all A_2 -hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),bot_bo535777328l_bool))) # label(fact_106_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 144 (all A_2 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool))) # label(fact_107_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 145 (all B_1 all A_2 all B ((-hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),B)) -> A_2 = B_1) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,B))))) # label(fact_108_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 146 (all B_1 all A_2 all B ((-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),B)) -> A_2 = B_1) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,B))))) # label(fact_109_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 147 (all B_1 all A_2 all B ((-hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),B)) -> A_2 = B_1) -> hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),insert1556680138e_bool(B_1,B))))) # label(fact_110_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 148 (all B_1 all A_2 all B ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) -> A_2 = B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B))))) # label(fact_111_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 149 (all A_2 all B_1 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,A))) -> (A_2 != B_1 -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A))))) # label(fact_112_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 150 (all A_2 all B_1 all A (is_fun_pname_bool(A_2) & is_fun_pname_bool(B_1) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,A))) -> (A_2 != B_1 -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A)))))) # label(fact_113_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 151 (all A_2 all B_1 all A (hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),insert1556680138e_bool(B_1,A))) -> (A_2 != B_1 -> hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),A))))) # label(fact_114_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 152 (all A_2 all B_1 all A (is_pname(A_2) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A))) -> (A_2 != B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)))))) # label(fact_115_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 153 (all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A)) -> A = B))) # label(fact_116_equalityI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 154 (all A all B (is_fun1661590463l_bool(A) & is_fun1661590463l_bool(B) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A)) -> A = B)))) # label(fact_117_equalityI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 155 (all A all B (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B)) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),A)) -> A = B))) # label(fact_118_equalityI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 156 (all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) -> A = B)))) # label(fact_119_equalityI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 157 (all C_1 all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),B))))) # label(fact_120_subsetD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 158 (all C_1 all A all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),A)) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),B))))) # label(fact_121_subsetD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 159 (all C_1 all A all B (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B)) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),A)) -> hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),B))))) # label(fact_122_subsetD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 160 (all C_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B))))) # label(fact_123_subsetD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 161 (all A all B_1 all F all X_2 (B_1 = hAPP_H356885323e_bool(F,X_2) -> (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_2131964411e_bool(F,A)))))) # label(fact_124_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 162 (all A all B_1 all F all X_2 (B_1 = hAPP_H1049623551e_bool(F,X_2) -> (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,B_1),image_1828608335e_bool(F,A)))))) # label(fact_125_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 163 (all A all B_1 all F all X_2 (B_1 = hAPP_p61793385e_bool(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_47868345e_bool(F,A)))))) # label(fact_126_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 164 (all A all B_1 all F all X_2 (B_1 = hAPP_p442853985e_bool(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,B_1),image_70449425e_bool(F,A)))))) # label(fact_127_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 165 (all A all B_1 all F all X_2 (B_1 = hAPP_f888949707_state(F,X_2) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_516545147_state(F,A)))))) # label(fact_128_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 166 (all A all B_1 all F all X_2 (B_1 = hAPP_f1387463497_state(F,X_2) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_18964633_state(F,A)))))) # label(fact_129_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 167 (all A all B_1 all F all X_2 (B_1 = hAPP_H1621176307_pname(F,X_2) -> (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_54689091_pname(F,A)))))) # label(fact_130_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 168 (all A all B_1 all F all X_2 (B_1 = hAPP_pname_pname(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_pname_pname(F,A)))))) # label(fact_131_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 169 (all A all B_1 all F all X_2 (B_1 = hAPP_f1297739591_pname(F,X_2) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_1283814551_pname(F,A)))))) # label(fact_132_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 170 (all A all B_1 all F all X_2 (B_1 = hAPP_f560369737_pname(F,X_2) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_187965177_pname(F,A)))))) # label(fact_133_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 171 (all A all B_1 all F all X_2 (B_1 = hAPP_p1422361149_state(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A)))))) # label(fact_134_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 172 (all A_2 all A (A = bot_bo1649642514l_bool -> -hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A)))) # label(fact_135_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 173 (all A_2 all A (A = bot_bo535777328l_bool -> -hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),A)))) # label(fact_136_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 174 (all A_2 all A (A = bot_bo620288102e_bool -> -hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A)))) # label(fact_137_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 175 (all A_2 all A (A = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)))) # label(fact_138_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 176 (all P_1 (collec1613912337l_bool(P_1) = bot_bo1537088220l_bool <-> (all X_1 (is_fun1661590463l_bool(X_1) -> -hBOOL(hAPP_f1935102916l_bool(P_1,X_1)))))) # label(fact_139_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 177 (all P_1 (collec488126193l_bool(P_1) = bot_bo1761158942l_bool <-> (all X_1 -hBOOL(hAPP_f166538662l_bool(P_1,X_1))))) # label(fact_140_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 178 (all P_1 (collec1823980261e_bool(P_1) = bot_bo535777328l_bool <-> (all X_1 -hBOOL(hAPP_f971112728l_bool(P_1,X_1))))) # label(fact_141_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 179 (all P_1 (collec1974731493e_bool(P_1) = bot_bo1649642514l_bool <-> (all X_1 (is_fun_pname_bool(X_1) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_1)))))) # label(fact_142_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 180 (all P_1 (collec307967673_state(P_1) = bot_bo620288102e_bool <-> (all X_1 -hBOOL(hAPP_H78829294e_bool(P_1,X_1))))) # label(fact_143_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 181 (all P_1 (collect_pname(P_1) = bot_bo844097828e_bool <-> (all X_1 (is_pname(X_1) -> -hBOOL(hAPP_pname_bool(P_1,X_1)))))) # label(fact_144_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 182 (all C_1 -hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),bot_bo1649642514l_bool))) # label(fact_145_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 183 (all C_1 -hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),bot_bo535777328l_bool))) # label(fact_146_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 184 (all C_1 -hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),bot_bo620288102e_bool))) # label(fact_147_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 185 (all C_1 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool))) # label(fact_148_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 186 (all P_1 (bot_bo1537088220l_bool = collec1613912337l_bool(P_1) <-> (all X_1 (is_fun1661590463l_bool(X_1) -> -hBOOL(hAPP_f1935102916l_bool(P_1,X_1)))))) # label(fact_149_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 187 (all P_1 (bot_bo1761158942l_bool = collec488126193l_bool(P_1) <-> (all X_1 -hBOOL(hAPP_f166538662l_bool(P_1,X_1))))) # label(fact_150_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 188 (all P_1 (bot_bo535777328l_bool = collec1823980261e_bool(P_1) <-> (all X_1 -hBOOL(hAPP_f971112728l_bool(P_1,X_1))))) # label(fact_151_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 189 (all P_1 (bot_bo1649642514l_bool = collec1974731493e_bool(P_1) <-> (all X_1 (is_fun_pname_bool(X_1) -> -hBOOL(hAPP_f1664156314l_bool(P_1,X_1)))))) # label(fact_152_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 190 (all P_1 (bot_bo620288102e_bool = collec307967673_state(P_1) <-> (all X_1 -hBOOL(hAPP_H78829294e_bool(P_1,X_1))))) # label(fact_153_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 191 (all P_1 (bot_bo844097828e_bool = collect_pname(P_1) <-> (all X_1 (is_pname(X_1) -> -hBOOL(hAPP_pname_bool(P_1,X_1)))))) # label(fact_154_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 192 (all A (is_fun1661590463l_bool(A) -> ((exists X_1 (is_fun_pname_bool(X_1) & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)))) <-> A != bot_bo1649642514l_bool))) # label(fact_155_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 193 (all A ((exists X_1 hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A))) <-> A != bot_bo535777328l_bool)) # label(fact_156_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 194 (all A ((exists X_1 hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A))) <-> A != bot_bo620288102e_bool)) # label(fact_157_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 195 (all A (is_fun_pname_bool(A) -> ((exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)))) <-> A != bot_bo844097828e_bool))) # label(fact_158_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 196 (all A (is_fun1661590463l_bool(A) -> ((all X_1 (is_fun_pname_bool(X_1) -> -hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)))) <-> A = bot_bo1649642514l_bool))) # label(fact_159_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 197 (all A ((all X_1 -hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A))) <-> A = bot_bo535777328l_bool)) # label(fact_160_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 198 (all A ((all X_1 -hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A))) <-> A = bot_bo620288102e_bool)) # label(fact_161_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 199 (all A (is_fun_pname_bool(A) -> ((all X_1 (is_pname(X_1) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)))) <-> A = bot_bo844097828e_bool))) # label(fact_162_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 200 (all A_2 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) -> insert_pname(A_2,A) = A))) # label(fact_168_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 201 (all A_2 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A)) -> insert1415133716_state(A_2,A) = A)) # label(fact_169_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 202 (all B_1 all A_2 all B (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B))))) # label(fact_170_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 203 (all B_1 all A_2 all B (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),B)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,B))))) # label(fact_171_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 204 (all B all X_2 all A (is_fun_pname_bool(B) & is_fun_pname_bool(A) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) -> (insert_pname(X_2,A) = insert_pname(X_2,B) <-> A = B))))) # label(fact_172_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 205 (all B all X_2 all A (-hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> (-hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) -> (insert1415133716_state(X_2,A) = insert1415133716_state(X_2,B) <-> A = B)))) # label(fact_173_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 206 (all Y_2 all A all X_2 (is_pname(Y_2) & is_pname(X_2) -> (hBOOL(hAPP_pname_bool(insert_pname(Y_2,A),X_2)) <-> Y_2 = X_2 | hBOOL(hAPP_pname_bool(A,X_2))))) # label(fact_174_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 207 (all Y_2 all A all X_2 (hBOOL(hAPP_H78829294e_bool(insert1415133716_state(Y_2,A),X_2)) <-> Y_2 = X_2 | hBOOL(hAPP_H78829294e_bool(A,X_2)))) # label(fact_175_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 208 (all A_2 all B_1 all A (is_pname(A_2) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A))) <-> A_2 = B_1 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))))) # label(fact_176_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 209 (all A_2 all B_1 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,A))) <-> A_2 = B_1 | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A)))) # label(fact_177_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 210 (all X_2 all Y_2 all A insert_pname(X_2,insert_pname(Y_2,A)) = insert_pname(Y_2,insert_pname(X_2,A))) # label(fact_178_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 211 (all X_2 all Y_2 all A insert1415133716_state(X_2,insert1415133716_state(Y_2,A)) = insert1415133716_state(Y_2,insert1415133716_state(X_2,A))) # label(fact_179_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 212 (all X_2 all A insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A)) # label(fact_180_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 213 (all X_2 all A insert1415133716_state(X_2,insert1415133716_state(X_2,A)) = insert1415133716_state(X_2,A)) # label(fact_181_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 214 (all A_2 all P_1 insert_pname(A_2,collect_pname(P_1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2))),P_1))) # label(fact_182_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 215 (all A_2 all P_1 insert1415133716_state(A_2,collec307967673_state(P_1)) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2))),P_1))) # label(fact_183_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 216 (all A_2 all P_1 insert1325755072e_bool(A_2,collec1974731493e_bool(P_1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2))),P_1))) # label(fact_184_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 217 (all A_2 all P_1 insert1556680138e_bool(A_2,collec1823980261e_bool(P_1)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2))),P_1))) # label(fact_185_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 218 (all A_2 all B insert_pname(A_2,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B)))) # label(fact_186_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 219 (all A_2 all B insert1415133716_state(A_2,B) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B)))) # label(fact_187_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 220 (all A_2 all B insert1325755072e_bool(A_2,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B)))) # label(fact_188_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 221 (all A_2 all B insert1556680138e_bool(A_2,B) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),B)))) # label(fact_189_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 222 (all A_2 all B hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(A_2,B)))) # label(fact_190_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 223 (all A_2 all B hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(A_2,B)))) # label(fact_191_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 224 (all A all B (A = B -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))))) # label(fact_192_equalityE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 225 (all A all B (A = B -> -(hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> -hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))))) # label(fact_193_equalityE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 226 (all C_2 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_2))))) # label(fact_194_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 227 (all C_2 all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),C_2)) -> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),C_2))))) # label(fact_195_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 228 (all X_2 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) # label(fact_196_set__mp) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 229 (all X_2 all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))))) # label(fact_197_set__mp) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 230 (all B all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) # label(fact_198_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 231 (all B all X_2 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))))) # label(fact_199_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 232 (all X_2 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))))) # label(fact_200_in__mono) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 233 (all X_2 all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))))) # label(fact_201_in__mono) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 234 (all A all B (A = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)))) # label(fact_202_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 235 (all A all B (A = B -> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A)))) # label(fact_203_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 236 (all A all B (A = B -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_204_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 237 (all A all B (A = B -> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)))) # label(fact_205_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 238 (all A all B (is_fun_pname_bool(A) & is_fun_pname_bool(B) -> (A = B <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))))) # label(fact_206_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 239 (all A all B (A = B <-> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A)))) # label(fact_207_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 240 (all A hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A))) # label(fact_208_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 241 (all A hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),A))) # label(fact_209_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 242 (all B_1 all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (B_1 = hAPP_p1422361149_state(F,X_2) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A)))))) # label(fact_210_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 243 (all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_p1422361149_state(F,X_2)),image_2003357581_state(F,A))))) # label(fact_211_imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 244 (all Z all F all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,Z),image_2003357581_state(F,A))) <-> (exists X_1 (is_pname(X_1) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) & Z = hAPP_p1422361149_state(F,X_1))))) # label(fact_212_image__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 245 (all P_1 all Q_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,P_1),Q_1)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1))) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))))) # label(fact_213_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 