TSTP Solution File: SWW471+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW471+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 01:17:06 EDT 2022
% Result : Timeout 300.05s 300.27s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW471+2 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 5 08:34:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.39/1.76 ============================== Prover9 ===============================
% 1.39/1.76 Prover9 (32) version 2009-11A, November 2009.
% 1.39/1.76 Process 11994 was started by sandbox on n020.cluster.edu,
% 1.39/1.76 Sun Jun 5 08:34:53 2022
% 1.39/1.76 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11808_n020.cluster.edu".
% 1.39/1.76 ============================== end of head ===========================
% 1.39/1.76
% 1.39/1.76 ============================== INPUT =================================
% 1.39/1.76
% 1.39/1.76 % Reading from file /tmp/Prover9_11808_n020.cluster.edu
% 1.39/1.76
% 1.39/1.76 set(prolog_style_variables).
% 1.39/1.76 set(auto2).
% 1.39/1.76 % set(auto2) -> set(auto).
% 1.39/1.76 % set(auto) -> set(auto_inference).
% 1.39/1.76 % set(auto) -> set(auto_setup).
% 1.39/1.76 % set(auto_setup) -> set(predicate_elim).
% 1.39/1.76 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.39/1.76 % set(auto) -> set(auto_limits).
% 1.39/1.76 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.39/1.76 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.39/1.76 % set(auto) -> set(auto_denials).
% 1.39/1.76 % set(auto) -> set(auto_process).
% 1.39/1.76 % set(auto2) -> assign(new_constants, 1).
% 1.39/1.76 % set(auto2) -> assign(fold_denial_max, 3).
% 1.39/1.76 % set(auto2) -> assign(max_weight, "200.000").
% 1.39/1.76 % set(auto2) -> assign(max_hours, 1).
% 1.39/1.76 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.39/1.76 % set(auto2) -> assign(max_seconds, 0).
% 1.39/1.76 % set(auto2) -> assign(max_minutes, 5).
% 1.39/1.76 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.39/1.76 % set(auto2) -> set(sort_initial_sos).
% 1.39/1.76 % set(auto2) -> assign(sos_limit, -1).
% 1.39/1.76 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.39/1.76 % set(auto2) -> assign(max_megs, 400).
% 1.39/1.76 % set(auto2) -> assign(stats, some).
% 1.39/1.76 % set(auto2) -> clear(echo_input).
% 1.39/1.76 % set(auto2) -> set(quiet).
% 1.39/1.76 % set(auto2) -> clear(print_initial_clauses).
% 1.39/1.76 % set(auto2) -> clear(print_given).
% 1.39/1.76 assign(lrs_ticks,-1).
% 1.39/1.76 assign(sos_limit,10000).
% 1.39/1.76 assign(order,kbo).
% 1.39/1.76 set(lex_order_vars).
% 1.39/1.76 clear(print_given).
% 1.39/1.76
% 1.39/1.76 % formulas(sos). % not echoed (856 formulas)
% 1.39/1.76
% 1.39/1.76 ============================== end of input ==========================
% 1.39/1.76
% 1.39/1.76 % From the command line: assign(max_seconds, 300).
% 1.39/1.76
% 1.39/1.76 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.39/1.76
% 1.39/1.76 % Formulas that are not ordinary clauses:
% 1.39/1.76 1 (all B_1_1 (is_fun_bool_bool(B_1_1) -> is_bool(big_la472677547n_bool(B_1_1)))) # label(gsy_c_Big__Operators_Olattice__class_OInf__fin_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 2 (all B_1_1 (is_fun1661590463l_bool(B_1_1) -> is_fun_pname_bool(big_la28065288e_bool(B_1_1)))) # label(gsy_c_Big__Operators_Olattice__class_OInf__fin_000tc__fun_Itc__Com__Opname_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 3 (all B_1_1 (is_fun_bool_bool(B_1_1) -> is_bool(big_la1480321694n_bool(B_1_1)))) # label(gsy_c_Big__Operators_Olattice__class_OSup__fin_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 4 (all B_1_1 (is_fun1661590463l_bool(B_1_1) -> is_fun_pname_bool(big_la841148155e_bool(B_1_1)))) # label(gsy_c_Big__Operators_Olattice__class_OSup__fin_000tc__fun_Itc__Com__Opname_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 5 (all B_1_1 all B_2_1 is_bool(finite1282449217_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 6 (all B_1_1 all B_2_1 is_bool(finite1669978781iple_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 7 (all B_1_1 all B_2_1 is_bool(finite774711482_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_001) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 8 (all B_1_1 all B_2_1 is_bool(finite89670078_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 9 (all B_1_1 all B_2_1 is_bool(finite950012314iple_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.76 10 (all B_1_1 all B_2_1 is_bool(finite506823037_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O_002) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 11 (all B_1_1 (is_bool(B_1_1) -> is_fun_bool_bool(semila310582991f_bool(B_1_1)))) # label(gsy_c_Lattices_Osemilattice__inf__class_Oinf_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 12 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_pname(hAPP_pname_pname(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 13 (all B_1_1 all B_2_1 (is_fun_pname_bool(B_1_1) & is_pname(B_2_1) -> is_bool(hAPP_pname_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 14 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 15 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun_bool_bool(hAPP_p393069232l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 16 (all B_1_1 all B_2_1 (is_pname(B_2_1) -> is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 17 (all B_1_1 all B_2_1 is_bool(hAPP_state_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 18 (all B_1_1 all B_2_1 is_fun_bool_bool(hAPP_s58564346l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ostate_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 19 (all B_1_1 all B_2_1 (is_fun_bool_bool(B_1_1) & is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 20 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun_pname_bool(hAPP_b76515610e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 21 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun_bool_bool(hAPP_b589554111l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 22 (all B_1_1 all B_2_1 is_pname(hAPP_H676960377_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 23 (all B_1_1 all B_2_1 is_bool(hAPP_H1421470952a_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__HOL__) # label(hypothesis) # label(non_clause). [assumption].
% 1.39/1.77 24 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H1991058245e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__fun_I) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 25 (all B_1_1 all B_2_1 is_fun_bool_bool(hAPP_H1017515220l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__fun_I_003) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 26 (all B_1_1 all B_2_1 is_bool(hAPP_H513860823e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 27 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H1632039476e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_004) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 28 (all B_1_1 all B_2_1 is_fun_bool_bool(hAPP_H226398757l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_005) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 29 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 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].
% 1.39/1.77 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].
% 1.39/1.77 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].
% 1.39/1.77 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].
% 1.39/1.77 34 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f42430548e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__fun_Itc__Com__Opname_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 35 (all B_1_1 all B_2_1 (is_fun_bool_bool(B_2_1) -> is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 36 (all B_1_1 all B_2_1 (is_fun_bool_bool(B_2_1) -> is_fun_bool_bool(hAPP_f961197973l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 37 (all B_1_1 all B_2_1 is_bool(hAPP_f540970102l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_Mtc) # label(hypothesis) # label(non_clause). [assumption].
% 1.39/1.77 38 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f1126670547e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_Mtc_006) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 39 (all B_1_1 all B_2_1 is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 40 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 41 (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_007) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 42 (all B_1_1 all B_2_1 is_bool(hAPP_f1557928608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 43 (all B_1_1 all B_2_1 is_bool(hAPP_f239102607l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It_008) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 44 (all Fun1 all Com all Fun2 all Fun1_2 all Com_1 all Fun2_2 (hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1),Com),Fun2) = hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1_2),Com_1),Fun2_2) <-> Fun1 = Fun1_2 & Com = Com_1 & Fun2 = Fun2_2)) # label(fact_0_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 45 (all Fun1 all Com all Fun2 all Fun1_2 all Com_1 all Fun2_2 (hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_2),Com_1),Fun2_2) <-> Fun1 = Fun1_2 & Com = Com_1 & Fun2 = Fun2_2)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 46 (all Ga all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(Ga),Ts)) <-> (all N ((all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ga)) -> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N),X)))) -> (all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ts)) -> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N),X)))))))) # label(fact_2_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 47 (all Ga all Ts (hBOOL(hAPP_f540970102l_bool(hoare_943851888lids_a(Ga),Ts)) <-> (all N ((all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ga)) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)))) -> (all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ts)) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)))))))) # label(fact_3_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 48 (all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),body)),Qa)),Procsa))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),body)),Qa)),Procsa))))) # label(fact_4_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 49 (all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),body)),Qa)),Procsa))))) # label(fact_5_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 50 (all C all A all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1))))) # label(fact_6_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 51 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1))))) # label(fact_7_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 52 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1))))) # label(fact_8_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 53 (all A all B_1 all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2)) -> (-hBOOL(hAPP_H513860823e_bool(A,X_2)) -> hBOOL(hAPP_H513860823e_bool(B_1,X_2))))) # label(fact_9_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 54 (all A all B_1 all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1),X_2)) -> (-hBOOL(hAPP_pname_bool(A,X_2)) -> hBOOL(hAPP_pname_bool(B_1,X_2))))) # label(fact_10_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 55 (all A all B_1 all X_2 (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2)) -> (-hBOOL(hAPP_H1421470952a_bool(A,X_2)) -> hBOOL(hAPP_H1421470952a_bool(B_1,X_2))))) # label(fact_11_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 56 (all A all B_1 all X_2 ((-hBOOL(hAPP_H513860823e_bool(B_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(A,X_2))) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2)))) # label(fact_12_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 57 (all A all B_1 all X_2 ((-hBOOL(hAPP_pname_bool(B_1,X_2)) -> hBOOL(hAPP_pname_bool(A,X_2))) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1),X_2)))) # label(fact_13_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 58 (all A all B_1 all X_2 ((-hBOOL(hAPP_H1421470952a_bool(B_1,X_2)) -> hBOOL(hAPP_H1421470952a_bool(A,X_2))) -> hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2)))) # label(fact_14_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 59 (all A all C all B_1 ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))))) # label(fact_15_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 60 (all A all C all B_1 ((-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))))) # label(fact_16_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 61 (all A all C all B_1 ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))))) # label(fact_17_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 62 (all A all B all F_1 all X_2 (B = hAPP_p1842370726_state(F_1,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f631639356e_bool(image_275883510_state(F_1),A)))))) # label(fact_18_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 63 (all A all B all F_1 all X_2 (B = hAPP_H676960377_pname(F_1,X_2) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A)))))) # label(fact_19_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 64 (all A all B all F_1 all X_2 (B = hAPP_p263283121iple_a(F_1,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)))))) # label(fact_20_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 65 (all F_1 all A all B_1 hAPP_f631639356e_bool(image_275883510_state(F_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F_1),A)),hAPP_f631639356e_bool(image_275883510_state(F_1),B_1))) # label(fact_21_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 66 (all F_1 all A all B_1 hAPP_f1182387808e_bool(image_1604514514_state(F_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f1182387808e_bool(image_1604514514_state(F_1),A)),hAPP_f1182387808e_bool(image_1604514514_state(F_1),B_1))) # label(fact_22_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 67 (all F_1 all A all B_1 hAPP_f1126670547e_bool(image_2068426537_pname(F_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A)),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),B_1))) # label(fact_23_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 68 (all F_1 all A all B_1 hAPP_f75870650a_bool(image_129517430iple_a(F_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f75870650a_bool(image_129517430iple_a(F_1),A)),hAPP_f75870650a_bool(image_129517430iple_a(F_1),B_1))) # label(fact_24_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 69 (all F_1 all A all B_1 hAPP_f271130963a_bool(image_1654749281iple_a(F_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),B_1))) # label(fact_25_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 70 (all F_1 all G all X (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F_1),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F_1,X)),hAPP_H513860823e_bool(G,X))))) # label(fact_26_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 71 (all F_1 all G all X (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F_1,X)),hAPP_pname_bool(G,X))))) # label(fact_27_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 72 (all F_1 all G all X (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F_1),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1421470952a_bool(F_1,X)),hAPP_H1421470952a_bool(G,X))))) # label(fact_28_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 73 (all F_1 all G all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F_1),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F_1,X_2)),hAPP_H513860823e_bool(G,X_2))))) # label(fact_29_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 74 (all F_1 all G all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F_1,X_2)),hAPP_pname_bool(G,X_2))))) # label(fact_30_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 75 (all F_1 all G all X_2 (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F_1),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1421470952a_bool(F_1,X_2)),hAPP_H1421470952a_bool(G,X_2))))) # label(fact_31_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 76 (all Ga all G_1 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts))))) # label(fact_32_cut) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 77 (all Ga all G_1 all Ts (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(G_1),Ts)) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),G_1)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts))))) # label(fact_33_cut) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 78 (all X_2 all Y_1 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),Z_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1))) # label(fact_34_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 79 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),Z_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1))) # label(fact_35_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 80 (all X_2 all Y_1 all Z_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),Z_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))))) # label(fact_36_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 81 (all X_2 all Y_1 all Z_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),Z_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1))) # label(fact_37_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 82 (all X_2 all Y_1 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),Z_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1))) # label(fact_38_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 83 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),Z_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1))) # label(fact_39_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 84 (all X_2 all Y_1 all Z_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),Z_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))))) # label(fact_40_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 85 (all X_2 all Y_1 all Z_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),Z_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1))) # label(fact_41_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 86 (all A_1 all B all C hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C))) # label(fact_42_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 87 (all A_1 all B all C hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),C) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C))) # label(fact_43_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 88 (all A_1 all B all C (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B)),C)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),C))))) # label(fact_44_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 89 (all A_1 all B all C hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B)),C) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),C))) # label(fact_45_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 90 (all X_2 all Y_1 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1))) # label(fact_46_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 91 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1))) # label(fact_47_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 92 (all X_2 all Y_1 all Z_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))))) # label(fact_48_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 93 (all X_2 all Y_1 all Z_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1))) # label(fact_49_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 94 (all X_2 all Y_1 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1))) # label(fact_50_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 95 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1))) # label(fact_51_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 96 (all X_2 all Y_1 all Z_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))))) # label(fact_52_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 97 (all X_2 all Y_1 all Z_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1))) # label(fact_53_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 98 (all B all A_1 all C hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C))) # label(fact_54_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 99 (all B all A_1 all C hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),C)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C))) # label(fact_55_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 100 (all B all A_1 all C (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),C))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),C))))) # label(fact_56_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 101 (all B all A_1 all C hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),C)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),C))) # label(fact_57_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 102 (all X_2 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) # label(fact_58_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 103 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) # label(fact_59_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 104 (all X_2 all Y_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)))) # label(fact_60_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 105 (all X_2 all Y_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) # label(fact_61_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 106 (all X_2 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) # label(fact_62_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 107 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) # label(fact_63_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 108 (all X_2 all Y_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)))) # label(fact_64_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 109 (all X_2 all Y_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) # label(fact_65_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 110 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) # label(fact_66_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 111 (all A_1 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) # label(fact_67_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 112 (all A_1 all B (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B)))) # label(fact_68_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 113 (all A_1 all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B)) # label(fact_69_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 114 (all X_2 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_2)) # label(fact_70_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 115 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),X_2)) # label(fact_71_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 116 (all X_2 all Y_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),X_2)))) # label(fact_72_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 117 (all X_2 all Y_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),X_2)) # label(fact_73_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 118 (all X_2 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_2)) # label(fact_74_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 119 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),X_2)) # label(fact_75_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 120 (all X_2 all Y_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),X_2)))) # label(fact_76_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 121 (all X_2 all Y_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),X_2)) # label(fact_77_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 122 (all A_1 all B hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1)) # label(fact_78_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 123 (all A_1 all B hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A_1)) # label(fact_79_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 124 (all A_1 all B (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),A_1)))) # label(fact_80_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 125 (all A_1 all B hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),A_1)) # label(fact_81_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 126 (all X_2 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),X_2) = X_2) # label(fact_82_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 127 (all X_2 (is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),X_2) = X_2)) # label(fact_83_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 128 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2)) <-> hBOOL(X_2))) # label(fact_84_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 129 (all X_2 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),X_2) = X_2) # label(fact_85_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 130 (all A_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),A_1) = A_1) # label(fact_86_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 131 (all A_1 (is_fun_pname_bool(A_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),A_1) = A_1)) # label(fact_87_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 132 (all A_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),A_1)) <-> hBOOL(A_1))) # label(fact_88_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 133 (all A_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),A_1) = A_1) # label(fact_89_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 134 (all B all F_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (B = hAPP_p1842370726_state(F_1,X_2) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f631639356e_bool(image_275883510_state(F_1),A)))))) # label(fact_90_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 135 (all B all F_1 all X_2 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> (B = hAPP_H676960377_pname(F_1,X_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A)))))) # label(fact_91_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 136 (all B all F_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (B = hAPP_p263283121iple_a(F_1,X_2) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)))))) # label(fact_92_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 137 (all F_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F_1,X_2)),hAPP_f631639356e_bool(image_275883510_state(F_1),A))))) # label(fact_93_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 138 (all F_1 all X_2 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H676960377_pname(F_1,X_2)),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A))))) # label(fact_94_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 139 (all F_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_p263283121iple_a(F_1,X_2)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))))) # label(fact_95_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 140 (all Z_1 all F_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Z_1),hAPP_f631639356e_bool(image_275883510_state(F_1),A))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) & Z_1 = hAPP_p1842370726_state(F_1,X))))) # label(fact_96_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 141 (all Z_1 all F_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Z_1),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) & Z_1 = hAPP_p263283121iple_a(F_1,X))))) # label(fact_97_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 142 (all A all C all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))))) # label(fact_98_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 143 (all A all C all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))))) # label(fact_99_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 144 (all A all C all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))))) # label(fact_100_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 145 (all B_1 all C all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))))) # label(fact_101_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 146 (all B_1 all C all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))))) # label(fact_102_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 147 (all B_1 all C all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))))) # label(fact_103_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 148 (all A all B_1 all X_2 (hBOOL(hAPP_H513860823e_bool(B_1,X_2)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2)))) # label(fact_104_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 149 (all A all B_1 all X_2 (hBOOL(hAPP_pname_bool(B_1,X_2)) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1),X_2)))) # label(fact_105_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 150 (all A all B_1 all X_2 (hBOOL(hAPP_H1421470952a_bool(B_1,X_2)) -> hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2)))) # label(fact_106_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 151 (all B_1 all A all X_2 (hBOOL(hAPP_H513860823e_bool(A,X_2)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2)))) # label(fact_107_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 152 (all B_1 all A all X_2 (hBOOL(hAPP_pname_bool(A,X_2)) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1),X_2)))) # label(fact_108_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 153 (all B_1 all A all X_2 (hBOOL(hAPP_H1421470952a_bool(A,X_2)) -> hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2)))) # label(fact_109_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 154 (all Pa all A all B_1 ((all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) -> hBOOL(hAPP_H513860823e_bool(Pa,X)))) <-> (all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A)) -> hBOOL(hAPP_H513860823e_bool(Pa,X)))) & (all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),B_1)) -> hBOOL(hAPP_H513860823e_bool(Pa,X)))))) # label(fact_110_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 155 (all Pa all A all B_1 ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) -> hBOOL(hAPP_pname_bool(Pa,X))))) <-> (all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) -> hBOOL(hAPP_pname_bool(Pa,X))))) & (all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_1)) -> hBOOL(hAPP_pname_bool(Pa,X))))))) # label(fact_111_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 156 (all Pa all A all B_1 ((all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) -> hBOOL(hAPP_H1421470952a_bool(Pa,X)))) <-> (all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A)) -> hBOOL(hAPP_H1421470952a_bool(Pa,X)))) & (all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),B_1)) -> hBOOL(hAPP_H1421470952a_bool(Pa,X)))))) # label(fact_112_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 157 (all Pa all A all B_1 ((exists X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) & hBOOL(hAPP_H513860823e_bool(Pa,X)))) <-> (exists X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A)) & hBOOL(hAPP_H513860823e_bool(Pa,X)))) | (exists X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),B_1)) & hBOOL(hAPP_H513860823e_bool(Pa,X)))))) # label(fact_113_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 158 (all Pa all A all B_1 ((exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) & hBOOL(hAPP_pname_bool(Pa,X)))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) & hBOOL(hAPP_pname_bool(Pa,X)))) | (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_1)) & hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_114_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 159 (all Pa all A all B_1 ((exists X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) & hBOOL(hAPP_H1421470952a_bool(Pa,X)))) <-> (exists X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A)) & hBOOL(hAPP_H1421470952a_bool(Pa,X)))) | (exists X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),B_1)) & hBOOL(hAPP_H1421470952a_bool(Pa,X)))))) # label(fact_115_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 160 (all A all B_1 all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1))) # label(fact_116_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 161 (all A all B_1 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1))) # label(fact_117_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 162 (all A all B_1 all C_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1))) # label(fact_118_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 163 (all C all A all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A)) | hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1)))) # label(fact_119_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 164 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) | hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)))) # label(fact_120_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 165 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)))) # label(fact_121_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 166 (all A all B_1 all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),C_1))) # label(fact_122_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 167 (all A all B_1 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1))) # label(fact_123_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 168 (all A all B_1 all C_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),C_1))) # label(fact_124_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 169 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) # label(fact_125_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 170 (all A all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) # label(fact_126_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 171 (all A all B_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) # label(fact_127_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 172 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A)) # label(fact_128_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 173 (all A all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A)) # label(fact_129_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 174 (all A all B_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),A)) # label(fact_130_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 175 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B_1)))) # label(fact_131_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 176 (all A all B_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),A))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B_1)))) # label(fact_132_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 177 (all A all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_1)))) # label(fact_133_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 178 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),A) = A) # label(fact_134_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 179 (all A (is_fun_pname_bool(A) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),A) = A)) # label(fact_135_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 180 (all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),A) = A) # label(fact_136_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 181 (all F_1 all G all A hAPP_f1182387808e_bool(image_1604514514_state(F_1),hAPP_f271130963a_bool(image_1654749281iple_a(G),A)) = hAPP_f631639356e_bool(image_275883510_state(hAPP_f1026488024_state(cOMBB_2118237115_pname(F_1),G)),A)) # label(fact_137_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 182 (all F_1 all G all A hAPP_f75870650a_bool(image_129517430iple_a(F_1),hAPP_f631639356e_bool(image_275883510_state(G),A)) = hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f113652738iple_a(cOMBB_2015474199_pname(F_1),G)),A)) # label(fact_138_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 183 (all R_1 all S_1 all X (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S_1)),X)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,R_1),S_1))))) # label(fact_139_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 184 (all R_1 all S_1 all X (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),R_1)),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),S_1)),X)) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,R_1),S_1))))) # label(fact_140_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 185 (all R_1 all S_1 all X (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S_1)),X)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S_1))))) # label(fact_141_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 186 (all Pa all Qa hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),Pa)),Qa)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,Pa)),hAPP_f759274231e_bool(collect_pname,Qa))) # label(fact_142_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 187 (all Pa all Qa hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),Pa)),Qa)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,Pa)),hAPP_f921536533e_bool(collec727977250_state,Qa))) # label(fact_143_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 188 (all Pa all Qa hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),Pa)),Qa)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(collec268032053iple_a,Pa)),hAPP_f1591852335a_bool(collec268032053iple_a,Qa))) # label(fact_144_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 189 (all B all F_1 all A (is_pname(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A))) -> -(all X (B = hAPP_H676960377_pname(F_1,X) -> -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))))))) # label(fact_145_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 190 (all B all F_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f631639356e_bool(image_275883510_state(F_1),A))) -> -(all X (is_pname(X) -> (B = hAPP_p1842370726_state(F_1,X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))))))) # label(fact_146_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 191 (all B all F_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))) -> -(all X (is_pname(X) -> (B = hAPP_p263283121iple_a(F_1,X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))))))) # label(fact_147_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 192 (all N_1 all Pa all Pn_1 all Qa (hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_1),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa))) <-> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(suc(N_1)),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa))))) # label(fact_148_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 193 (all N_1 all Pa all Pn_1 all Qa (hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_1),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa))) <-> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(suc(N_1)),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))))) # label(fact_149_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 194 (all Y_1 -(all Fun1_1 all Com_2 all Fun2_1 Y_1 != hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1_1),Com_2),Fun2_1))) # label(fact_150_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 195 (all Y_1 -(all Fun1_1 all Com_2 all Fun2_1 Y_1 != hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_1),Com_2),Fun2_1))) # label(fact_151_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 196 (all Pn_1 all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),body)),Qa)),Procsa))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa))) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procsa)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p1637813682e_bool(Qa,Pn_1))),bot_bo1055319631e_bool)))))) # label(fact_152_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 197 (all Pn_1 all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa))) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procsa)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_p635540397e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p635540397e_bool(Qa,Pn_1))),bot_bo1181479936a_bool)))))) # label(fact_153_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 198 (all F_1 all G all M_3 all N_3 (M_3 = N_3 -> ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3)) -> hAPP_p1842370726_state(F_1,X) = hAPP_p1842370726_state(G,X)))) -> hAPP_f631639356e_bool(image_275883510_state(F_1),M_3) = hAPP_f631639356e_bool(image_275883510_state(G),N_3)))) # label(fact_154_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 199 (all F_1 all G all M_3 all N_3 (M_3 = N_3 -> ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3)) -> hAPP_p263283121iple_a(F_1,X) = hAPP_p263283121iple_a(G,X)))) -> hAPP_f271130963a_bool(image_1654749281iple_a(F_1),M_3) = hAPP_f271130963a_bool(image_1654749281iple_a(G),N_3)))) # label(fact_155_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 200 (all Pa all Pn_1 all Qa hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(zero_zero_nat),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)))) # label(fact_156_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 201 (all Pa all Pn_1 all Qa hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(zero_zero_nat),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)))) # label(fact_157_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 202 (all Pname_3 all Pname_2 (is_pname(Pname_3) & is_pname(Pname_2) -> (hAPP_pname_com(body,Pname_3) = hAPP_pname_com(body,Pname_2) <-> Pname_3 = Pname_2))) # label(fact_158_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 203 (all Pn all S0 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn))),S0),S1_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,Pn)),S0),S1_1)))) # label(fact_159_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 204 (all P all S_2 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,P)),S_2),S1_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P))),S_2),S1_1)))) # label(fact_160_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 205 (all X_2 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),X_2) = X_2) # label(fact_161_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 206 (all X_2 (is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),X_2) = X_2)) # label(fact_162_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 207 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2)) <-> hBOOL(X_2))) # label(fact_163_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 208 (all X_2 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),X_2) = X_2) # label(fact_164_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 209 (all A_1 -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),bot_bo1181479936a_bool))) # label(fact_165_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 210 (all A_1 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),bot_bo1055319631e_bool))) # label(fact_166_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 211 (all A_1 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),bot_bo844097828e_bool))) # label(fact_167_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 212 (all A_1 all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A))) -> (A_1 != B -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))))) # label(fact_168_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 213 (all A_1 all B all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),A))) -> (A_1 != B -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))))) # label(fact_169_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 214 (all A_1 all B all A (is_pname(A_1) & is_pname(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),A))) -> (A_1 != B -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)))))) # label(fact_170_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 215 (all B all A_1 all B_1 ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B_1)) -> A_1 = B) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))))) # label(fact_171_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 216 (all B all A_1 all B_1 ((-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B_1)) -> A_1 = B) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),B_1))))) # label(fact_172_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 217 (all B all A_1 all B_1 ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_1)) -> A_1 = B) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),B_1))))) # label(fact_173_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 218 (all A_1 all A bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)) # label(fact_174_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 219 (all A_1 all A bot_bo1181479936a_bool != hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)) # label(fact_175_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 220 (all A_1 all A bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A)) # label(fact_176_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 221 (all A_1 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) != bot_bo1055319631e_bool) # label(fact_177_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 222 (all A_1 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) != bot_bo1181479936a_bool) # label(fact_178_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 223 (all A_1 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A) != bot_bo844097828e_bool) # label(fact_179_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.77 224 (all X (hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X)) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),bot_bo1181479936a_bool)))) # label(fact_180_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 225 (all X (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),bot_bo1055319631e_bool)))) # label(fact_181_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 226 (all X (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),bot_bo844097828e_bool)))) # label(fact_182_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 227 (all A_1 all B_1 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)))) # label(fact_186_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 228 (all A_1 all B_1 hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)))) # label(fact_187_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 229 (all A_1 all B_1 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)))) # label(fact_188_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 230 (all A ((all X -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))) <-> A = bot_bo1181479936a_bool)) # label(fact_189_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 231 (all A ((all X -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A))) <-> A = bot_bo1055319631e_bool)) # label(fact_190_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 232 (all A (is_fun_pname_bool(A) -> ((all X (is_pname(X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)))) <-> A = bot_bo844097828e_bool))) # label(fact_191_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 233 (all A_1 hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) # label(fact_192_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 234 (all A_1 hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_H1190454433a_bool(fequal879838495iple_a,A_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) # label(fact_193_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 235 (all A_1 hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)) # label(fact_194_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 236 (all A ((exists X hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))) <-> A != bot_bo1181479936a_bool)) # label(fact_195_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 237 (all A ((exists X hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A))) <-> A != bot_bo1055319631e_bool)) # label(fact_196_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 238 (all A (is_fun_pname_bool(A) -> ((exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)))) <-> A != bot_bo844097828e_bool))) # label(fact_197_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 239 (all A_1 hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) # label(fact_198_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 240 (all A_1 hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) # label(fact_199_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 241 (all A_1 hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)) # label(fact_200_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 