246 (all P_1 all Q_1 (hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,P_1),Q_1)))) <-> hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(P_1))) & hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(Q_1))))) # label(fact_214_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 247 (all P_1 all Q_1 (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,P_1),Q_1)))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1))) & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))))) # label(fact_215_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 248 (all P_1 all Q_1 (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,P_1),Q_1)))) <-> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(P_1))) & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(Q_1))))) # label(fact_216_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 249 (all X_1 all Xa insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa)))) # label(fact_217_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 250 (all X_1 all Xa insert1415133716_state(X_1,Xa) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),X_1)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),Xa)))) # label(fact_218_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 251 (all X_1 all Xa insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa)))) # label(fact_219_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 252 (all X_1 all Xa insert1556680138e_bool(X_1,Xa) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),X_1)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),Xa)))) # label(fact_220_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 253 (all A_2 all B_1 (is_pname(A_2) & is_pname(B_1) -> (insert_pname(A_2,bot_bo844097828e_bool) = insert_pname(B_1,bot_bo844097828e_bool) -> A_2 = B_1))) # label(fact_221_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 254 (all A_2 all B_1 (insert1415133716_state(A_2,bot_bo620288102e_bool) = insert1415133716_state(B_1,bot_bo620288102e_bool) -> A_2 = B_1)) # label(fact_222_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 255 (all B_1 all A_2 (is_pname(B_1) & is_pname(A_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool))) -> B_1 = A_2))) # label(fact_223_singletonE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 256 (all B_1 all A_2 (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),insert1415133716_state(A_2,bot_bo620288102e_bool))) -> B_1 = A_2)) # label(fact_224_singletonE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 257 (all A_2 all B_1 all C_1 all D_1 (is_pname(A_2) & is_pname(B_1) & is_pname(C_1) & is_pname(D_1) -> (insert_pname(A_2,insert_pname(B_1,bot_bo844097828e_bool)) = insert_pname(C_1,insert_pname(D_1,bot_bo844097828e_bool)) <-> A_2 = C_1 & B_1 = D_1 | A_2 = D_1 & B_1 = C_1))) # label(fact_225_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 258 (all A_2 all B_1 all C_1 all D_1 (insert1415133716_state(A_2,insert1415133716_state(B_1,bot_bo620288102e_bool)) = insert1415133716_state(C_1,insert1415133716_state(D_1,bot_bo620288102e_bool)) <-> A_2 = C_1 & B_1 = D_1 | A_2 = D_1 & B_1 = C_1)) # label(fact_226_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 259 (all B_1 all A_2 (is_pname(B_1) & is_pname(A_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool))) <-> B_1 = A_2))) # label(fact_227_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 260 (all B_1 all A_2 (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),insert1415133716_state(A_2,bot_bo620288102e_bool))) <-> B_1 = A_2)) # label(fact_228_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 261 (all A_2 all A insert_pname(A_2,A) != bot_bo844097828e_bool) # label(fact_229_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 262 (all A_2 all A insert1415133716_state(A_2,A) != bot_bo620288102e_bool) # label(fact_230_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 263 (all A_2 all A bot_bo844097828e_bool != insert_pname(A_2,A)) # label(fact_231_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 264 (all A_2 all A bot_bo620288102e_bool != insert1415133716_state(A_2,A)) # label(fact_232_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 265 (all A_2 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)))) # label(fact_233_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 266 (all A_2 all A (hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(A_2,A))) <-> hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)))) # label(fact_234_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 267 (all A_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A))) <-> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)))) # label(fact_235_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 268 (all A_2 all A (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(A_2,A))) <-> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)))) # label(fact_236_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 269 (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_237_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 270 (all A (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),bot_bo620288102e_bool)) <-> A = bot_bo620288102e_bool)) # label(fact_238_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 271 (all F all A (is_fun_pname_bool(A) -> (image_2003357581_state(F,A) = bot_bo620288102e_bool <-> A = bot_bo844097828e_bool))) # label(fact_239_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 272 (all F image_2003357581_state(F,bot_bo844097828e_bool) = bot_bo620288102e_bool) # label(fact_240_image__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 273 (all F all A (is_fun_pname_bool(A) -> (bot_bo620288102e_bool = image_2003357581_state(F,A) <-> A = bot_bo844097828e_bool))) # label(fact_241_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 274 (all A all B (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))))) # label(fact_242_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 275 (all A all B (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B)) -> (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B)) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))))) # label(fact_243_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 276 (all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_244_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 277 (all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> (hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))))) # label(fact_245_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 278 (all A all B (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) -> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))))) # label(fact_246_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 279 (all A all B (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B)) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B)) -> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))))) # label(fact_247_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 280 (all A all B (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))))) # label(fact_248_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 281 (all A all B (hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))))) # label(fact_249_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 282 (all A_2 all C_2 all D (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),D)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_2,C_2)),insert_pname(A_2,D))))) # label(fact_250_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 283 (all A_2 all C_2 all D (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,C_2),D)) -> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(A_2,C_2)),insert1415133716_state(A_2,D))))) # label(fact_251_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 284 (all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) <-> hBOOL(hAPP_pname_bool(A,X_2)))) # label(fact_252_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 285 (all X_2 all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) <-> hBOOL(hAPP_H78829294e_bool(A,X_2)))) # label(fact_253_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 286 (all P_1 (is_fun_pname_bool(P_1) -> collect_pname(P_1) = P_1)) # label(fact_254_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 287 (all P_1 collec307967673_state(P_1) = P_1) # label(fact_255_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 288 (all P_1 (is_fun1661590463l_bool(P_1) -> collec1974731493e_bool(P_1) = P_1)) # label(fact_256_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 289 (all P_1 collec1823980261e_bool(P_1) = P_1) # label(fact_257_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 290 (all B_1 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(B_1,B))))) # label(fact_258_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 291 (all B_1 all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) -> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(B_1,B))))) # label(fact_259_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 292 (all B all X_2 all A (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))))) # label(fact_260_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 293 (all B all X_2 all A (-hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(X_2,B))) <-> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))))) # label(fact_261_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 294 (all X_2 all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_262_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 295 (all X_2 all A all B (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(X_2,A)),B)) <-> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)))) # label(fact_263_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 296 (all B all A_2 hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_2,B)))) # label(fact_264_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 297 (all B all A_2 hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),insert1415133716_state(A_2,B)))) # label(fact_265_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 298 (all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> insert1415133716_state(hAPP_p1422361149_state(F,X_2),image_2003357581_state(F,A)) = image_2003357581_state(F,A))) # label(fact_266_insert__image) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 299 (all F all A_2 all B image_2003357581_state(F,insert_pname(A_2,B)) = insert1415133716_state(hAPP_p1422361149_state(F,A_2),image_2003357581_state(F,B))) # label(fact_267_image__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 300 (all F all A all B (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) -> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,image_2003357581_state(F,A)),image_2003357581_state(F,B))))) # label(fact_268_image__mono) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 301 (all B all F all A (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A))) <-> (exists AA (is_fun_pname_bool(AA) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A)) & B = image_2003357581_state(F,AA))))) # label(fact_269_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 302 (all M all A_2 all B_1 (hAPP_p799580910on_com(M,A_2) = some_com(B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),dom_pname_com(M))))) # label(fact_270_domI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 303 (all P_1 all A_2 ((hBOOL(hAPP_pname_bool(P_1,A_2)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(P_1,A_2)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = bot_bo844097828e_bool))) # label(fact_271_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 304 (all P_1 all A_2 ((hBOOL(hAPP_H78829294e_bool(P_1,A_2)) -> collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),P_1)) = insert1415133716_state(A_2,bot_bo620288102e_bool)) & (-hBOOL(hAPP_H78829294e_bool(P_1,A_2)) -> collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),P_1)) = bot_bo620288102e_bool))) # label(fact_272_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 305 (all P_1 all A_2 ((hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = bot_bo1649642514l_bool))) # label(fact_273_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 306 (all P_1 all A_2 ((hBOOL(hAPP_f971112728l_bool(P_1,A_2)) -> collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),P_1)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)) & (-hBOOL(hAPP_f971112728l_bool(P_1,A_2)) -> collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),P_1)) = bot_bo535777328l_bool))) # label(fact_274_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 307 (all P_1 all A_2 ((hBOOL(hAPP_pname_bool(P_1,A_2)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(P_1,A_2)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = bot_bo844097828e_bool))) # label(fact_275_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 308 (all P_1 all A_2 ((hBOOL(hAPP_H78829294e_bool(P_1,A_2)) -> collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,A_2)),P_1)) = insert1415133716_state(A_2,bot_bo620288102e_bool)) & (-hBOOL(hAPP_H78829294e_bool(P_1,A_2)) -> collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,A_2)),P_1)) = bot_bo620288102e_bool))) # label(fact_276_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 309 (all P_1 all A_2 ((hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool)) & (-hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) -> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = bot_bo1649642514l_bool))) # label(fact_277_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 310 (all P_1 all A_2 ((hBOOL(hAPP_f971112728l_bool(P_1,A_2)) -> collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)) & (-hBOOL(hAPP_f971112728l_bool(P_1,A_2)) -> collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = bot_bo535777328l_bool))) # label(fact_278_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 311 (all A_2 collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)) = insert_pname(A_2,bot_bo844097828e_bool)) # label(fact_279_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 312 (all A_2 collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool)) # label(fact_280_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 313 (all A_2 collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool)) # label(fact_281_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 314 (all A_2 collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)) # label(fact_282_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 315 (all A_2 collect_pname(hAPP_p61793385e_bool(fequal_pname,A_2)) = insert_pname(A_2,bot_bo844097828e_bool)) # label(fact_283_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 316 (all A_2 collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool)) # label(fact_284_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 317 (all A_2 collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool)) # label(fact_285_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 318 (all A_2 collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)) # label(fact_286_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 319 (all C_1 all G (hBOOL(hoare_165779456gleton) -> ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),dom_pname_com(body))) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_1)),bot_bo620288102e_bool)))))) -> (hBOOL(wt(C_1)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool))))))) # label(fact_287_MGF__lemma1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 320 (all Pn all B_2 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = some_com(B_2) -> hBOOL(wt(B_2))))) # label(fact_288_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 321 (all B_1 all F all A (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A))) -> -(all X_1 (is_pname(X_1) -> (B_1 = hAPP_p1422361149_state(F,X_1) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))))))) # label(fact_289_imageE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 322 (all P_1 all A all Fa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) -> ((all A_1 all F_1 (is_pname(A_1) & 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_1),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),F_1)) -> (hBOOL(hAPP_f1664156314l_bool(P_1,F_1)) -> hBOOL(hAPP_f1664156314l_bool(P_1,insert_pname(A_1,F_1))))))))) -> hBOOL(hAPP_f1664156314l_bool(P_1,Fa))))))) # label(fact_290_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 323 (all P_1 all A all Fa (hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Fa),A)) -> (hBOOL(hAPP_f971112728l_bool(P_1,bot_bo620288102e_bool)) -> ((all A_1 all F_1 (hBOOL(hAPP_f971112728l_bool(finite364844667_state,F_1)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_1),A)) -> (-hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_1),F_1)) -> (hBOOL(hAPP_f971112728l_bool(P_1,F_1)) -> hBOOL(hAPP_f971112728l_bool(P_1,insert1415133716_state(A_1,F_1)))))))) -> hBOOL(hAPP_f971112728l_bool(P_1,Fa))))))) # label(fact_291_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 324 (all P_1 all A all Fa (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) -> ((all A_1 all F_1 (is_fun_pname_bool(A_1) & is_fun1661590463l_bool(F_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),A)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),F_1)) -> (hBOOL(hAPP_f1935102916l_bool(P_1,F_1)) -> hBOOL(hAPP_f1935102916l_bool(P_1,insert1325755072e_bool(A_1,F_1))))))))) -> hBOOL(hAPP_f1935102916l_bool(P_1,Fa))))))) # label(fact_292_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 325 (all P_1 all A all Fa (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa)) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,Fa),A)) -> (hBOOL(hAPP_f166538662l_bool(P_1,bot_bo535777328l_bool)) -> ((all A_1 all F_1 (hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,F_1)) -> (hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_1),A)) -> (-hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_1),F_1)) -> (hBOOL(hAPP_f166538662l_bool(P_1,F_1)) -> hBOOL(hAPP_f166538662l_bool(P_1,insert1556680138e_bool(A_1,F_1)))))))) -> hBOOL(hAPP_f166538662l_bool(P_1,Fa))))))) # label(fact_293_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 326 (all P (hBOOL(wt(hAPP_pname_com(body_1,P))) -> -(all Y_1 hAPP_p799580910on_com(body,P) != some_com(Y_1)))) # label(fact_294_WTs__elim__cases_I7_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 327 (all B all A ((all X_1 (is_pname(X_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)))) # label(fact_295_subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 328 (all B all A ((all X_1 (hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A)) -> hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),B)))) -> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)))) # label(fact_296_subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 329 (all F all A all B (hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A))) -> (exists C (is_fun_pname_bool(C) & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C)) & B = image_2003357581_state(F,C)))))) # label(fact_297_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 330 (all Pname_1 all Pname (is_pname(Pname_1) & is_pname(Pname) -> (hAPP_pname_com(body_1,Pname_1) = hAPP_pname_com(body_1,Pname) <-> Pname_1 = Pname))) # label(fact_299_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 331 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 332 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 333 (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].
% 0.96/1.28 334 (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].
% 0.96/1.28 335 (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].
% 0.96/1.28 336 (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].
% 0.96/1.28 337 (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].
% 0.96/1.28 338 (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].
% 0.96/1.28 339 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 340 (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].
% 0.96/1.28 341 (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].
% 0.96/1.28 342 (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].
% 0.96/1.28 343 (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].
% 0.96/1.28 344 (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].
% 0.96/1.28 345 (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].
% 0.96/1.28 346 (all P all Q (is_pname(P) -> hAPP_pname_pname(cOMBK_pname_pname(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 347 (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].
% 0.96/1.28 348 (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].
% 0.96/1.28 349 (all P all Q all R hAPP_pname_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].
% 0.96/1.28 350 (all P all Q all R hAPP_pname_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].
% 0.96/1.28 351 (all P all Q all R hAPP_pname_bool(hAPP_p61793385e_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].
% 0.96/1.28 352 (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].
% 0.96/1.28 353 (all P all Q (is_pname(P) -> hAPP_f1297739591_pname(cOMBK_948730864e_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 354 (all P all Q (is_fun_pname_bool(P) -> hAPP_p61793385e_bool(cOMBK_37193422_pname(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 355 (all X all Y (-hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 356 (all X all Y (X != Y | hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 357 (all P all Q all R hAPP_pname_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].
% 0.96/1.28 358 (all P all Q all R hAPP_f1664156314l_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].
% 0.96/1.28 359 (all P all Q all R hAPP_p393069232l_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].
% 0.96/1.28 360 (all P all Q all R hAPP_f1664156314l_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].
% 0.96/1.28 361 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_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].
% 0.96/1.28 362 (all P all Q (is_bool(P) -> hAPP_H78829294e_bool(cOMBK_659609255_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 363 (all P all Q (is_pname(P) -> hAPP_H1621176307_pname(cOMBK_168215364_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 364 (all P all Q hAPP_p1422361149_state(cOMBK_367030522_pname(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 365 (all X all Y (-hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 366 (all X all Y (X != Y | hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 367 (all P all Q all R hAPP_p1422361149_state(cOMBB_699532858_pname(P,Q),R) = hAPP_c1126217667_state(P,hAPP_pname_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____jfehddehev__O) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 368 (all P all Q all R hAPP_H78829294e_bool(cOMBB_2144135922_state(P,Q),R) = hAPP_bool_bool(P,hAPP_H78829294e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 369 (all P all Q all R hAPP_H78829294e_bool(cOMBS_458705923l_bool(P,Q),R) = hAPP_bool_bool(hAPP_H1187982158l_bool(P,R),hAPP_H78829294e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 370 (all P all Q all R hAPP_f1476298914l_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_006) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 371 (all P all Q all R hAPP_f1935102916l_bool(cOMBS_811933079l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f32027384l_bool(P,R),hAPP_f1935102916l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 372 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f434788991l_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].
% 0.96/1.28 373 (all P all Q (is_bool(P) -> hAPP_f971112728l_bool(cOMBK_129401207e_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____jfe) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 374 (all P all Q (is_pname(P) -> hAPP_f560369737_pname(cOMBK_1589414042e_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____jf) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 375 (all P all Q hAPP_f888949707_state(cOMBK_1503445380e_bool(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___007) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 376 (all P all Q (is_fun_pname_bool(P) -> hAPP_H356885323e_bool(cOMBK_2035509764_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 377 (all P all Q hAPP_p442853985e_bool(cOMBK_1706929794_pname(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 378 (all P all Q all R hAPP_f971112728l_bool(cOMBB_1522210668e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f971112728l_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].
% 0.96/1.28 379 (all P all Q all R hAPP_H1187982158l_bool(cOMBB_962198420_state(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_H78829294e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 380 (all P all Q all R hAPP_f971112728l_bool(cOMBS_2066081387l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f637090980l_bool(P,R),hAPP_f971112728l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 381 (all P all Q all R hAPP_f32027384l_bool(cOMBB_689948150l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1935102916l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 382 (all P all Q all R hAPP_f1664156314l_bool(hAPP_f559147733l_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_010) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 383 (all P all Q (is_bool(P) -> hAPP_f166538662l_bool(cOMBK_482404831l_bool(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 384 (all P all Q all R hAPP_H78829294e_bool(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(P),Q),R) = hAPP_H78829294e_bool(hAPP_H1049623551e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 385 (all P all Q all R hAPP_f637090980l_bool(cOMBB_1585081418e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f971112728l_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].
% 0.96/1.48 386 (all P all Q all R hAPP_f166538662l_bool(cOMBS_1358309691l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f2143399574l_bool(P,R),hAPP_f166538662l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 387 (all P all Q hAPP_f1387463497_state(cOMBK_701929478e_bool(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___012) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 388 (all P all Q hAPP_H1049623551e_bool(cOMBK_1039769424_state(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_013) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 389 (all P all Q all R hAPP_f1935102916l_bool(hAPP_f510955609l_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].
% 0.96/1.48 390 (all P all Q all R hAPP_H78829294e_bool(hAPP_f98417237e_bool(cOMBC_1734175330l_bool(P),Q),R) = hAPP_f971112728l_bool(hAPP_H30606679l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___014) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 391 (all P all Q all R hAPP_f2143399574l_bool(cOMBB_404111180l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f166538662l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_015) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 392 (all P all Q all R hAPP_f971112728l_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(P),Q),R) = hAPP_f971112728l_bool(hAPP_f72706945l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 393 (all P all Q all R hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(P),Q),R) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 394 (all P all Q all R hAPP_f971112728l_bool(hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(P),Q),R) = hAPP_f166538662l_bool(hAPP_f210337421l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_016) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 395 (all P all Q all R hAPP_f166538662l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(P),Q),R) = hAPP_f166538662l_bool(hAPP_f585161855l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48 396 (all P all Q all R hAPP_f468958928l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(P),Q),R) = hAPP_f468958928l_bool(hAPP_f667366769l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfe) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.48
% 0.96/1.48 ============================== end of process non-clausal formulas ===
% 0.96/1.48
% 0.96/1.48 ============================== PROCESS INITIAL CLAUSES ===============
% 0.96/1.48
% 0.96/1.48 ============================== PREDICATE ELIMINATION =================
% 0.96/1.48
% 0.96/1.48 ============================== end predicate elimination =============
% 0.96/1.48
% 0.96/1.48 Auto_denials: (non-Horn, no changes).