242 (all Pa all A_1 ((hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A_1))),Pa)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) & (-hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A_1))),Pa)) = bot_bo1055319631e_bool))) # label(fact_201_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 243 (all Pa all A_1 ((hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(fequal879838495iple_a,A_1))),Pa)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) & (-hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(fequal879838495iple_a,A_1))),Pa)) = bot_bo1181479936a_bool))) # label(fact_202_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 244 (all Pa all A_1 ((hBOOL(hAPP_pname_bool(Pa,A_1)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A_1))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_1)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A_1))),Pa)) = bot_bo844097828e_bool))) # label(fact_203_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 245 (all Pa all A_1 ((hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),Pa)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)) & (-hBOOL(hAPP_H513860823e_bool(Pa,A_1)) -> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),Pa)) = bot_bo1055319631e_bool))) # label(fact_204_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 246 (all Pa all A_1 ((hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),Pa)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)) & (-hBOOL(hAPP_H1421470952a_bool(Pa,A_1)) -> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),Pa)) = bot_bo1181479936a_bool))) # label(fact_205_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 247 (all Pa all A_1 ((hBOOL(hAPP_pname_bool(Pa,A_1)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_1)) -> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),Pa)) = bot_bo844097828e_bool))) # label(fact_206_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 248 (all Pa (bot_bo1181479936a_bool = hAPP_f1591852335a_bool(collec268032053iple_a,Pa) <-> (all X -hBOOL(hAPP_H1421470952a_bool(Pa,X))))) # label(fact_207_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 249 (all Pa (bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,Pa) <-> (all X (is_pname(X) -> -hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_208_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 250 (all Pa (bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,Pa) <-> (all X -hBOOL(hAPP_H513860823e_bool(Pa,X))))) # label(fact_209_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 251 (all X_2 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) <-> hBOOL(hAPP_H1421470952a_bool(A,X_2)))) # label(fact_210_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 252 (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_211_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 253 (all Pa hAPP_f1591852335a_bool(collec268032053iple_a,Pa) = Pa) # label(fact_212_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 254 (all Pa (is_fun_pname_bool(Pa) -> hAPP_f759274231e_bool(collect_pname,Pa) = Pa)) # label(fact_213_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 255 (all C -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),bot_bo1181479936a_bool))) # label(fact_214_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 256 (all C -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),bot_bo1055319631e_bool))) # label(fact_215_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 257 (all C -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool))) # label(fact_216_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 258 (all A_1 all B_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B_1)))) # label(fact_217_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 259 (all A_1 all B_1 hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B_1)))) # label(fact_218_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 260 (all A_1 all B_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_1)))) # label(fact_219_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 261 (all A_1 all Pa hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(collec727977250_state,Pa)) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fimplies),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1)))),Pa))) # label(fact_220_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 262 (all A_1 all Pa hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(collec268032053iple_a,Pa)) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fimplies),hAPP_f1591852335a_bool(cOMBB_1799513916iple_a(fNot),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1)))),Pa))) # label(fact_221_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 263 (all A_1 all Pa hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(collect_pname,Pa)) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fimplies),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1)))),Pa))) # label(fact_222_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 264 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))) <-> B = A_1)) # label(fact_223_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 265 (all B all A_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))) <-> B = A_1)) # label(fact_224_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 266 (all B all A_1 (is_pname(B) & is_pname(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool))) <-> B = A_1))) # label(fact_225_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 267 (all X_2 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) # label(fact_226_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 268 (all X_2 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) # label(fact_227_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 269 (all X_2 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) # label(fact_228_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 270 (all X_2 all Y_1 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A))) # label(fact_229_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 271 (all X_2 all Y_1 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_1),A)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A))) # label(fact_230_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 272 (all X_2 all Y_1 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A))) # label(fact_231_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 273 (all A_1 all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A))) <-> A_1 = B | hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)))) # label(fact_232_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 274 (all A_1 all B all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),A))) <-> A_1 = B | hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)))) # label(fact_233_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 275 (all A_1 all B all A (is_pname(A_1) & is_pname(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),A))) <-> A_1 = B | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))))) # label(fact_234_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 276 (all Pa (hAPP_f1591852335a_bool(collec268032053iple_a,Pa) = bot_bo1181479936a_bool <-> (all X -hBOOL(hAPP_H1421470952a_bool(Pa,X))))) # label(fact_235_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 277 (all Pa (hAPP_f759274231e_bool(collect_pname,Pa) = bot_bo844097828e_bool <-> (all X (is_pname(X) -> -hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_236_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 278 (all Pa (hAPP_f921536533e_bool(collec727977250_state,Pa) = bot_bo1055319631e_bool <-> (all X -hBOOL(hAPP_H513860823e_bool(Pa,X))))) # label(fact_237_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 279 (all A_1 all B all C all D (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D),bot_bo1055319631e_bool)) <-> A_1 = C & B = D | A_1 = D & B = C)) # label(fact_238_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 280 (all A_1 all B all C all D (hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),bot_bo1181479936a_bool)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,C),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,D),bot_bo1181479936a_bool)) <-> A_1 = C & B = D | A_1 = D & B = C)) # label(fact_239_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 281 (all A_1 all B all C all D (is_pname(A_1) & is_pname(B) & is_pname(C) & is_pname(D) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D),bot_bo844097828e_bool)) <-> A_1 = C & B = D | A_1 = D & B = C))) # label(fact_240_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 282 (all Y_1 all A all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_H513860823e_bool(A,X_2)))) # label(fact_241_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 283 (all Y_1 all A all X_2 (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_1),A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_H1421470952a_bool(A,X_2)))) # label(fact_242_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 284 (all Y_1 all A all X_2 (is_pname(Y_1) & is_pname(X_2) -> (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_pname_bool(A,X_2))))) # label(fact_243_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 285 (all B_1 all X_2 all A (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) -> (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1) <-> A = B_1)))) # label(fact_244_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 286 (all B_1 all X_2 all A (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),B_1)) -> (hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),B_1) <-> A = B_1)))) # label(fact_245_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 287 (all B_1 all X_2 all A (is_fun_pname_bool(B_1) & 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_1)) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_1) <-> A = B_1))))) # label(fact_246_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 288 (all A_1 all A (A = bot_bo1181479936a_bool -> -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)))) # label(fact_247_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 289 (all A_1 all A (A = bot_bo1055319631e_bool -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)))) # label(fact_248_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 290 (all A_1 all A (A = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)))) # label(fact_249_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 291 (all B all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))))) # label(fact_250_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 292 (all B all A_1 all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B_1)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),B_1))))) # label(fact_251_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 293 (all B all A_1 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),B_1))))) # label(fact_252_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 294 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) = A)) # label(fact_253_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 295 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) = A)) # label(fact_254_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 296 (all A_1 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A) = A))) # label(fact_255_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 297 (all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool))) -> B = A_1)) # label(fact_256_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 298 (all B all A_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool))) -> B = A_1)) # label(fact_257_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 299 (all B all A_1 (is_pname(B) & is_pname(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool))) -> B = A_1))) # label(fact_258_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 300 (all A_1 all B (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool) -> A_1 = B)) # label(fact_259_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 301 (all A_1 all B (hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),bot_bo1181479936a_bool) -> A_1 = B)) # label(fact_260_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 302 (all A_1 all B (is_pname(A_1) & is_pname(B) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),bot_bo844097828e_bool) -> A_1 = B))) # label(fact_261_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 303 (all U_1 all C_2 all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),U_1)) -> U_1 = T_1))) # label(fact_262_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 304 (all A_1 all A hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)),A)) # label(fact_263_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 305 (all A_1 all A hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)),A)) # label(fact_264_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 306 (all A_1 all A hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)),A)) # label(fact_265_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 307 (all X all Xa hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),Xa) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),X))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),Xa)))) # label(fact_266_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 308 (all X all Xa hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),Xa) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),X))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),Xa)))) # label(fact_267_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 309 (all X all Xa hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),Xa) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),X))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),Xa)))) # label(fact_268_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 310 (all Ga all T all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))) & hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts)))) # label(fact_269_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 311 (all Ga all T all Ts (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),Ts))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),bot_bo1181479936a_bool))) & hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts)))) # label(fact_270_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 312 (all Ts all Ga all T (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts)))))) # label(fact_271_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 313 (all Ts all Ga all T (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),bot_bo1181479936a_bool))) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),Ts)))))) # label(fact_272_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 314 (all C all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> hAPP_f631639356e_bool(image_275883510_state(hAPP_H1797237070_state(cOMBK_90103121_pname,C)),A) = bot_bo1055319631e_bool) & (A != bot_bo844097828e_bool -> hAPP_f631639356e_bool(image_275883510_state(hAPP_H1797237070_state(cOMBK_90103121_pname,C)),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool)))) # label(fact_273_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 315 (all C all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_pname,C)),A) = bot_bo1181479936a_bool) & (A != bot_bo844097828e_bool -> hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_pname,C)),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,C),bot_bo1181479936a_bool)))) # label(fact_274_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 316 (all C all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f631639356e_bool(image_275883510_state(hAPP_H1797237070_state(cOMBK_90103121_pname,C)),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool))) # label(fact_275_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 317 (all C all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f759274231e_bool(image_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool))) # label(fact_276_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 318 (all C all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_pname,C)),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,C),bot_bo1181479936a_bool))) # label(fact_277_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 319 (all F_1 all A_1 all B_1 hAPP_f631639356e_bool(image_275883510_state(F_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F_1,A_1)),hAPP_f631639356e_bool(image_275883510_state(F_1),B_1))) # label(fact_278_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 320 (all F_1 all A_1 all B_1 hAPP_f271130963a_bool(image_1654749281iple_a(F_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_p263283121iple_a(F_1,A_1)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),B_1))) # label(fact_279_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 321 (all F_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F_1,X_2)),hAPP_f631639356e_bool(image_275883510_state(F_1),A)) = hAPP_f631639356e_bool(image_275883510_state(F_1),A))) # label(fact_280_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 322 (all F_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_pname_pname(F_1,X_2)),hAPP_f759274231e_bool(image_pname_pname(F_1),A)) = hAPP_f759274231e_bool(image_pname_pname(F_1),A))) # label(fact_281_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 323 (all F_1 all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_p263283121iple_a(F_1,X_2)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)) = hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))) # label(fact_282_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 324 (all A all A_1 all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) # label(fact_283_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 325 (all A all A_1 all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) # label(fact_284_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 326 (all A all A_1 all B_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) # label(fact_285_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 327 (all A_1 all B_1 all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1))) # label(fact_286_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 328 (all A_1 all B_1 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1))) # label(fact_287_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 329 (all A_1 all B_1 all C_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1))) # label(fact_288_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 330 (all F_1 all A (is_fun_pname_bool(A) -> (bot_bo1055319631e_bool = hAPP_f631639356e_bool(image_275883510_state(F_1),A) <-> A = bot_bo844097828e_bool))) # label(fact_289_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 331 (all F_1 all A (is_fun_pname_bool(A) -> (bot_bo1181479936a_bool = hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A) <-> A = bot_bo844097828e_bool))) # label(fact_290_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 332 (all F_1 hAPP_f631639356e_bool(image_275883510_state(F_1),bot_bo844097828e_bool) = bot_bo1055319631e_bool) # label(fact_291_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 333 (all F_1 hAPP_f271130963a_bool(image_1654749281iple_a(F_1),bot_bo844097828e_bool) = bot_bo1181479936a_bool) # label(fact_292_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 334 (all F_1 all A (is_fun_pname_bool(A) -> (hAPP_f631639356e_bool(image_275883510_state(F_1),A) = bot_bo1055319631e_bool <-> A = bot_bo844097828e_bool))) # label(fact_293_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 335 (all F_1 all A (is_fun_pname_bool(A) -> (hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A) = bot_bo1181479936a_bool <-> A = bot_bo844097828e_bool))) # label(fact_294_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 336 (all Pa all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),bot_bo1055319631e_bool)) -> hBOOL(hAPP_H513860823e_bool(Pa,X)))) # label(fact_295_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 337 (all Pa all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),bot_bo1181479936a_bool)) -> hBOOL(hAPP_H1421470952a_bool(Pa,X)))) # label(fact_296_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 338 (all Pa all X (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),bot_bo844097828e_bool)) -> hBOOL(hAPP_pname_bool(Pa,X)))) # label(fact_297_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 339 (all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),B_1) = B_1) # label(fact_298_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 340 (all B_1 (is_fun_pname_bool(B_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B_1) = B_1)) # label(fact_299_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 341 (all B_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,bot_bo1181479936a_bool),B_1) = B_1) # label(fact_300_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 342 (all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),bot_bo1055319631e_bool) = A) # label(fact_301_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 343 (all A (is_fun_pname_bool(A) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),bot_bo844097828e_bool) = A)) # label(fact_302_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 344 (all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),bot_bo1181479936a_bool) = A) # label(fact_303_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 345 (all A all B_1 (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = bot_bo1055319631e_bool <-> A = bot_bo1055319631e_bool & B_1 = bot_bo1055319631e_bool)) # label(fact_304_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 346 (all A all B_1 (is_fun_pname_bool(A) & is_fun_pname_bool(B_1) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) = bot_bo844097828e_bool <-> A = bot_bo844097828e_bool & B_1 = bot_bo844097828e_bool))) # label(fact_305_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 347 (all A all B_1 (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) = bot_bo1181479936a_bool <-> A = bot_bo1181479936a_bool & B_1 = bot_bo1181479936a_bool)) # label(fact_306_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 348 (all Ga all Pa all C all Qa all C_1 ((hBOOL(C_1) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool)))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),Pa))),C_1)),C),Qa)),bot_bo1181479936a_bool))))) # label(fact_307_constant) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 349 (all Ga all Pa all C all Qa all C_1 ((hBOOL(C_1) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(cOMBB_1757942702_state(cOMBC_231445413l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),Pa))),C_1)),C),Qa)),bot_bo1055319631e_bool))))) # label(fact_308_constant) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 350 (all Ga hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),bot_bo1055319631e_bool))) # label(fact_309_empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 351 (all Ga hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),bot_bo1181479936a_bool))) # label(fact_310_empty) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 352 (all X_2 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),X_2) = X_2) # label(fact_311_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 353 (all X_2 (is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),X_2) = X_2)) # label(fact_312_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 354 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,bot_bot_bool),X_2)) <-> hBOOL(X_2))) # label(fact_313_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 355 (all X_2 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,bot_bo1181479936a_bool),X_2) = X_2) # label(fact_314_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 356 (all X_2 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),bot_bo1055319631e_bool) = X_2) # label(fact_315_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 357 (all X_2 (is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),bot_bo844097828e_bool) = X_2)) # label(fact_316_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 358 