% 0.96/1.48
% 0.96/1.48 Term ordering decisions:
% 0.96/1.48 Function symbol KB weights: bot_bo844097828e_bool=1. bot_bo620288102e_bool=1. ord_le1285840794e_bool=1. member_pname=1. member1338687867_state=1. ord_le313189616e_bool=1. finite_finite_pname=1. finite364844667_state=1. finite595471783e_bool=1. bot_bo1649642514l_bool=1. finite464017571e_bool=1. bot_bo535777328l_bool=1. fconj=1. fdisj=1. member2114907555e_bool=1. member799430823e_bool=1. finite786885583l_bool=1. finite796539827l_bool=1. ord_le675606854l_bool=1. ord_le287025148l_bool=1. fequal1111551311_state=1. fequal1311889615e_bool=1. fequal533582459e_bool=1. fequal_pname=1. hoare_Mirabelle_MGT=1. body=1. body_1=1. fFalse=1. fimplies=1. hoare_165779456gleton=1. bot_bo1537088220l_bool=1. fNot=1. bot_bo1761158942l_bool=1. wT_bodies=1. bool=1. fa=1. ord_le1375671464l_bool=1. ord_le889598034l_bool=1. pname=1. fTrue=1. pn=1. the_com=1. finite1491191519l_bool=1. finite34021339l_bool=1. y=1. hAPP_f971112728l_bool=1. hAPP_f1664156314l_bool=1. hAPP_f1935102916l_bool=1. insert1415133716_state=1. hAPP_f166538662l_bool=1. insert_pname=1. hAPP_f72706945l_bool=1. hAPP_f434788991l_bool=1. hAPP_p338031245l_bool=1. hAPP_H30606679l_bool=1. image_2003357581_state=1. hAPP_H78829294e_bool=1. hAPP_pname_bool=1. hAPP_f389811538l_bool=1. hAPP_f468958928l_bool=1. insert1325755072e_bool=1. hAPP_bool_bool=1. insert1556680138e_bool=1. hAPP_f510955609l_bool=1. hAPP_f210337421l_bool=1. hAPP_f556039215l_bool=1. hAPP_f585161855l_bool=1. hAPP_p61793385e_bool=1. hAPP_H1049623551e_bool=1. hAPP_b589554111l_bool=1. cOMBS_350070575l_bool=1. cOMBS_568398431l_bool=1. cOMBB_1585081418e_bool=1. cOMBB_2095475776e_bool=1. cOMBB_675860798_pname=1. cOMBB_962198420_state=1. cOMBS_2066081387l_bool=1. cOMBS_458705923l_bool=1. hAPP_p1422361149_state=1. hAPP_pname_com=1. hAPP_c1126217667_state=1. hAPP_p799580910on_com=1. image_1283814551_pname=1. image_187965177_pname=1. image_2131964411e_bool=1. image_47868345e_bool=1. image_54689091_pname=1. image_pname_pname=1. image_1828608335e_bool=1. image_18964633_state=1. image_516545147_state=1. image_70449425e_bool=1. hAPP_f1759205631l_bool=1. hAPP_f667366769l_bool=1. hAPP_f559147733l_bool=1. hAPP_f759274231e_bool=1. cOMBB_307249310e_bool=1. cOMBB_404111180l_bool=1. cOMBB_647938656_pname=1. cOMBB_689948150l_bool=1. cOMBB_699532858_pname=1. cOMBS_1358309691l_bool=1. cOMBS_811933079l_bool=1. fun=1. hAPP_H1621176307_pname=1. hAPP_H356885323e_bool=1. hAPP_f1201187855l_bool=1. hAPP_f1297739591_pname=1. hAPP_f560369737_pname=1. hAPP_f98417237e_bool=1. hAPP_pname_pname=1. image_1619336331_pname=1. image_1705983821_pname=1. cOMBB_1522210668e_bool=1. cOMBB_2144135922_state=1. cOMBB_923936821_pname=1. hAPP_H1187982158l_bool=1. hAPP_f1022807134l_bool=1. hAPP_f1387463497_state=1. hAPP_f1476298914l_bool=1. hAPP_f2143399574l_bool=1. hAPP_f32027384l_bool=1. hAPP_f595608956l_bool=1. hAPP_f637090980l_bool=1. hAPP_f888949707_state=1. hAPP_option_com_com=1. hAPP_p393069232l_bool=1. hAPP_p442853985e_bool=1. image_1210605179l_bool=1. image_1642285373l_bool=1. image_1761575943l_bool=1. image_288317893l_bool=1. image_677922117_state=1. image_892968839_state=1. hAPP_f2134636538on_com=1. hAPP_f2138803836on_com=1. insert1117693814l_bool=1. insert203537868l_bool=1. f23=1. f34=1. f35=1. collec1974731493e_bool=1. collect_pname=1. collec1823980261e_bool=1. collec307967673_state=1. hoare_1598289066_state=1. collec1613912337l_bool=1. cOMBC_1284144636l_bool=1. cOMBC_449066458l_bool=1. collec488126193l_bool=1. dom_pname_com=1. cOMBC_1149511130e_bool=1. cOMBC_654211620e_bool=1. some_com=1. wt=1. cOMBK_1039769424_state=1. cOMBK_1503445380e_bool=1. cOMBK_1589414042e_bool=1. cOMBK_168215364_state=1. cOMBK_1706929794_pname=1. cOMBK_2035509764_state=1. cOMBK_367030522_pname=1. cOMBK_37193422_pname=1. cOMBK_701929478e_bool=1. cOMBK_948730864e_bool=1. cOMBK_pname_pname=1. cOMBC_1058051404l_bool=1. cOMBC_1114453604l_bool=1. cOMBC_1734175330l_bool=1. cOMBC_1988546018l_bool=1. cOMBK_1857069011e_bool=1. cOMBK_bool_pname=1. dom_fu2081503504ol_com=1. cOMBC_1691491604l_bool=1. cOMBC_336095980l_bool=1. cOMBC_747715418l_bool=1. cOMBC_7971162l_bool=1. cOMBK_129401207e_bool=1. cOMBK_482404831l_bool=1. cOMBK_659609255_state=1. dom_fu1342267980ol_com=1. collec256567069l_bool=1. collec792590109l_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. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f33=1. f21=1. f22=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f36=1.
% 0.96/1.48
% 0.96/1.48 ============================== end of process initial clauses ========
% 0.96/1.48
% 0.96/1.48 ============================== CLAUSES FOR SEARCH ====================
% 15.96/16.28
% 15.96/16.28 ============================== end of clauses for search =============
% 15.96/16.28
% 15.96/16.28 ============================== SEARCH ================================
% 15.96/16.28
% 15.96/16.28 % Starting search at 0.28 seconds.
% 15.96/16.28
% 15.96/16.28 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 1.02 sec).