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),bot_bot_bool)) <-> hBOOL(X_2))) # label(fact_317_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 359 (all X_2 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),bot_bo1181479936a_bool) = X_2) # label(fact_318_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 360 (all X_2 all Y_1 (hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) = bot_bo1055319631e_bool <-> X_2 = bot_bo1055319631e_bool & Y_1 = bot_bo1055319631e_bool)) # label(fact_319_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 361 (all X_2 all Y_1 (is_fun_pname_bool(X_2) & is_fun_pname_bool(Y_1) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) = bot_bo844097828e_bool <-> X_2 = bot_bo844097828e_bool & Y_1 = bot_bo844097828e_bool))) # label(fact_320_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 362 (all X_2 all Y_1 ((hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)) <-> hBOOL(bot_bot_bool)) <-> (hBOOL(X_2) <-> hBOOL(bot_bot_bool)) & (hBOOL(Y_1) <-> hBOOL(bot_bot_bool)))) # label(fact_321_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 363 (all X_2 all Y_1 (hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) = bot_bo1181479936a_bool <-> X_2 = bot_bo1181479936a_bool & Y_1 = bot_bo1181479936a_bool)) # label(fact_322_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 364 (all N_4 all T_2 (hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(suc(N_4)),T_2)) -> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_4),T_2)))) # label(fact_323_triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 365 (all N_4 all T_2 (hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(suc(N_4)),T_2)) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_4),T_2)))) # label(fact_324_triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 366 (all A_1 all B_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),B_1)) # label(fact_325_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 367 (all A_1 all B_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),B_1)) # label(fact_326_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 368 (all A_1 all B_1 hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),B_1)) # label(fact_327_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 369 (all Ga all Pa all Pn_1 all Qa (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1181479936a_bool))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1181479936a_bool))))) # label(fact_328_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 370 (all Ga all Pa all Pn_1 all Qa (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1055319631e_bool))))) # label(fact_329_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 371 (all Pa all Pn_1 all Qa all Ga (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1181479936a_bool))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1181479936a_bool))))) # label(fact_330_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 372 (all Pa all Pn_1 all Qa all Ga (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1055319631e_bool))))) # label(fact_331_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 373 (all N_1 all Ts ((all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ts)) -> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(suc(N_1)),X)))) -> (all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ts)) -> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_1),X)))))) # label(fact_332_triples__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 374 (all N_1 all Ts ((all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ts)) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(suc(N_1)),X)))) -> (all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ts)) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_1),X)))))) # label(fact_333_triples__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 375 (all Ga all C all Qa all Pa ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3)) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(Qa,Z_3)))),bot_bo1181479936a_bool))))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool))))) # label(fact_334_escape) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 376 (all Ga all C all Qa all Pa ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Qa,Z_3)))),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool))))) # label(fact_335_escape) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 377 (all Pa all Ga all P_1 all C all Qa (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,P_1),C),Qa)),bot_bo1181479936a_bool))) -> ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_3),S_3)))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool)))))) # label(fact_336_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 378 (all Pa all Ga all P_1 all C all Qa (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Qa)),bot_bo1055319631e_bool))) -> ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_3),S_3)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool)))))) # label(fact_337_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 379 (all Qa all Ga all Pa all C all Q_1 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Q_1)),bot_bo1181479936a_bool))) -> ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_3),S_3)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_3),S_3)))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool)))))) # label(fact_338_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 380 (all Qa all Ga all Pa all C all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Q_1)),bot_bo1055319631e_bool))) -> ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_3),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_3),S_3)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool)))))) # label(fact_339_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 381 (all Fa all Fun1 all Com all Fun2 hoare_1674107620_state(Fa,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2)) = zero_zero_nat) # label(fact_340_triple_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 382 (all Fa all Fun1 all Com all Fun2 hoare_953425885size_a(Fa,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1),Com),Fun2)) = zero_zero_nat) # label(fact_341_triple_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 383 (all C hoare_Mirabelle_MGT(C) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,fequal_state),C),evalc(C))) # label(fact_342_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 384 (all Fun1 all Com all Fun2 size_s346246881_state(hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2)) = zero_zero_nat) # label(fact_343_triple_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 385 (all Fun1 all Com all Fun2 size_s315943222iple_a(hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1),Com),Fun2)) = zero_zero_nat) # label(fact_344_triple_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 386 (all Qa all Pa all Ga all P_1 all C all Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) -> ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3)) -> (all S_4 ((all Z_4 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_4),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_4),S_4)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_3),S_4)))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool)))))) # label(fact_345_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 387 (all Qa all Pa all Ga all P_1 all C all Q_1 (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,P_1),C),Q_1)),bot_bo1181479936a_bool))) -> ((all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3)) -> (all S_4 ((all Z_4 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_4),S_3)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_4),S_4)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_3),S_4)))))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool)))))) # label(fact_346_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 388 (all X_2 hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2) # label(fact_347_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 389 (all X_2 hAPP_f124283079iple_a(the_el1436340927iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),bot_bo1181479936a_bool)) = X_2) # label(fact_348_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 390 (all X_2 (is_pname(X_2) -> hAPP_f1297739591_pname(the_elem_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = X_2)) # label(fact_349_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 391 (all M zero_zero_nat != suc(M)) # label(fact_350_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 392 (all Nat_4 zero_zero_nat != suc(Nat_4)) # label(fact_351_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 393 (all M suc(M) != zero_zero_nat) # label(fact_352_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 394 (all Nat_3 suc(Nat_3) != zero_zero_nat) # label(fact_353_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 395 (all M zero_zero_nat != suc(M)) # label(fact_354_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 396 (all M suc(M) != zero_zero_nat) # label(fact_355_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 397 (all X (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_356_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 398 (all X (hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_357_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 399 (all X (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_358_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 400 (all X_1 all Y (suc(X_1) = suc(Y) -> X_1 = Y)) # label(fact_360_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 401 (all Nat_2 all Nat_1 (suc(Nat_2) = suc(Nat_1) <-> Nat_2 = Nat_1)) # label(fact_361_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 402 (all N_2 suc(N_2) != N_2) # label(fact_362_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 403 (all N_2 N_2 != suc(N_2)) # label(fact_363_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 404 (all X_2 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_364_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 405 (all X_2 (hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_365_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 406 (all X_2 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_366_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 407 (all Y (Y != zero_zero_nat -> -(all Nat Y != suc(Nat)))) # label(fact_367_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 408 (all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N (hBOOL(hAPP_nat_bool(Pa,suc(N))) -> hBOOL(hAPP_nat_bool(Pa,N)))) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))))) # label(fact_368_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 409 (all N_1 all Pa (hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) -> ((all N (hBOOL(hAPP_nat_bool(Pa,N)) -> hBOOL(hAPP_nat_bool(Pa,suc(N))))) -> hBOOL(hAPP_nat_bool(Pa,N_1))))) # label(fact_369_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 410 (all N_2 (N_2 != zero_zero_nat -> (exists M_2 N_2 = suc(M_2)))) # label(fact_370_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 411 (all Pn all S0 all N_2 all S1_1 (hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn)),S0,N_2),S1_1)) -> hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,Pn),S0,suc(N_2)),S1_1)))) # label(fact_371_evaln_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 412 (all Ga all Pa hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),skip),Pa)),bot_bo1055319631e_bool)))) # label(fact_372_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 413 (all Ga all Pa hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),skip),Pa)),bot_bo1181479936a_bool)))) # label(fact_373_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 414 (all S_2 all N_2 all T_1 (hBOOL(hAPP_state_bool(evaln(skip,S_2,N_2),T_1)) -> T_1 = S_2)) # label(fact_374_evaln__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 415 (all S_2 all N_2 hBOOL(hAPP_state_bool(evaln(skip,S_2,N_2),S_2))) # label(fact_375_evaln_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 416 (all S_2 hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),S_2))) # label(fact_376_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 417 (all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),T_1)) -> T_1 = S_2)) # label(fact_377_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 418 (all C_2 all S_2 all N_2 all S_5 (hBOOL(hAPP_state_bool(evaln(C_2,S_2,N_2),S_5)) -> hBOOL(hAPP_state_bool(evaln(C_2,S_2,suc(N_2)),S_5)))) # label(fact_378_evaln__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 419 (all C all S all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),T)) <-> (exists N hBOOL(hAPP_state_bool(evaln(C,S,N),T))))) # label(fact_379_eval__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 420 (all C_2 all S_2 all N_2 all T_1 (hBOOL(hAPP_state_bool(evaln(C_2,S_2,N_2),T_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1)))) # label(fact_380_evaln__evalc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 421 (all Pname_1 hAPP_pname_com(body,Pname_1) != skip) # label(fact_381_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 422 (all Pname_1 skip != hAPP_pname_com(body,Pname_1)) # label(fact_382_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 423 (all N_1 all Pa all C all Qa (hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_1),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa))) <-> (all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3)) -> (all S_4 (hBOOL(hAPP_state_bool(evaln(C,S_3,N_1),S_4)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_3),S_4)))))))) # label(fact_383_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 424 (all N_1 all Pa all C all Qa (hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_1),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa))) <-> (all Z_3 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3)) -> (all S_4 (hBOOL(hAPP_state_bool(evaln(C,S_3,N_1),S_4)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_3),S_4)))))))) # label(fact_384_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 425 (all P all S_2 all N_2 all S1_1 (hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,P),S_2,N_2),S1_1)) -> -(all N (N_2 = suc(N) -> -hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P)),S_2,N),S1_1)))))) # label(fact_385_evaln__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 426 (all C_2 all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1)) -> (exists N hBOOL(hAPP_state_bool(evaln(C_2,S_2,N),T_1))))) # label(fact_386_evalc__evaln) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 427 (all Ga all Pa all B all C hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),Pa))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B))),while(B,C)),Pa)),bot_bo1055319631e_bool)))) # label(fact_387_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 428 (all Ga all Pa all B all C hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),Pa))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B))),while(B,C)),Pa)),bot_bo1181479936a_bool)))) # label(fact_388_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 429 (all D all R_1 all Ga all Pa all C all Qa (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Qa),D),R_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),semi(C,D)),R_1)),bot_bo1055319631e_bool)))))) # label(fact_389_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 430 (all D all R_1 all Ga all Pa all C all Qa (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool))) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Qa),D),R_1)),bot_bo1181479936a_bool))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),semi(C,D)),R_1)),bot_bo1181479936a_bool)))))) # label(fact_390_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 431 (all X_3 hAPP_f2143211163_state(the_el23965208_state,X_3) = hAPP_f2143211163_state(the_Ho10452358_state,hAPP_f1456107715e_bool(cOMBB_1653402815_state(hAPP_f854625363l_bool(fequal1746921144e_bool,X_3)),hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,insert1835143293_state),bot_bo1055319631e_bool)))) # label(fact_391_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 432 (all X_3 hAPP_f124283079iple_a(the_el1436340927iple_a,X_3) = hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_f772297704a_bool(cOMBB_1501709507iple_a(hAPP_f430043647l_bool(fequal1258664663a_bool,X_3)),hAPP_f1665407592a_bool(hAPP_f549683569a_bool(cOMBC_708118077a_bool,insert873085594iple_a),bot_bo1181479936a_bool)))) # label(fact_392_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.78 433 (all X_3 hAPP_f1297739591_pname(the_elem_pname,X_3) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_3)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool)))) # label(fact_393_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 434 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U)) -> ((all P_2 (is_pname(P_2) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Q_1,P_2))),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Qa,P_2))),bot_bo1055319631e_bool)))))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),C0)),Q_1)),U))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),C0)),Qa)),U))))))) # label(fact_394_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 435 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U)) -> ((all P_2 (is_pname(P_2) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_p635540397e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Q_1,P_2))),bot_bo1181479936a_bool))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_p635540397e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Qa,P_2))),bot_bo1181479936a_bool)))))) -> (hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),P_1)),C0)),Q_1)),U))) -> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),C0)),Qa)),U))))))) # label(fact_395_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 436 (all C all N_1 all B all S (-hBOOL(hAPP_state_bool(B,S)) -> hBOOL(hAPP_state_bool(evaln(while(B,C),S,N_1),S)))) # label(fact_396_evaln_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 437 (all S2_1 all C all N_1 all S1 all B all S0_1 (hBOOL(hAPP_state_bool(B,S0_1)) -> (hBOOL(hAPP_state_bool(evaln(C,S0_1,N_1),S1)) -> (hBOOL(hAPP_state_bool(evaln(while(B,C),S1,N_1),S2_1)) -> hBOOL(hAPP_state_bool(evaln(while(B,C),S0_1,N_1),S2_1)))))) # label(fact_397_evaln_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 438 (all S2_1 all C all S1 all B all S0_1 (hBOOL(hAPP_state_bool(B,S0_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0_1),S1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S1),S2_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S0_1),S2_1)))))) # label(fact_398_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 439 (all C all B all S (-hBOOL(hAPP_state_bool(B,S)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S),S)))) # label(fact_399_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 440 (all C1_1 all S2 all C0_1 all S0 all N_2 all S1_1 (hBOOL(hAPP_state_bool(evaln(C0_1,S0,N_2),S1_1)) -> (hBOOL(hAPP_state_bool(evaln(C1_1,S1_1,N_2),S2)) -> hBOOL(hAPP_state_bool(evaln(semi(C0_1,C1_1),S0,N_2),S2))))) # label(fact_400_evaln_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 441 (all C1_1 all S2 all C0_1 all S0 all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0_1),S0),S1_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S1_1),S2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0_1,C1_1)),S0),S2))))) # label(fact_401_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 442 (all Com1 all Com2 all Fun_1 all Com_1 semi(Com1,Com2) != while(Fun_1,Com_1)) # label(fact_402_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 443 (all Fun_1 all Com_1 all Com1 all Com2 while(Fun_1,Com_1) != semi(Com1,Com2)) # label(fact_403_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 444 (all Com1 all Com2 all Com1_3 all Com2_3 (semi(Com1,Com2) = semi(Com1_3,Com2_3) <-> Com1 = Com1_3 & Com2 = Com2_3)) # label(fact_404_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 445 (all Fun all Com all Fun_1 all Com_1 (while(Fun,Com) = while(Fun_1,Com_1) <-> Fun = Fun_1 & Com = Com_1)) # label(fact_405_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 446 (all Pname_2 all Fun all Com hAPP_pname_com(body,Pname_2) != while(Fun,Com)) # label(fact_406_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 447 (all Fun all Com all Pname_2 while(Fun,Com) != hAPP_pname_com(body,Pname_2)) # label(fact_407_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 448 (all Fun_1 all Com_1 skip != while(Fun_1,Com_1)) # label(fact_408_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 449 (all Fun_1 all Com_1 while(Fun_1,Com_1) != skip) # label(fact_409_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 450 (all Pname_1 all Com1_1 all Com2_1 hAPP_pname_com(body,Pname_1) != semi(Com1_1,Com2_1)) # label(fact_410_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 451 (all Com1_1 all Com2_1 all Pname_1 semi(Com1_1,Com2_1) != hAPP_pname_com(body,Pname_1)) # label(fact_411_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 452 (all Com1_2 all Com2_2 skip != semi(Com1_2,Com2_2)) # label(fact_412_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 453 (all Com1_2 all Com2_2 semi(Com1_2,Com2_2) != skip) # label(fact_413_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 454 (all C1_1 all C2_1 all S_2 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1_1,C2_1)),S_2),T_1)) -> -(all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S_2),S1_2)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2_1),S1_2),T_1)))))) # label(fact_414_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 455 (all C1_1 all C2_1 all S_2 all N_2 all T_1 (hBOOL(hAPP_state_bool(evaln(semi(C1_1,C2_1),S_2,N_2),T_1)) -> -(all S1_2 (hBOOL(hAPP_state_bool(evaln(C1_1,S_2,N_2),S1_2)) -> -hBOOL(hAPP_state_bool(evaln(C2_1,S1_2,N_2),T_1)))))) # label(fact_415_evaln__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 456 (all H all F (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(H),F))))) # label(fact_416_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 457 (all H all F (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F)) -> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f271130963a_bool(image_1654749281iple_a(H),F))))) # label(fact_417_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 458 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A))))) # label(fact_418_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 459 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A))))) # label(fact_419_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 460 (all A_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A))))) # label(fact_420_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 461 (all Qa all Pa (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Pa))) | hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Qa))) -> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),Pa)),Qa)))))) # label(fact_424_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 462 (all Qa all Pa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Pa))) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Qa))) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),Pa)),Qa)))))) # label(fact_425_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 463 (all Pa all Qa (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),Pa)),Qa)))) <-> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Pa))) & hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Qa))))) # label(fact_426_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 464 (all Pa all Qa (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),Pa)),Qa)))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Pa))) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Qa))))) # label(fact_427_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 465 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)))) # label(fact_428_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 466 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A))) <-> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)))) # label(fact_429_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 467 (all