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=43.000, iters=3395
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=39.000, iters=3409
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=38.000, iters=3342
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=37.000, iters=3459
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=34.000, iters=3406
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=33.000, iters=3364
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=32.000, iters=3344
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=30.000, iters=3394
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=29.000, iters=3358
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=27.000, iters=3352
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=26.000, iters=3355
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=25.000, iters=3348
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=22.000, iters=3447
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=19.000, iters=3345
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=18.000, iters=3351
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=17.000, iters=3334
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=16.000, iters=3340
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=15.000, iters=3335
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=14.000, iters=3481
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=13.000, iters=3333
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=12.000, iters=3445
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=10.000, iters=3343
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=9.000, iters=3345
% 15.96/16.28
% 15.96/16.28 Low Water (keep): wt=8.000, iters=3334
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=2981, wt=111.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=2978, wt=95.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4083, wt=81.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=3158, wt=71.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4346, wt=66.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=3157, wt=62.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=2759, wt=61.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4343, wt=58.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=3043, wt=57.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=3129, wt=54.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4115, wt=53.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4389, wt=52.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4359, wt=51.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4123, wt=49.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4910, wt=48.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=4378, wt=47.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=5108, wt=46.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=12880, wt=41.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=13042, wt=34.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=12879, wt=33.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=13051, wt=32.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=15015, wt=27.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=12883, wt=26.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=15456, wt=24.000
% 15.96/16.28
% 15.96/16.28 Low Water (displace): id=15545, wt=8.000
% 15.96/16.28
% 15.96/16.28 ============================== PROOF =================================
% 15.96/16.28 % SZS status Theorem
% 15.96/16.28 % SZS output start Refutation
% 15.96/16.28
% 15.96/16.28 % Proof 1 at 14.76 (+ 0.32) seconds.
% 15.96/16.28 % Length of proof is 69.
% 15.96/16.28 % Level of proof is 10.
% 15.96/16.28 % Maximum clause weight is 23.000.
% 15.96/16.28 % Given clauses 11598.
% 15.96/16.28
% 15.96/16.28 46 (all G all G_1 all Ts (hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts)) -> (hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,G_1),G)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))))) # label(fact_3_thin) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 76 (all A hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),A))) # label(fact_33_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 140 (all C_1 (hBOOL(hoare_165779456gleton) -> (hBOOL(wT_bodies) -> (hBOOL(wt(C_1)) -> hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool))))))) # label(fact_103_MGF) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 178 (all P_1 (collec1823980261e_bool(P_1) = bot_bo535777328l_bool <-> (all X_1 -hBOOL(hAPP_f971112728l_bool(P_1,X_1))))) # label(fact_141_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 215 (all A_2 all P_1 insert1415133716_state(A_2,collec307967673_state(P_1)) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2))),P_1))) # label(fact_183_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 217 (all A_2 all P_1 insert1556680138e_bool(A_2,collec1823980261e_bool(P_1)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2))),P_1))) # label(fact_185_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 219 (all A_2 all B insert1415133716_state(A_2,B) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B)))) # label(fact_187_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 221 (all A_2 all B insert1556680138e_bool(A_2,B) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),B)))) # label(fact_189_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 287 (all P_1 collec307967673_state(P_1) = P_1) # label(fact_255_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 289 (all P_1 collec1823980261e_bool(P_1) = P_1) # label(fact_257_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 310 (all P_1 all A_2 ((hBOOL(hAPP_f971112728l_bool(P_1,A_2)) -> collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)) & (-hBOOL(hAPP_f971112728l_bool(P_1,A_2)) -> collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = bot_bo535777328l_bool))) # label(fact_278_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 312 (all A_2 collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool)) # label(fact_280_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 314 (all A_2 collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)) # label(fact_282_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 316 (all A_2 collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool)) # label(fact_284_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 318 (all A_2 collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)) # label(fact_286_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 320 (all Pn all B_2 (hBOOL(wT_bodies) -> (hAPP_p799580910on_com(body,Pn) = some_com(B_2) -> hBOOL(wt(B_2))))) # label(fact_288_WT__bodiesD) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 364 (all P all Q hAPP_p1422361149_state(cOMBK_367030522_pname(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 366 (all X all Y (X != Y | hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) # label(axiom) # label(non_clause). [assumption].
% 15.96/16.28 453 -hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(A),B)) | -hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),C)) | hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(C),B)) # label(fact_3_thin) # label(axiom). [clausify(46)].
% 15.96/16.28 484 hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),A)) # label(fact_33_empty__subsetI) # label(axiom). [clausify(76)].
% 15.96/16.28 602 -hBOOL(hoare_165779456gleton) | -hBOOL(wT_bodies) | -hBOOL(wt(A)) | hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,A),bot_bo620288102e_bool))) # label(fact_103_MGF) # label(axiom). [clausify(140)].
% 15.96/16.28 650 collec1823980261e_bool(A) != bot_bo535777328l_bool | -hBOOL(hAPP_f971112728l_bool(A,B)) # label(fact_141_Collect__empty__eq) # label(axiom). [clausify(178)].
% 15.96/16.28 725 collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A))),B)) = insert1415133716_state(A,collec307967673_state(B)) # label(fact_183_insert__Collect) # label(axiom). [clausify(215)].
% 15.96/16.28 728 insert1556680138e_bool(A,collec1823980261e_bool(B)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A))),B)) # label(fact_185_insert__Collect) # label(axiom). [clausify(217)].
% 15.96/16.28 729 collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A))),B)) = insert1556680138e_bool(A,collec1823980261e_bool(B)). [copy(728),flip(a)].
% 15.96/16.28 731 collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B))) = insert1415133716_state(A,B) # label(fact_187_insert__compr) # label(axiom). [clausify(219)].
% 15.96/16.28 732 insert1415133716_state(A,B) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B))). [copy(731),flip(a)].
% 15.96/16.28 734 insert1556680138e_bool(A,B) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),B))) # label(fact_189_insert__compr) # label(axiom). [clausify(221)].
% 15.96/16.28 853 collec307967673_state(A) = A # label(fact_255_Collect__def) # label(axiom). [clausify(287)].
% 15.96/16.28 855 collec1823980261e_bool(A) = A # label(fact_257_Collect__def) # label(axiom). [clausify(289)].
% 15.96/16.28 916 -hBOOL(hAPP_f971112728l_bool(A,B)) | insert1556680138e_bool(B,bot_bo535777328l_bool) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,B)),A)) # label(fact_278_Collect__conv__if2) # label(axiom). [clausify(310)].
% 15.96/16.28 917 -hBOOL(hAPP_f971112728l_bool(A,B)) | cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),B)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),bot_bo535777328l_bool)) = cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,B)),A). [copy(916),rewrite([734(4),855(13),855(18)])].
% 15.96/16.28 918 hBOOL(hAPP_f971112728l_bool(A,B)) | collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,B)),A)) = bot_bo535777328l_bool # label(fact_278_Collect__conv__if2) # label(axiom). [clausify(310)].
% 15.96/16.28 919 hBOOL(hAPP_f971112728l_bool(A,B)) | cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,B)),A) = bot_bo535777328l_bool. [copy(918),rewrite([855(8)])].
% 15.96/16.28 922 collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)) = insert1415133716_state(A,bot_bo620288102e_bool) # label(fact_280_singleton__conv) # label(axiom). [clausify(312)].
% 15.96/16.28 923 cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)) = hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A). [copy(922),rewrite([853(4),732(5),853(14)]),flip(a)].
% 15.96/16.28 926 insert1556680138e_bool(A,bot_bo535777328l_bool) = collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A)) # label(fact_282_singleton__conv) # label(axiom). [clausify(314)].
% 15.96/16.28 927 cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),bot_bo535777328l_bool)) = hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A). [copy(926),rewrite([734(2),855(11),855(14)])].
% 15.96/16.28 930 collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,A)) = insert1415133716_state(A,bot_bo620288102e_bool) # label(fact_284_singleton__conv2) # label(axiom). [clausify(316)].
% 15.96/16.28 931 hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A) = hAPP_H1049623551e_bool(fequal1111551311_state,A). [copy(930),rewrite([853(3),732(4),923(12),853(6)]),flip(a)].
% 15.96/16.28 934 insert1556680138e_bool(A,bot_bo535777328l_bool) = collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,A)) # label(fact_286_singleton__conv2) # label(axiom). [clausify(318)].
% 15.96/16.28 935 hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A) = hAPP_f72706945l_bool(fequal1311889615e_bool,A). [copy(934),rewrite([734(2),927(10),855(4),855(6)])].
% 15.96/16.28 942 -hBOOL(wT_bodies) | some_com(A) != hAPP_p799580910on_com(body,B) | hBOOL(wt(A)) # label(fact_288_WT__bodiesD) # label(axiom). [clausify(320)].
% 15.96/16.28 1026 hAPP_p1422361149_state(cOMBK_367030522_pname(A),B) = A # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) # label(axiom). [clausify(364)].
% 15.96/16.28 1028 A != B | hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,B),A)) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) # label(axiom). [clausify(366)].
% 15.96/16.28 1069 hBOOL(hoare_165779456gleton) # label(conj_0) # label(hypothesis). [assumption].
% 15.96/16.28 1070 hBOOL(wT_bodies) # label(conj_1) # label(hypothesis). [assumption].
% 15.96/16.28 1074 hAPP_p799580910on_com(body,pn) = some_com(y) # label(conj_5) # label(hypothesis). [assumption].
% 15.96/16.28 1076 -hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))) # label(conj_7) # label(negated_conjecture). [assumption].
% 15.96/16.28 1077 -hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y))),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),bot_bo620288102e_bool)))). [copy(1076),rewrite([732(12),931(14),853(20)])].
% 15.96/16.28 1103 cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(fequal1111551311_state,A)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B)) = cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(fequal1111551311_state,A))),B). [back_rewrite(725),rewrite([931(5),853(8),853(8),732(8),931(11),853(16)]),flip(a)].
% 15.96/16.28 1115 -hBOOL(wt(A)) | hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,A)))),bot_bo620288102e_bool))). [back_rewrite(602),rewrite([732(12),931(14),1103(19),853(19)]),unit_del(a,1069),unit_del(b,1070)].
% 15.96/16.28 1139 cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(fequal1311889615e_bool,A)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),B)) = cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(fequal1311889615e_bool,A))),B). [back_rewrite(729),rewrite([935(5),855(8),855(8),734(8),935(11),855(16)]),flip(a)].
% 15.96/16.28 1211 bot_bo535777328l_bool != A | -hBOOL(hAPP_f971112728l_bool(A,B)). [back_rewrite(650),rewrite([855(1)]),flip(a)].
% 15.96/16.28 1230 -hBOOL(hAPP_f971112728l_bool(A,B)) | cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(fequal1311889615e_bool,B))),bot_bo535777328l_bool) = cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,B)),A). [back_rewrite(917),rewrite([935(6),1139(11)])].
% 15.96/16.28 1232 cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(fequal1111551311_state,A))),bot_bo620288102e_bool) = hAPP_H1049623551e_bool(fequal1111551311_state,A). [back_rewrite(923),rewrite([931(4),1103(9),931(11)])].
% 15.96/16.28 1241 cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(fequal1311889615e_bool,A))),bot_bo535777328l_bool) = hAPP_f72706945l_bool(fequal1311889615e_bool,A). [back_rewrite(927),rewrite([935(4),1139(9),935(11)])].
% 15.96/16.28 1253 some_com(A) != hAPP_p799580910on_com(body,B) | hBOOL(wt(A)). [back_unit_del(942),unit_del(a,1070)].
% 15.96/16.28 1255 -hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)))). [back_rewrite(1077),rewrite([1103(19),1232(18)])].
% 15.96/16.28 1295 -hBOOL(wt(A)) | hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,A)))). [back_rewrite(1115),rewrite([1232(14)])].
% 15.96/16.28 1296 -hBOOL(hAPP_f971112728l_bool(A,B)) | cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,B)),A) = hAPP_f72706945l_bool(fequal1311889615e_bool,B). [back_rewrite(1230),rewrite([1241(10)]),flip(b)].
% 15.96/16.28 2016 cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A)),hAPP_f72706945l_bool(ord_le1285840794e_bool,B)) = bot_bo535777328l_bool | -hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(B),C)) | hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(A),C)). [resolve(919,a,453,b)].
% 15.96/16.28 2541 hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,A),A)). [resolve(1028,a,1026,a),rewrite([1026(4)])].
% 15.96/16.28 4233 hBOOL(wt(y)). [resolve(1253,a,1074,a(flip))].
% 15.96/16.28 4463 cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A)),hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool)) = hAPP_f72706945l_bool(fequal1311889615e_bool,A). [resolve(1296,a,484,a)].
% 15.96/16.28 4834 hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)))). [resolve(4233,a,1295,a)].
% 15.96/16.28 9684 hAPP_f72706945l_bool(fequal1311889615e_bool,A) != bot_bo535777328l_bool. [resolve(2541,a,1211,b),flip(a)].
% 15.96/16.28 25937 hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(A),hAPP_H1049623551e_bool(fequal1111551311_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)))). [resolve(4834,a,2016,b),rewrite([4463(8)]),unit_del(a,9684)].
% 15.96/16.28 25938 $F. [resolve(25937,a,1255,a)].
% 15.96/16.28
% 15.96/16.28 % SZS output end Refutation
% 15.96/16.28 ============================== end of proof ==========================
% 15.96/16.28
% 15.96/16.28 ============================== STATISTICS ============================
% 15.96/16.28
% 15.96/16.28 Given=11598. Generated=539083. Kept=25375. proofs=1.
% 15.96/16.28 Usable=11441. Sos=9864. Demods=801. Limbo=5, Disabled=4641. Hints=0.
% 15.96/16.28 Megabytes=88.75.
% 15.96/16.28 User_CPU=14.76, System_CPU=0.32, Wall_clock=15.
% 15.96/16.28
% 15.96/16.28 ============================== end of statistics =====================
% 15.96/16.28
% 15.96/16.28 ============================== end of search =========================
% 15.96/16.28
% 15.96/16.28 THEOREM PROVED
% 15.96/16.28 % SZS status Theorem
% 15.96/16.28
% 15.96/16.28 Exiting with 1 proof.
% 15.96/16.28
% 15.96/16.28 Process 23115 exit (max_proofs) Mon Jun 6 03:00:20 2022
% 15.96/16.28 Prover9 interrupted
%------------------------------------------------------------------------------