A_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)))) # label(fact_430_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 468 (all F all Ga (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),Ga))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)))) # label(fact_431_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 469 (all F all Ga (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),Ga))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F)) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Ga)))) # label(fact_432_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 470 (all F all Ga (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F),Ga))) <-> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F)) & hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,Ga)))) # label(fact_433_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 471 (all Ga all F (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),Ga)))))) # label(fact_434_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 472 (all Ga all F (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Ga)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),Ga)))))) # label(fact_435_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 473 (all Ga all F (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,Ga)) -> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F),Ga)))))) # label(fact_436_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 474 (all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) <-> A_1 = bot_bo1055319631e_bool | (exists A_3 exists A_2 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_2),A_3) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_3)))))) # label(fact_437_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 475 (all A_1 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A_1)) <-> A_1 = bot_bo1181479936a_bool | (exists A_3 exists A_2 (A_1 = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_2),A_3) & hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A_3)))))) # label(fact_438_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 476 (all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) <-> A_1 = bot_bo844097828e_bool | (exists A_3 exists A_2 (is_fun_pname_bool(A_3) & is_pname(A_2) & A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_3) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_3))))))) # label(fact_439_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 477 (all Pa all F (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)) -> ((all X all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),F_2))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F)))))) # label(fact_440_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 478 (all Pa all F (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F)) -> (hBOOL(hAPP_f540970102l_bool(Pa,bot_bo1181479936a_bool)) -> ((all X all F_2 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F_2)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),F_2)) -> (hBOOL(hAPP_f540970102l_bool(Pa,F_2)) -> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),F_2))))))) -> hBOOL(hAPP_f540970102l_bool(Pa,F)))))) # label(fact_441_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 479 (all Pa all F (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool)) -> ((all X all F_2 (is_pname(X) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,F_2)) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),F_2)))))))) -> hBOOL(hAPP_f1664156314l_bool(Pa,F)))))) # label(fact_442_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 480 (all F_1 all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(F_1),A))) -> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,hAPP_f998786331e_bool(cOMBB_799949246_pname(fequal1531560888_state),F_1)),hAPP_p1842370726_state(F_1,X))))))))))) # label(fact_443_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 481 (all F_1 all A (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))) -> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_H1991058245e_bool(hAPP_f687460073e_bool(cOMBC_1693967286a_bool,hAPP_f1311175287a_bool(cOMBB_858699740_pname(fequal879838495iple_a),F_1)),hAPP_p263283121iple_a(F_1,X))))))))))) # label(fact_444_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 482 (all B all C all S all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S),T)) -> ((T = S -> hBOOL(hAPP_state_bool(B,S))) -> -(hBOOL(hAPP_state_bool(B,S)) -> (all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),S1_2)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S1_2),T)))))))) # label(fact_445_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 483 (all B all C all S all N_1 all T (hBOOL(hAPP_state_bool(evaln(while(B,C),S,N_1),T)) -> ((T = S -> hBOOL(hAPP_state_bool(B,S))) -> -(hBOOL(hAPP_state_bool(B,S)) -> (all S1_2 (hBOOL(hAPP_state_bool(evaln(C,S,N_1),S1_2)) -> -hBOOL(hAPP_state_bool(evaln(while(B,C),S1_2,N_1),T)))))))) # label(fact_446_evaln__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 484 (all A (A != bot_bo1055319631e_bool <-> (exists X exists B_2 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),B_2) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),B_2)))))) # label(fact_447_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 485 (all A (A != bot_bo1181479936a_bool <-> (exists X exists B_2 (A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),B_2) & -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),B_2)))))) # label(fact_448_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 486 (all A (is_fun_pname_bool(A) -> (A != bot_bo844097828e_bool <-> (exists X exists B_2 (is_pname(X) & is_fun_pname_bool(B_2) & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_2))))))) # label(fact_449_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 487 (all B_1 all A all F_1 all F (is_fun_pname_bool(B_1) & is_fun_pname_bool(A) -> (hBOOL(finite89670078_pname(F_1,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_1)) -> (B_1 != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,A)),hAPP_f1297739591_pname(F,B_1))))))))) # label(fact_450_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 488 (all B_1 all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,B_1)) -> (B_1 != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,A)),hAPP_f124283079iple_a(F,B_1)))))))) # label(fact_451_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 489 (all B_1 all A all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1)) -> (B_1 != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,A)),hAPP_f2143211163_state(F,B_1)))))))) # label(fact_452_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 490 (all X_2 all A all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_2),hAPP_f2143211163_state(F,A)))))) # label(fact_453_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 491 (all X_2 all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),hAPP_f124283079iple_a(F,A)))))) # label(fact_454_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 492 (all X_2 all A all F_1 all F (is_fun_pname_bool(A) -> (hBOOL(finite89670078_pname(F_1,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X_2),hAPP_f1297739591_pname(F,A))))))) # label(fact_455_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 493 (all F_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f631639356e_bool(image_275883510_state(F_1),A) = finite216774046_pname(semila447562797e_bool,hAPP_f621094798e_bool(hAPP_f1505732693e_bool(cOMBC_173904839e_bool,hAPP_f1191449183e_bool(cOMBB_557071226_pname(insert1835143293_state),F_1)),bot_bo1055319631e_bool),bot_bo1055319631e_bool,A))) # label(fact_456_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 494 (all F_1 all A (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A) = finite979333485_pname(semila1498788770a_bool,hAPP_f1646799884a_bool(hAPP_f2022238777a_bool(cOMBC_1527561185a_bool,hAPP_f1728520198a_bool(cOMBB_1191710871_pname(insert873085594iple_a),F_1)),bot_bo1181479936a_bool),bot_bo1181479936a_bool,A))) # label(fact_457_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 495 (all Pa all F (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F)) -> (F != bot_bo1055319631e_bool -> ((all X hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),bot_bo1055319631e_bool)))) -> ((all X all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (F_2 != bot_bo1055319631e_bool -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),F_2)))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F))))))) # label(fact_458_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 496 (all Pa all F (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F)) -> (F != bot_bo1181479936a_bool -> ((all X hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),bot_bo1181479936a_bool)))) -> ((all X all F_2 (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F_2)) -> (F_2 != bot_bo1181479936a_bool -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),F_2)) -> (hBOOL(hAPP_f540970102l_bool(Pa,F_2)) -> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),F_2)))))))) -> hBOOL(hAPP_f540970102l_bool(Pa,F))))))) # label(fact_459_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 497 (all Pa all F (is_fun_pname_bool(F) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F)) -> (F != bot_bo844097828e_bool -> ((all X (is_pname(X) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),bot_bo844097828e_bool))))) -> ((all X all F_2 (is_pname(X) & is_fun_pname_bool(F_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2)) -> (F_2 != bot_bo844097828e_bool -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),F_2)) -> (hBOOL(hAPP_f1664156314l_bool(Pa,F_2)) -> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),F_2))))))))) -> hBOOL(hAPP_f1664156314l_bool(Pa,F)))))))) # label(fact_460_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 498 (all X_2 all A all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),hAPP_f124283079iple_a(F,A)) = hAPP_f124283079iple_a(F,A))))) # label(fact_461_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 499 (all X_2 all A all F_1 all F (hBOOL(finite89670078_pname(F_1,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X_2),hAPP_f1297739591_pname(F,A)) = hAPP_f1297739591_pname(F,A))))) # label(fact_462_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 500 (all N_3 all H all F_1 all F (is_fun_pname_bool(N_3) -> (hBOOL(finite89670078_pname(F_1,F)) -> ((all X all Y_2 (is_pname(X) & is_pname(Y_2) -> hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X),Y_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_pname_pname(H,X)),hAPP_pname_pname(H,Y_2)))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N_3)) -> (N_3 != bot_bo844097828e_bool -> hAPP_pname_pname(H,hAPP_f1297739591_pname(F,N_3)) = hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(image_pname_pname(H),N_3)))))))) # label(fact_463_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 501 (all N_3 all H all F_1 all F (hBOOL(finite950012314iple_a(F_1,F)) -> ((all X all Y_2 hAPP_H678412245iple_a(H,hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X),Y_2)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_H678412245iple_a(H,X)),hAPP_H678412245iple_a(H,Y_2))) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,N_3)) -> (N_3 != bot_bo1181479936a_bool -> hAPP_H678412245iple_a(H,hAPP_f124283079iple_a(F,N_3)) = hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(image_306007685iple_a(H),N_3))))))) # label(fact_464_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 502 (all N_3 all H all F_1 all F (hBOOL(finite506823037_state(F_1,F)) -> ((all X all Y_2 hAPP_H563960305_state(H,hAPP_H563960305_state(hAPP_H521649881_state(F_1,X),Y_2)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_H563960305_state(H,X)),hAPP_H563960305_state(H,Y_2))) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,N_3)) -> (N_3 != bot_bo1055319631e_bool -> hAPP_H563960305_state(H,hAPP_f2143211163_state(F,N_3)) = hAPP_f2143211163_state(F,hAPP_f921536533e_bool(image_650584225_state(H),N_3))))))) # label(fact_465_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 503 (all X_2 all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A)) -> (A != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_2),hAPP_f2143211163_state(F,A))))))) # label(fact_466_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 504 (all X_2 all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> (A != bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),hAPP_f124283079iple_a(F,A))))))) # label(fact_467_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 505 (all X_2 all A all F_1 all F (is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F_1,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (A != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X_2),hAPP_f1297739591_pname(F,A)))))))) # label(fact_468_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 506 (all X_2 all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2)) # label(fact_469_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 507 (all X_2 all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),bot_bo1181479936a_bool)) = X_2)) # label(fact_470_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 508 (all X_2 all F_1 all F (is_pname(X_2) -> (hBOOL(finite1282449217_pname(F_1,F)) -> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = X_2))) # label(fact_471_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 509 (all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> ((all X all Y_2 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F_1,X),Y_2)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(F,A)),A))))))) # label(fact_472_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 510 (all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> ((all X all Y_2 hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X),Y_2)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_2),bot_bo1181479936a_bool))))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_f124283079iple_a(F,A)),A))))))) # label(fact_473_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 511 (all A all F_1 all F (is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F_1,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> ((all X all Y_2 (is_pname(X) & is_pname(Y_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(F,A)),A)))))))) # label(fact_474_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 512 (all C2_1 all S2 all N2 all T2 all C1_1 all S1_1 all N1 all T1 (hBOOL(hAPP_state_bool(evaln(C1_1,S1_1,N1),T1)) -> (hBOOL(hAPP_state_bool(evaln(C2_1,S2,N2),T2)) -> (exists N (hBOOL(hAPP_state_bool(evaln(C1_1,S1_1,N),T1)) & hBOOL(hAPP_state_bool(evaln(C2_1,S2,N),T2))))))) # label(fact_475_evaln__max2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 513 (all A_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> (exists B_2 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_2) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B_2)))))) # label(fact_476_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 514 (all A_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> (exists B_2 (A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_2) & -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B_2)))))) # label(fact_477_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 515 (all A_1 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> (exists B_2 (is_fun_pname_bool(B_2) & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_2) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_2))))))) # label(fact_478_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 516 (all X_2 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A)) -> -(all B_2 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_2) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_2)))))) # label(fact_479_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 517 (all X_2 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) -> -(all B_2 (A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),B_2) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),B_2)))))) # label(fact_480_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 518 (all X_2 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> -(all B_2 (is_fun_pname_bool(B_2) -> (A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2)))))))) # label(fact_481_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 519 (all A ((all Y_2 -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Y_2),A))) -> A = bot_bo1181479936a_bool)) # label(fact_482_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 520 (all A (is_fun_pname_bool(A) -> ((all Y_2 (is_pname(Y_2) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_2),A)))) -> A = bot_bo844097828e_bool))) # label(fact_483_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 521 (all A ((all Y_2 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_2),A))) -> A = bot_bo1055319631e_bool)) # label(fact_484_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 522 (all B_1 all A (is_fun_bool_bool(B_1) & is_fun_bool_bool(A) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (A != bot_bo806936373l_bool -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_1)) -> (B_1 != bot_bo806936373l_bool -> (hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A),B_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(A)),big_la1480321694n_bool(B_1)))))))))) # label(fact_485_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 523 (all B_1 all A (is_fun1661590463l_bool(B_1) & is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_1)) -> (B_1 != bot_bo1649642514l_bool -> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(A)),big_la841148155e_bool(B_1)))))))) # label(fact_486_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 524 (all B_1 all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (A != bot_bo1325454745l_bool -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B_1)) -> (B_1 != bot_bo1325454745l_bool -> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(A)),big_la1640362552e_bool(B_1))))))) # label(fact_487_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 525 (all B_1 all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (A != bot_bo1325387246l_bool -> (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,B_1)) -> (B_1 != bot_bo1325387246l_bool -> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f997688506l_bool(semila1827648460l_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(A)),big_la1993344855a_bool(B_1))))))) # label(fact_488_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 526 (all X_2 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),big_la1480321694n_bool(A))) <-> hBOOL(big_la1480321694n_bool(A)))))) # label(fact_489_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 527 (all X_2 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),big_la841148155e_bool(A)) = big_la841148155e_bool(A)))) # label(fact_490_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 528 (all X_2 all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),big_la1640362552e_bool(A)) = big_la1640362552e_bool(A)))) # label(fact_491_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 529 (all X_2 all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,X_2),A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),big_la1993344855a_bool(A)) = big_la1993344855a_bool(A)))) # label(fact_492_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 530 (all X_2 all A (is_fun_bool_bool(A) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) -> (A != bot_bo806936373l_bool -> (hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),big_la1480321694n_bool(A))))))))) # label(fact_493_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 531 (all X_2 all A (is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) -> (A != bot_bo1649642514l_bool -> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),big_la841148155e_bool(A))))))) # label(fact_494_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 532 (all X_2 all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (-hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A)) -> (A != bot_bo1325454745l_bool -> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),A)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),big_la1640362552e_bool(A)))))) # label(fact_495_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 533 (all X_2 all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (-hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,X_2),A)) -> (A != bot_bo1325387246l_bool -> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,X_2),A)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),big_la1993344855a_bool(A)))))) # label(fact_496_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 534 (all X_2 all A (is_fun_bool_bool(A) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (A != bot_bo806936373l_bool -> (hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),big_la1480321694n_bool(A)))))))) # label(fact_497_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 535 (all X_2 all A (is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),big_la841148155e_bool(A)))))) # label(fact_498_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 536 (all X_2 all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (A != bot_bo1325454745l_bool -> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),A)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),big_la1640362552e_bool(A))))) # label(fact_499_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 537 (all X_2 all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (A != bot_bo1325387246l_bool -> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,X_2),A)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),big_la1993344855a_bool(A))))) # label(fact_500_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 538 (all N_3 all H (is_fun_bool_bool(N_3) -> ((all X all Y_2 (is_bool(X) & is_bool(Y_2) -> (hBOOL(hAPP_bool_bool(H,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Y_2))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(H,X)),hAPP_bool_bool(H,Y_2)))))) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,N_3)) -> (N_3 != bot_bo806936373l_bool -> (hBOOL(hAPP_bool_bool(H,big_la1480321694n_bool(N_3))) <-> hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(image_bool_bool(H),N_3))))))))) # label(fact_501_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 539 (all N_3 all H (is_fun1661590463l_bool(N_3) -> ((all X all Y_2 (is_fun_pname_bool(X) & is_fun_pname_bool(Y_2) -> hAPP_f759274231e_bool(H,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(H,X)),hAPP_f759274231e_bool(H,Y_2)))) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N_3)) -> (N_3 != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(H,big_la841148155e_bool(N_3)) = big_la841148155e_bool(hAPP_f559147733l_bool(image_2063528359e_bool(H),N_3))))))) # label(fact_502_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 540 (all N_3 all H ((all X all Y_2 hAPP_f921536533e_bool(H,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Y_2)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(H,X)),hAPP_f921536533e_bool(H,Y_2))) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,N_3)) -> (N_3 != bot_bo1325454745l_bool -> hAPP_f921536533e_bool(H,big_la1640362552e_bool(N_3)) = big_la1640362552e_bool(hAPP_f1970439265l_bool(image_505022149e_bool(H),N_3)))))) # label(fact_503_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 541 (all N_3 all H ((all X all Y_2 hAPP_f1591852335a_bool(H,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Y_2)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(H,X)),hAPP_f1591852335a_bool(H,Y_2))) -> (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,N_3)) -> (N_3 != bot_bo1325387246l_bool -> hAPP_f1591852335a_bool(H,big_la1993344855a_bool(N_3)) = big_la1993344855a_bool(hAPP_f960623701l_bool(image_119931871a_bool(H),N_3)))))) # label(fact_504_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 542 (all A (is_fun_bool_bool(A) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (A != bot_bo806936373l_bool -> ((all X all Y_2 (is_bool(X) & is_bool(Y_2) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Y_2)),hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X),hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,Y_2),bot_bo806936373l_bool)))))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,big_la1480321694n_bool(A)),A))))))) # label(fact_505_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 543 (all A (is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> ((all X all Y_2 (is_fun_pname_bool(X) & is_fun_pname_bool(Y_2) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Y_2)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_2),bot_bo1649642514l_bool)))))) -> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,big_la841148155e_bool(A)),A))))))) # label(fact_506_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 544 (all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (A != bot_bo1325454745l_bool -> ((all X all Y_2 hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Y_2)),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,Y_2),bot_bo1325454745l_bool))))) -> hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,big_la1640362552e_bool(A)),A)))))) # label(fact_507_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 545 (all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (A != bot_bo1325387246l_bool -> ((all X all Y_2 hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Y_2)),hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,X),hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,Y_2),bot_bo1325387246l_bool))))) -> hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,big_la1993344855a_bool(A)),A)))))) # label(fact_508_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 546 (all B_1 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_1)) -> (hAPP_f961197973l_bool(semila1551573549l_bool(A),B_1) != bot_bo806936373l_bool -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A),B_1))),big_la1480321694n_bool(hAPP_f961197973l_bool(semila1551573549l_bool(A),B_1)))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(A)),big_la1480321694n_bool(B_1)))))))) # label(fact_509_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 547 (all B_1 all A (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_1)) -> (hAPP_f559147733l_bool(semila1130628874l_bool(A),B_1) != bot_bo1649642514l_bool -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B_1))),big_la841148155e_bool(hAPP_f559147733l_bool(semila1130628874l_bool(A),B_1))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(A)),big_la841148155e_bool(B_1)))))) # label(fact_510_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 548 (all B_1 all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B_1)) -> (hAPP_f1970439265l_bool(semila1410775201l_bool(A),B_1) != bot_bo1325454745l_bool -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A),B_1))),big_la1640362552e_bool(hAPP_f1970439265l_bool(semila1410775201l_bool(A),B_1))) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(A)),big_la1640362552e_bool(B_1)))))) # label(fact_511_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 549 (all B_1 all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,B_1)) -> (hAPP_f960623701l_bool(semila1746965734l_bool(A),B_1) != bot_bo1325387246l_bool -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f997688506l_bool(semila1827648460l_bool,A),B_1))),big_la1993344855a_bool(hAPP_f960623701l_bool(semila1746965734l_bool(A),B_1))) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(A)),big_la1993344855a_bool(B_1)))))) # label(fact_512_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 550 (all B_1 all A (is_fun_bool_bool(B_1) & is_fun_bool_bool(A) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (A != bot_bo806936373l_bool -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_1)) -> (B_1 != bot_bo806936373l_bool -> (hAPP_f961197973l_bool(semila1551573549l_bool(A),B_1) = bot_bo806936373l_bool -> (hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A),B_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(A)),big_la1480321694n_bool(B_1))))))))))) # label(fact_513_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 551 (all B_1 all A (is_fun1661590463l_bool(B_1) & is_fun1661590463l_bool(A) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (A != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_1)) -> (B_1 != bot_bo1649642514l_bool -> (hAPP_f559147733l_bool(semila1130628874l_bool(A),B_1) = bot_bo1649642514l_bool -> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(A)),big_la841148155e_bool(B_1))))))))) # label(fact_514_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 552 (all B_1 all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (A != bot_bo1325454745l_bool -> (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B_1)) -> (B_1 != bot_bo1325454745l_bool -> (hAPP_f1970439265l_bool(semila1410775201l_bool(A),B_1) = bot_bo1325454745l_bool -> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(A)),big_la1640362552e_bool(B_1)))))))) # label(fact_515_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 553 (all B_1 all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (A != bot_bo1325387246l_bool -> (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,B_1)) -> (B_1 != bot_bo1325387246l_bool -> (hAPP_f960623701l_bool(semila1746965734l_bool(A),B_1) = bot_bo1325387246l_bool -> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f997688506l_bool(semila1827648460l_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(A)),big_la1993344855a_bool(B_1)))))))) # label(fact_516_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 554 (all B_1 all C all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) -> (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)))))) # label(fact_517_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 555 (all B_1 all C all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)))))) # label(fact_518_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 556 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) -> -(hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) -> -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1))))) # label(fact_519_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 557 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1))))) # label(fact_520_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 558 (all X_2 hAPP_f759274231e_bool(semila1635148844e_bool(X_2),bot_bo844097828e_bool) = bot_bo844097828e_bool) # label(fact_521_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 559 (all X_2 hAPP_f1591852335a_bool(semila671163144a_bool(X_2),bot_bo1181479936a_bool) = bot_bo1181479936a_bool) # label(fact_522_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 560 (all X_2 hAPP_f921536533e_bool(semila2145357127e_bool(X_2),bot_bo1055319631e_bool) = bot_bo1055319631e_bool) # label(fact_523_inf__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 561 (all X_2 hAPP_f759274231e_bool(semila1635148844e_bool(bot_bo844097828e_bool),X_2) = bot_bo844097828e_bool) # label(fact_524_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 562 (all X_2 hAPP_f1591852335a_bool(semila671163144a_bool(bot_bo1181479936a_bool),X_2) = bot_bo1181479936a_bool) # label(fact_525_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 563 (all X_2 hAPP_f921536533e_bool(semila2145357127e_bool(bot_bo1055319631e_bool),X_2) = bot_bo1055319631e_bool) # label(fact_526_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 564 (all Y_1 all Z_1 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(Y_1),Z_1)),X_2)) <-> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),X_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Z_1),X_2))))) # label(fact_527_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 565 (all Y_1 all Z_1 all X_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),Z_1)),X_2) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),X_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Z_1),X_2))) # label(fact_528_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 566 (all Y_1 all Z_1 all X_2 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),Z_1)),X_2) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Z_1),X_2))) # label(fact_529_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 567 (all Y_1 all Z_1 all X_2 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),Z_1)),X_2) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),X_2)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Z_1),X_2))) # label(fact_530_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 568 (all Y_1 all Z_1 all X_2 (hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1)),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(Y_1),X_2)),hAPP_bool_bool(semila310582991f_bool(Z_1),X_2))))) # label(fact_531_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 569 (all Y_1 all Z_1 all X_2 hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)),X_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),X_2)),hAPP_f759274231e_bool(semila1635148844e_bool(Z_1),X_2))) # label(fact_532_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 570 (all Y_1 all Z_1 all X_2 hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)),X_2) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),X_2)),hAPP_f921536533e_bool(semila2145357127e_bool(Z_1),X_2))) # label(fact_533_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 571 (all Y_1 all Z_1 all X_2 hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)),X_2) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),X_2)),hAPP_f1591852335a_bool(semila671163144a_bool(Z_1),X_2))) # label(fact_534_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 572 (all X_2 all Y_1 all Z_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(semila310582991f_bool(Y_1),Z_1))) <-> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))))) # label(fact_535_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 573 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),Z_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1))) # label(fact_536_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 574 (all X_2 all Y_1 all Z_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),Z_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1))) # label(fact_537_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 575 (all X_2 all Y_1 all Z_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),Z_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1))) # label(fact_538_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 576 (all X_2 all Y_1 all Z_1 (hBOOL(hAPP_bool_bool(semila310582991f_bool(X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(X_2),Y_1)),hAPP_bool_bool(semila310582991f_bool(X_2),Z_1))))) # label(fact_539_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 577 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(semila1635148844e_bool(X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Y_1)),hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Z_1))) # label(fact_540_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 578 (all X_2 all Y_1 all Z_1 hAPP_f921536533e_bool(semila2145357127e_bool(X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Y_1)),hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Z_1))) # label(fact_541_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 579 (all X_2 all Y_1 all Z_1 hAPP_f1591852335a_bool(semila671163144a_bool(X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Y_1)),hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Z_1))) # label(fact_542_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 580 (all X_2 all Y_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(semila310582991f_bool(X_2),Y_1))) <-> hBOOL(X_2))) # label(fact_543_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 581 (all X_2 all Y_1 (is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Y_1)) = X_2)) # label(fact_544_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 582 (all X_2 all Y_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Y_1)) = X_2) # label(fact_545_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 583 (all X_2 all Y_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Y_1)) = X_2) # label(fact_546_sup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 584 (all X_2 all Y_1 (hBOOL(hAPP_bool_bool(semila310582991f_bool(X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1))) <-> hBOOL(X_2))) # label(fact_547_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 585 (all X_2 all Y_1 (is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(semila1635148844e_bool(X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) = X_2)) # label(fact_548_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 586 (all X_2 all Y_1 hAPP_f921536533e_bool(semila2145357127e_bool(X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) = X_2) # label(fact_549_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 587 (all X_2 all Y_1 hAPP_f1591852335a_bool(semila671163144a_bool(X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) = X_2) # label(fact_550_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 588 (all A all B_1 (hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) = bot_bo844097828e_bool <-> (all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) -> (all Xa (is_pname(Xa) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B_1)) -> X != Xa)))))))) # label(fact_551_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 589 (all A all B_1 (hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) = bot_bo1181479936a_bool <-> (all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A)) -> (all Xa (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Xa),B_1)) -> X != Xa)))))) # label(fact_552_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 590 (all A all B_1 (hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) = bot_bo1055319631e_bool <-> (all X (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A)) -> (all Xa (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Xa),B_1)) -> X != Xa)))))) # label(fact_553_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 591 (all A hAPP_f759274231e_bool(semila1635148844e_bool(A),bot_bo844097828e_bool) = bot_bo844097828e_bool) # label(fact_554_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 592 (all A hAPP_f1591852335a_bool(semila671163144a_bool(A),bot_bo1181479936a_bool) = bot_bo1181479936a_bool) # label(fact_555_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 593 (all A hAPP_f921536533e_bool(semila2145357127e_bool(A),bot_bo1055319631e_bool) = bot_bo1055319631e_bool) # label(fact_556_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 594 (all B_1 hAPP_f759274231e_bool(semila1635148844e_bool(bot_bo844097828e_bool),B_1) = bot_bo844097828e_bool) # label(fact_557_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 595 (all B_1 hAPP_f1591852335a_bool(semila671163144a_bool(bot_bo1181479936a_bool),B_1) = bot_bo1181479936a_bool) # label(fact_558_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 596 (all B_1 hAPP_f921536533e_bool(semila2145357127e_bool(bot_bo1055319631e_bool),B_1) = bot_bo1055319631e_bool) # label(fact_559_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.79 597 (all A all B_1 hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),A))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B_1)))) # label(fact_560_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 598 (all A all B_1 hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_1)))) # label(fact_561_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 599 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) & hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)))) # label(fact_562_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 600 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)))) # label(fact_563_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 601 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)))) # label(fact_564_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 602 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)))) # label(fact_565_IntD1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 603 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)))) # label(fact_566_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 604 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)))) # label(fact_567_IntD2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 605 (all Pa all Qa hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),Pa)),Qa)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(collec268032053iple_a,Pa)),hAPP_f1591852335a_bool(collec268032053iple_a,Qa))) # label(fact_568_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 606 (all Pa all Qa hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),Pa)),Qa)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(collect_pname,Pa)),hAPP_f759274231e_bool(collect_pname,Qa))) # label(fact_569_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 607 (all X_2 all A all Pa (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(collec268032053iple_a,Pa)))) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A)) & hBOOL(hAPP_H1421470952a_bool(Pa,X_2)))) # label(fact_570_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 608 (all X_2 all A all Pa (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(collect_pname,Pa)))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) & hBOOL(hAPP_pname_bool(Pa,X_2)))) # label(fact_571_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 609 (all R_1 all S_1 all X (hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),R_1)),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),S_1)),X)) <-> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(semila671163144a_bool(R_1),S_1))))) # label(fact_572_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 610 (all R_1 all S_1 all X (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S_1)),X)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(semila1635148844e_bool(R_1),S_1))))) # label(fact_573_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 611 (all A all B_1 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1))),hAPP_f759274231e_bool(semila1635148844e_bool(C_1),A)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A))) # label(fact_574_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 612 (all A all B_1 all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1))),hAPP_f921536533e_bool(semila2145357127e_bool(C_1),A)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A))) # label(fact_575_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 613 (all A all B_1 all C_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1))),hAPP_f1591852335a_bool(semila671163144a_bool(C_1),A)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1))),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,C_1),A))) # label(fact_576_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 614 (all B_1 all C_1 all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)),A) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A))) # label(fact_577_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 615 (all B_1 all C_1 all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)),A) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A))) # label(fact_578_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 616 (all B_1 all C_1 all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)),A) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),A)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,C_1),A))) # label(fact_579_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 617 (all B_1 all C_1 all A hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(B_1),A)),hAPP_f759274231e_bool(semila1635148844e_bool(C_1),A))) # label(fact_580_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 618 (all B_1 all C_1 all A hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)),A) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(B_1),A)),hAPP_f921536533e_bool(semila2145357127e_bool(C_1),A))) # label(fact_581_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 619 (all B_1 all C_1 all A hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)),A) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(B_1),A)),hAPP_f1591852335a_bool(semila671163144a_bool(C_1),A))) # label(fact_582_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 620 (all A all B_1 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1))) # label(fact_583_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 621 (all A all B_1 all C_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),C_1))) # label(fact_584_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 622 (all A all B_1 all C_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),C_1))) # label(fact_585_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 623 (all A all B_1 all C_1 hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)),hAPP_f759274231e_bool(semila1635148844e_bool(A),C_1))) # label(fact_586_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 624 (all A all B_1 all C_1 hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)),hAPP_f921536533e_bool(semila2145357127e_bool(A),C_1))) # label(fact_587_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 625 (all A all B_1 all C_1 hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)),hAPP_f1591852335a_bool(semila671163144a_bool(A),C_1))) # label(fact_588_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 626 (all B_1 all A_1 all C_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1)) -> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)))) # label(fact_589_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 627 (all B_1 all A_1 all C_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1)) -> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)))) # label(fact_590_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 628 (all B_1 all A_1 all C_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1)) -> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)))) # label(fact_591_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 629 (all B_1 all A_1 all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)))) # label(fact_592_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 630 (all B_1 all A_1 all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)))) # label(fact_593_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 631 (all B_1 all A_1 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)))) # label(fact_594_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 632 (all B_1 all A_1 all C_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1)) -> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1))) # label(fact_595_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 633 (all B_1 all A_1 all C_1 (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1)) -> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1))) # label(fact_596_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 634 (all B_1 all A_1 all C_1 (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1)) -> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1))) # label(fact_597_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 635 (all B_1 all A_1 all A (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1))) # label(fact_598_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 636 (all B_1 all A_1 all A (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) # label(fact_599_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 637 (all B_1 all A_1 all A (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) # label(fact_600_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 638 (all A_1 all A all B_1 hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1))) # label(fact_601_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 639 (all A_1 all A all B_1 hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) # label(fact_602_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 640 (all A_1 all A all B_1 hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) # label(fact_603_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 641 (all B_1 all A_1 all C_1 ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1)) -> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1)) -> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)))) # label(fact_604_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 642 (all B_1 all A_1 all C_1 ((hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1)) -> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1))) & (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1)) -> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)))) # label(fact_605_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 643 (all B_1 all A_1 all C_1 ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1)) -> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1)) -> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)))) # label(fact_606_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 644 (all B_1 all A_1 all A ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) -> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)))) # label(fact_607_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 645 (all B_1 all A_1 all A ((hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) & (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) -> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)))) # label(fact_608_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 646 (all B_1 all A_1 all A ((hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) & (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)))) # label(fact_609_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 647 (all Pa all F_1 all G all S_1 hAPP_f631639356e_bool(image_275883510_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,hAPP_f1405979047_state(cOMBB_707293872_pname(if_Hoa533980679_state),Pa)),F_1)),G)),S_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F_1),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,Pa)))),hAPP_f631639356e_bool(image_275883510_state(G),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),Pa)))))) # label(fact_610_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 648 (all Pa all F_1 all G all S_1 hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f1044063253iple_a(hAPP_f1401255196iple_a(cOMBS_1128650103iple_a,hAPP_f866544818iple_a(hAPP_f428084316iple_a(cOMBS_546756116iple_a,hAPP_f653022294iple_a(cOMBB_1916528323_pname(if_Hoa638970256iple_a),Pa)),F_1)),G)),S_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f271130963a_bool(image_1654749281iple_a(F_1),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,Pa)))),hAPP_f271130963a_bool(image_1654749281iple_a(G),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),Pa)))))) # label(fact_611_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 649 (all B_1 all A all F_1 all F (hBOOL(finite1282449217_pname(F_1,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_1)) -> (hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) != bot_bo844097828e_bool -> hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))),hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,A)),hAPP_f1297739591_pname(F,B_1))))))) # label(fact_612_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 650 (all B_1 all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,B_1)) -> (hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) != bot_bo1181479936a_bool -> hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))),hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,A)),hAPP_f124283079iple_a(F,B_1))))))) # label(fact_613_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 651 (all B_1 all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1)) -> (hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) != bot_bo1055319631e_bool -> hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))),hAPP_f2143211163_state(F,hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1))) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,A)),hAPP_f2143211163_state(F,B_1))))))) # label(fact_614_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 652 (all B_1 all A all F_1 all F (is_fun_pname_bool(B_1) & is_fun_pname_bool(A) -> (hBOOL(finite1282449217_pname(F_1,F)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) -> (A != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_1)) -> (B_1 != bot_bo844097828e_bool -> (hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,A)),hAPP_f1297739591_pname(F,B_1)))))))))) # label(fact_615_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 653 (all B_1 all A all F_1 all F (hBOOL(finite1669978781iple_a(F_1,F)) -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) -> (A != bot_bo1181479936a_bool -> (hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,B_1)) -> (B_1 != bot_bo1181479936a_bool -> (hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) = bot_bo1181479936a_bool -> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,A)),hAPP_f124283079iple_a(F,B_1))))))))) # label(fact_616_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 654 (all B_1 all A all F_1 all F (hBOOL(finite774711482_state(F_1,F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) -> (A != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1)) -> (B_1 != bot_bo1055319631e_bool -> (hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,A)),hAPP_f2143211163_state(F,B_1))))))))) # label(fact_617_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 655 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 (is_bool(X) & is_bool(Y_2) & is_bool(Z_2) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),hAPP_bool_bool(semila310582991f_bool(Y_2),Z_2))) <-> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Z_2)))))) -> (hBOOL(hAPP_bool_bool(semila310582991f_bool(X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(X_2),Y_1)),hAPP_bool_bool(semila310582991f_bool(X_2),Z_1)))))) # label(fact_618_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 656 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 (is_fun_pname_bool(X) & is_fun_pname_bool(Y_2) & is_fun_pname_bool(Z_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),hAPP_f759274231e_bool(semila1635148844e_bool(Y_2),Z_2)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Z_2)))) -> hAPP_f759274231e_bool(semila1635148844e_bool(X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Y_1)),hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Z_1)))) # label(fact_619_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 657 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),hAPP_f921536533e_bool(semila2145357127e_bool(Y_2),Z_2)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Z_2))) -> hAPP_f921536533e_bool(semila2145357127e_bool(X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Y_1)),hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Z_1)))) # label(fact_620_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 658 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),hAPP_f1591852335a_bool(semila671163144a_bool(Y_2),Z_2)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Y_2)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Z_2))) -> hAPP_f1591852335a_bool(semila671163144a_bool(X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Y_1)),hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Z_1)))) # label(fact_621_distrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 659 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 (is_bool(X) & is_bool(Y_2) & is_bool(Z_2) -> (hBOOL(hAPP_bool_bool(semila310582991f_bool(X),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z_2))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(X),Y_2)),hAPP_bool_bool(semila310582991f_bool(X),Z_2)))))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(semila310582991f_bool(Y_1),Z_1))) <-> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1)))))) # label(fact_622_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 660 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 (is_fun_pname_bool(X) & is_fun_pname_bool(Y_2) & is_fun_pname_bool(Z_2) -> hAPP_f759274231e_bool(semila1635148844e_bool(X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(X),Y_2)),hAPP_f759274231e_bool(semila1635148844e_bool(X),Z_2)))) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),Z_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1)))) # label(fact_623_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 661 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 hAPP_f921536533e_bool(semila2145357127e_bool(X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_2),Z_2)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(X),Y_2)),hAPP_f921536533e_bool(semila2145357127e_bool(X),Z_2))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),Z_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1)))) # label(fact_624_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 662 (all X_2 all Y_1 all Z_1 ((all X all Y_2 all Z_2 hAPP_f1591852335a_bool(semila671163144a_bool(X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_2),Z_2)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(X),Y_2)),hAPP_f1591852335a_bool(semila671163144a_bool(X),Z_2))) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),Z_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1)))) # label(fact_625_distrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 663 (all A_1 all A (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_1),A)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),big_la472677547n_bool(A))) <-> hBOOL(A_1))))) # label(fact_626_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 664 (all A_1 all A (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),A)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),big_la28065288e_bool(A)) = A_1)))) # label(fact_627_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 665 (all A_1 all A (hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A)) -> (hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_1),A)) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),big_la508066411e_bool(A)) = A_1))) # label(fact_628_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 666 (all A_1 all A (hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A)) -> (hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,A_1),A)) -> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),big_la1164677860a_bool(A)) = A_1))) # label(fact_629_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 667 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1))) -> -(hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1))))) # label(fact_630_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 668 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1))))) # label(fact_631_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 669 (all B_1 all C all A (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) -> (-hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1)))))) # label(fact_632_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 670 (all B_1 all C all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1)))))) # label(fact_633_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 671 (all A all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(minus_1015773161e_bool(B_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) # label(fact_634_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 672 (all A all B_1 hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),A)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) # label(fact_635_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 673 (all A all B_1 hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(minus_469558085a_bool(B_1),A)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) # label(fact_636_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 674 (all B_1 all A hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(minus_1015773161e_bool(B_1),A)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A)) # label(fact_637_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 675 (all B_1 all A hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),A)),A) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A)) # label(fact_638_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 676 (all B_1 all A hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(minus_469558085a_bool(B_1),A)),A) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),A)) # label(fact_639_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 677 (all A all B_1 all C_1 hAPP_f759274231e_bool(minus_1015773161e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(minus_1015773161e_bool(A),C_1)),hAPP_f759274231e_bool(minus_1015773161e_bool(B_1),C_1))) # label(fact_640_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 678 (all A all B_1 all C_1 hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A),C_1)),hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),C_1))) # label(fact_641_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 679 (all A all B_1 all C_1 hAPP_f1591852335a_bool(minus_469558085a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(minus_469558085a_bool(A),C_1)),hAPP_f1591852335a_bool(minus_469558085a_bool(B_1),C_1))) # label(fact_642_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 680 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1))) -> -hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)))) # label(fact_643_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 681 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1))) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)))) # label(fact_644_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 682 (all C all A all B_1 (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1))) -> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)))) # label(fact_645_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 683 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)))) # label(fact_646_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 684 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)))) # label(fact_647_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 685 (all M all N_2 hAPP_nat_nat(minus_minus_nat(suc(M)),suc(N_2)) = hAPP_nat_nat(minus_minus_nat(M),N_2)) # label(fact_648_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 686 (all M all N_2 all K_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(suc(M)),N_2)),suc(K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N_2)),K_1)) # label(fact_649_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 687 (all N_2 hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N_2) = zero_zero_nat) # label(fact_650_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 688 (all M hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M) # label(fact_651_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 689 (all M hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat) # label(fact_652_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 690 (all M all N_2 (hAPP_nat_nat(minus_minus_nat(M),N_2) = zero_zero_nat -> (hAPP_nat_nat(minus_minus_nat(N_2),M) = zero_zero_nat -> M = N_2))) # label(fact_653_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 691 (all I_1 all Pa all K (hBOOL(hAPP_nat_bool(Pa,K)) -> ((all N (hBOOL(hAPP_nat_bool(Pa,suc(N))) -> hBOOL(hAPP_nat_bool(Pa,N)))) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K),I_1)))))) # label(fact_654_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 692 (all I all J all K_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),K_1)),J)) # label(fact_655_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 693 (all M_1 all N_1 hAPP_nat_nat(minus_minus_nat(M_1),suc(N_1)) = nat_case_nat(zero_zero_nat,cOMBI_nat,hAPP_nat_nat(minus_minus_nat(M_1),N_1))) # label(fact_656_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 694 (all N_2 hAPP_nat_nat(minus_minus_nat(suc(N_2)),one_one_nat) = N_2) # label(fact_657_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 695 (all M all N_2 hAPP_nat_nat(minus_minus_nat(M),suc(N_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N_2)) # label(fact_658_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 696 (all N_2 suc(N_2) = plus_plus_nat(N_2,one_one_nat)) # label(fact_660_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 697 (all N_2 suc(N_2) = plus_plus_nat(one_one_nat,N_2)) # label(fact_661_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 698 (all M all K_1 all N_2 hAPP_nat_nat(minus_minus_nat(plus_plus_nat(M,K_1)),plus_plus_nat(N_2,K_1)) = hAPP_nat_nat(minus_minus_nat(M),N_2)) # label(fact_662_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 699 (all K_1 all M all N_2 hAPP_nat_nat(minus_minus_nat(plus_plus_nat(K_1,M)),plus_plus_nat(K_1,N_2)) = hAPP_nat_nat(minus_minus_nat(M),N_2)) # label(fact_663_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 700 (all I all J all K_1 hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J)),K_1) = hAPP_nat_nat(minus_minus_nat(I),plus_plus_nat(J,K_1))) # label(fact_664_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 701 (all N_2 all M hAPP_nat_nat(minus_minus_nat(plus_plus_nat(N_2,M)),N_2) = M) # label(fact_665_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 702 (all M all N_2 hAPP_nat_nat(minus_minus_nat(plus_plus_nat(M,N_2)),N_2) = M) # label(fact_666_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 703 (all N_2 all M hAPP_nat_nat(minus_minus_nat(N_2),plus_plus_nat(N_2,M)) = zero_zero_nat) # label(fact_667_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 704 (all M all N_2 plus_plus_nat(M,N_2) = plus_plus_nat(N_2,M)) # label(fact_668_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 705 (all X_1 all Y all Z plus_plus_nat(X_1,plus_plus_nat(Y,Z)) = plus_plus_nat(Y,plus_plus_nat(X_1,Z))) # label(fact_669_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 706 (all M all N_2 all K_1 plus_plus_nat(plus_plus_nat(M,N_2),K_1) = plus_plus_nat(M,plus_plus_nat(N_2,K_1))) # label(fact_670_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 707 (all K all M_1 all N_1 (plus_plus_nat(K,M_1) = plus_plus_nat(K,N_1) <-> M_1 = N_1)) # label(fact_671_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 708 (all M_1 all K all N_1 (plus_plus_nat(M_1,K) = plus_plus_nat(N_1,K) <-> M_1 = N_1)) # label(fact_672_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 709 (all M all N_2 plus_plus_nat(suc(M),N_2) = plus_plus_nat(M,suc(N_2))) # label(fact_673_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 710 (all M all N_2 plus_plus_nat(suc(M),N_2) = suc(plus_plus_nat(M,N_2))) # label(fact_674_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 711 (all M all N_2 plus_plus_nat(M,suc(N_2)) = suc(plus_plus_nat(M,N_2))) # label(fact_675_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 712 (all M_1 all N_1 (suc(zero_zero_nat) = plus_plus_nat(M_1,N_1) <-> M_1 = suc(zero_zero_nat) & N_1 = zero_zero_nat | M_1 = zero_zero_nat & N_1 = suc(zero_zero_nat))) # label(fact_676_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 713 (all M_1 all N_1 (plus_plus_nat(M_1,N_1) = suc(zero_zero_nat) <-> M_1 = suc(zero_zero_nat) & N_1 = zero_zero_nat | M_1 = zero_zero_nat & N_1 = suc(zero_zero_nat))) # label(fact_677_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 714 (all N_2 plus_plus_nat(zero_zero_nat,N_2) = N_2) # label(fact_678_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 715 (all M plus_plus_nat(M,zero_zero_nat) = M) # label(fact_679_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 716 (all M_1 all N_1 (plus_plus_nat(M_1,N_1) = zero_zero_nat <-> M_1 = zero_zero_nat & N_1 = zero_zero_nat)) # label(fact_680_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 717 (all M all N_2 (plus_plus_nat(M,N_2) = M -> N_2 = zero_zero_nat)) # label(fact_681_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 718 (all N_2 all M ((M = zero_zero_nat -> plus_plus_nat(M,N_2) = N_2) & (M != zero_zero_nat -> plus_plus_nat(M,N_2) = suc(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat),N_2))))) # label(fact_682_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 719 (all Com1_1 all Com2_1 com_size(semi(Com1_1,Com2_1)) = plus_plus_nat(plus_plus_nat(com_size(Com1_1),com_size(Com2_1)),suc(zero_zero_nat))) # label(fact_683_com_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 720 (all Pname com_size(hAPP_pname_com(body,Pname)) = zero_zero_nat) # label(fact_684_com_Osize_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 721 (all Fun all Com com_size(while(Fun,Com)) = plus_plus_nat(com_size(Com),suc(zero_zero_nat))) # label(fact_686_com_Osize_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 722 (all Com1_1 all Com2_1 size_size_com(semi(Com1_1,Com2_1)) = plus_plus_nat(plus_plus_nat(size_size_com(Com1_1),size_size_com(Com2_1)),suc(zero_zero_nat))) # label(fact_687_com_Osize_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 723 (all Pname size_size_com(hAPP_pname_com(body,Pname)) = zero_zero_nat) # label(fact_688_com_Osize_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 724 (all Fun all Com size_size_com(while(Fun,Com)) = plus_plus_nat(size_size_com(Com),suc(zero_zero_nat))) # label(fact_690_com_Osize_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 725 (all Fun all Com1 all Com2 size_size_com(cond(Fun,Com1,Com2)) = plus_plus_nat(plus_plus_nat(size_size_com(Com1),size_size_com(Com2)),suc(zero_zero_nat))) # label(fact_691_com_Osize_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 726 (all C0 all C1 all N_1 all S1 all B all S (-hBOOL(hAPP_state_bool(B,S)) -> (hBOOL(hAPP_state_bool(evaln(C1,S,N_1),S1)) -> hBOOL(hAPP_state_bool(evaln(cond(B,C0,C1),S,N_1),S1))))) # label(fact_692_evaln_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 727 (all C1 all C0 all N_1 all S1 all B all S (hBOOL(hAPP_state_bool(B,S)) -> (hBOOL(hAPP_state_bool(evaln(C0,S,N_1),S1)) -> hBOOL(hAPP_state_bool(evaln(cond(B,C0,C1),S,N_1),S1))))) # label(fact_693_evaln_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 728 (all B all C1 all C2 all S all N_1 all T (hBOOL(hAPP_state_bool(evaln(cond(B,C1,C2),S,N_1),T)) -> ((hBOOL(hAPP_state_bool(B,S)) -> -hBOOL(hAPP_state_bool(evaln(C1,S,N_1),T))) -> -(-hBOOL(hAPP_state_bool(B,S)) -> -hBOOL(hAPP_state_bool(evaln(C2,S,N_1),T)))))) # label(fact_694_evaln__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 729 (all B all C1 all C2 all S all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B,C1,C2)),S),T)) -> ((hBOOL(hAPP_state_bool(B,S)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S),T))) -> -(-hBOOL(hAPP_state_bool(B,S)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S),T)))))) # label(fact_695_evalc__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 730 (all C1 all C0 all S1 all B all S (hBOOL(hAPP_state_bool(B,S)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S),S1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B,C0,C1)),S),S1))))) # label(fact_696_evalc_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 731 (all C0 all C1 all S1 all B all S (-hBOOL(hAPP_state_bool(B,S)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S),S1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B,C0,C1)),S),S1))))) # label(fact_697_evalc_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 732 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 733 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 734 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 735 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 736 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 737 (all Q all P (-hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 738 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 739 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 740 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 741 (all Q all P (hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 742 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 743 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 744 (all P hAPP_nat_nat(cOMBI_nat,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 745 (all X_1 all Y (is_pname(X_1) & is_pname(Y) -> -hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 746 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 747 (all X_1 all Y (-hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 748 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 749 (all P all Q (is_bool(P) -> hAPP_pname_bool(hAPP_b76515610e_bool(cOMBK_bool_pname,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 750 (all P all Q (is_pname(P) -> hAPP_pname_pname(hAPP_p1170154830_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].
% 1.39/1.80 751 (all X_1 all Y (is_fun_pname_bool(X_1) & is_fun_pname_bool(Y) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 752 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 753 (all P all Q hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 754 (all X_1 all Y hAPP_H678412245iple_a(hAPP_H1455657330iple_a(hAPP_b385840250iple_a(if_Hoa638970256iple_a,fTrue),X_1),Y) = X_1) # label(help_If_1_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 755 (all X_1 all Y hAPP_H678412245iple_a(hAPP_H1455657330iple_a(hAPP_b385840250iple_a(if_Hoa638970256iple_a,fFalse),X_1),Y) = Y) # label(help_If_2_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 756 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 757 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(cOMBB_647938656_pname(P),Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 758 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 759 (all P all Q all R hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 760 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,P),Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 761 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 762 (all P all Q all R hAPP_pname_bool(hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 763 (all P all Q all R hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 764 (all X_1 all Y (-hBOOL(hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(fequal879838495iple_a,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 765 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(fequal879838495iple_a,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 766 (all P all Q hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(cOMBK_631994958_state,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 767 (all X_1 all Y hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fTrue),X_1),Y) = X_1) # label(help_If_1_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 768 (all X_1 all Y hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fFalse),X_1),Y) = Y) # label(help_If_2_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 769 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 770 (all X_1 all Y (-hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 771 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 772 (all P all Q all R hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 773 (all P all Q (is_bool(P) -> hAPP_H1421470952a_bool(hAPP_b119575286a_bool(cOMBK_151824839iple_a,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 774 (all P all Q all R hAPP_pname_com(hAPP_f96342628me_com(cOMBB_923936821_pname(P),Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 775 (all P all Q hAPP_p263283121iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 776 (all P all Q all R hAPP_p393069232l_bool(hAPP_f1402196763l_bool(cOMBB_675860798_pname(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 777 (all P all Q all R hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 778 (all P all Q all R hAPP_pname_bool(hAPP_f42430548e_bool(cOMBB_530759491_pname(P),Q),R) = hAPP_f1664156314l_bool(P,hAPP_p61793385e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 779 (all P all Q all R hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 780 (all P all Q all R hAPP_s1806633685e_bool(hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_s1874344717e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__fun_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 781 (all X_1 all Y (-hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(fequal1258664663a_bool,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 782 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(fequal1258664663a_bool,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 783 (all P all Q (is_bool(P) -> hAPP_H513860823e_bool(hAPP_b1245957081e_bool(cOMBK_1079618832_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg___010) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 784 (all P all Q hAPP_p1842370726_state(hAPP_H1797237070_state(cOMBK_90103121_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 785 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(cOMBB_1799513916iple_a(P),Q),R) = hAPP_bool_bool(P,hAPP_H1421470952a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 786 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1017515220l_bool(P,R),hAPP_H1421470952a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 787 (all P all Q all R hAPP_pname_bool(hAPP_H1991058245e_bool(hAPP_f687460073e_bool(cOMBC_1693967286a_bool,P),Q),R) = hAPP_H1421470952a_bool(hAPP_p2127663045a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 788 (all X_1 all Y (-hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_011) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 789 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_012) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 790 (all P all Q all R hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 791 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBB_416661851_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel_013) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 792 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 793 (all P all Q all R hAPP_pname_bool(hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_p877885514e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__014) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 794 (all P all Q all R hAPP_p61793385e_bool(hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 795 (all P all Q all R hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_s1226857760e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 796 (all P all Q all R hAPP_H1017515220l_bool(hAPP_f997599971l_bool(cOMBB_1782929690iple_a(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1421470952a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 797 (all P all Q all R hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_a2036067514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 798 (all P all Q all R hAPP_H226398757l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_017) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 799 (all P all Q all R hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,P),Q),R) = hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 800 (all P all Q all R hAPP_p263283121iple_a(hAPP_f1044063253iple_a(hAPP_f1401255196iple_a(cOMBS_1128650103iple_a,P),Q),R) = hAPP_H678412245iple_a(hAPP_p363087182iple_a(P,R),hAPP_p263283121iple_a(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 801 (all P all Q all R hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(cOMBB_1759179140_state(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_s1806633685e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_018) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 802 (all P all Q all R hAPP_p263283121iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,P),Q),R) = hAPP_f150255961iple_a(hAPP_p344936018iple_a(P,R),hAPP_p635540397e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_It__a_Mtc__fun_Itc__Com__Osta) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 803 (all P all Q all R hAPP_p1842370726_state(hAPP_f1026488024_state(cOMBB_2118237115_pname(P),Q),R) = hAPP_H928324994_state(P,hAPP_p263283121iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 804 (all P all Q all R hAPP_p263283121iple_a(hAPP_f113652738iple_a(cOMBB_2015474199_pname(P),Q),R) = hAPP_H1600811558iple_a(P,hAPP_p1842370726_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 805 (all P all Q all R hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_a849909144l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 806 (all P all Q all R hAPP_H513860823e_bool(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 807 (all P all Q all R hAPP_p1842370726_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,P),Q),R) = hAPP_H563960305_state(hAPP_p80247908_state(P,R),hAPP_p1842370726_state(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__019) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 808 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f772297704a_bool(cOMBB_1501709507iple_a(P),Q),R) = hAPP_f540970102l_bool(P,hAPP_H1190454433a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 809 (all P all Q all R hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,P),Q),R) = hAPP_f540970102l_bool(hAPP_H1840393229l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_020) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 810 (all P all Q all R hAPP_p2127663045a_bool(hAPP_f1311175287a_bool(cOMBB_858699740_pname(P),Q),R) = hAPP_H1190454433a_bool(P,hAPP_p263283121iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_021) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 811 (all P all Q all R hAPP_p1842370726_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,P),Q),R) = hAPP_f588507005_state(hAPP_p1712839024_state(P,R),hAPP_p1637813682e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 812 (all P all Q all R hAPP_s1874344717e_bool(hAPP_f873506917e_bool(cOMBB_1757942702_state(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_s2001034685l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_022) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 813 (all P all Q all R hAPP_p344936018iple_a(hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,P),Q),R) = hAPP_c1407587404iple_a(hAPP_p1263586117iple_a(P,R),hAPP_pname_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_It_) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 814 (all P all Q all R hAPP_H513860823e_bool(hAPP_f1456107715e_bool(cOMBB_1653402815_state(P),Q),R) = hAPP_f1760790145l_bool(P,hAPP_H1645666623e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_023) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 815 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___024) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 816 (all P all Q all R hAPP_p877885514e_bool(hAPP_f998786331e_bool(cOMBB_799949246_pname(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_p1842370726_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___025) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 817 (all P all Q all R hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_a849909144l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_026) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 818 (all P all Q all R hAPP_p2127663045a_bool(hAPP_f1646799884a_bool(hAPP_f2022238777a_bool(cOMBC_1527561185a_bool,P),Q),R) = hAPP_f1591852335a_bool(hAPP_p54391842a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____dd) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 819 (all P all Q all R hAPP_p1712839024_state(hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,P),Q),R) = hAPP_c408625258_state(hAPP_p2032835427_state(P,R),hAPP_pname_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 820 (all P all Q all R hAPP_s1226857760e_bool(hAPP_f1138284024e_bool(cOMBB_20296667_state(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_s2001034685l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_027) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 821 (all P all Q all R hAPP_p363087182iple_a(hAPP_f866544818iple_a(hAPP_f428084316iple_a(cOMBS_546756116iple_a,P),Q),R) = hAPP_H1455657330iple_a(hAPP_p321057131iple_a(P,R),hAPP_p263283121iple_a(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__028) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 822 (all P all Q all R hAPP_p877885514e_bool(hAPP_f621094798e_bool(hAPP_f1505732693e_bool(cOMBC_173904839e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_p1682965390e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____dd_029) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.80 823 (all P all Q all R hAPP_H1190454433a_bool(hAPP_f1665407592a_bool(hAPP_f549683569a_bool(cOMBC_708118077a_bool,P),Q),R) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_030) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 824 (all P all Q all R hAPP_p321057131iple_a(hAPP_f653022294iple_a(cOMBB_1916528323_pname(P),Q),R) = hAPP_b385840250iple_a(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 825 (all P all Q all R hAPP_p80247908_state(hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,P),Q),R) = hAPP_H521649881_state(hAPP_p964374716_state(P,R),hAPP_p1842370726_state(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__031) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 826 (all P all Q all R hAPP_p1263586117iple_a(hAPP_f1504849325iple_a(cOMBB_109684016_pname(P),Q),R) = hAPP_f1807945453iple_a(P,hAPP_p635540397e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 827 (all P all Q all R hAPP_p54391842a_bool(hAPP_f1728520198a_bool(cOMBB_1191710871_pname(P),Q),R) = hAPP_H1641355846a_bool(P,hAPP_p263283121iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_032) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 828 (all P all Q all R hAPP_H1645666623e_bool(hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___033) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 829 (all P all Q all R hAPP_p964374716_state(hAPP_f1405979047_state(cOMBB_707293872_pname(P),Q),R) = hAPP_b798484845_state(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp_034) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 830 (all P all Q all R hAPP_p2032835427_state(hAPP_f950918952_state(cOMBB_2123334001_pname(P),Q),R) = hAPP_f1949912908_state(P,hAPP_p1637813682e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 831 (all P all Q all R hAPP_p1682965390e_bool(hAPP_f1191449183e_bool(cOMBB_557071226_pname(P),Q),R) = hAPP_H727730819e_bool(P,hAPP_p1842370726_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___035) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.81 832 (all N ((all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,g),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),p)),body)),q)),procs)))) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)))) -> (all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),p)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),q)),procs))) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption].
% 1.39/1.81 833 -((all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),g)) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(n),X)))) -> (all X (hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),p)),body)),q)),procs))) -> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(n),X))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.20/2.48
% 2.20/2.48 ============================== end of process non-clausal formulas ===
% 2.20/2.48
% 2.20/2.48 ============================== PROCESS INITIAL CLAUSES ===============
% 2.20/2.48
% 2.20/2.48 ============================== PREDICATE ELIMINATION =================
% 2.20/2.48
% 2.20/2.48 ============================== end predicate elimination =============
% 2.20/2.48
% 2.20/2.48 Auto_denials: (non-Horn, no changes).
% 2.20/2.48
% 2.20/2.48 Term ordering decisions:
% 2.20/2.48 Function symbol KB weights: semila1168014441p_bool=1. member_pname=1. semila278973382e_bool=1. semila1498788770a_bool=1. semila447562797e_bool=1. member1713797107iple_a=1. bot_bo1055319631e_bool=1. bot_bo1181479936a_bool=1. bot_bo844097828e_bool=1. insert1835143293_state=1. insert873085594iple_a=1. member1758697444_state=1. insert_pname=1. finite_finite_pname=1. zero_zero_nat=1. hoare_1760757500iple_a=1. hoare_1575745797_state=1. finite1655202547iple_a=1. finite784854244_state=1. collect_pname=1. collec268032053iple_a=1. body=1. fconj=1. finite_finite_bool=1. bot_bo806936373l_bool=1. bot_bot_bool=1. fdisj=1. cOMBS_568398431l_bool=1. body_1=1. collec727977250_state=1. the_com=1. cOMBC_1058051404l_bool=1. cOMBS_1148211387l_bool=1. bot_bo1649642514l_bool=1. cOMBS_2104302062iple_a=1. cOMBS_260455419iple_a=1. finite595471783e_bool=1. cOMBC_1552014468l_bool=1. fequal1531560888_state=1. fequal879838495iple_a=1. cOMBS_1401555724_state=1. cOMBS_1615712031_state=1. fequal_pname=1. finite652815363a_bool=1. finite899049100e_bool=1. bot_bo1325387246l_bool=1. bot_bo1325454745l_bool=1. cOMBS_1248383340l_bool=1. member_bool=1. cOMBC_764456866l_bool=1. fFalse=1. fNot=1. cOMBC_1149511130e_bool=1. cOMBC_1424981238e_bool=1. cOMBC_839220826a_bool=1. skip=1. member799430823e_bool=1. fTrue=1. fimplies=1. insert_bool=1. one_one_nat=1. semila1866150931l_bool=1. cOMBC_231445413l_bool=1. fequal_state=1. member1154012931a_bool=1. member402455436e_bool=1. procs=1. cOMBK_1347789874_pname=1. cOMBK_90103121_pname=1. insert1325755072e_bool=1. insert1805675420a_bool=1. insert1991711667e_bool=1. p=1. q=1. cOMBC_2027030106e_bool=1. cOMBC_41962815e_bool=1. cOMBC_471052088e_bool=1. cOMBK_1458035955bool_a=1. cOMBK_631994958_state=1. cOMBS_1378840469l_bool=1. fequal1258664663a_bool=1. fequal1746921144e_bool=1. fequal533582459e_bool=1. if_Hoa533980679_state=1. if_Hoa638970256iple_a=1. semila1782091504l_bool=1. semila1827648460l_bool=1. semila2055205435l_bool=1. bool=1. cOMBC_1123258281e_bool=1. cOMBC_1527561185a_bool=1. cOMBC_1693967286a_bool=1. cOMBC_173904839e_bool=1. cOMBC_290948233e_bool=1. cOMBC_488258100e_bool=1. cOMBC_708118077a_bool=1. cOMBC_892787026e_bool=1. cOMBC_952831051e_bool=1. cOMBI_nat=1. cOMBK_1079618832_state=1. cOMBK_151824839iple_a=1. cOMBK_bool_pname=1. cOMBK_pname_pname=1. cOMBS_1128650103iple_a=1. cOMBS_381334199_state=1. cOMBS_546756116iple_a=1. cOMBS_843273363_state=1. g=1. pname=1. the_el1436340927iple_a=1. the_el23965208_state=1. the_elem_pname=1. bot_bot_nat=1. n=1. the_Ho10452358_state=1. the_Ho746640593iple_a=1. the_pname=1. c1=1. hAPP_f759274231e_bool=1. hAPP_f1591852335a_bool=1. hAPP_f921536533e_bool=1. hAPP_bool_bool=1. hAPP_f1664156314l_bool=1. hAPP_f540970102l_bool=1. hAPP_f1760790145l_bool=1. hAPP_b589554111l_bool=1. hAPP_f1388330588e_bool=1. hAPP_p338031245l_bool=1. hAPP_f1026156344a_bool=1. hAPP_f1583986009e_bool=1. hAPP_H1840393229l_bool=1. hAPP_state_bool=1. hAPP_H1641355846a_bool=1. hAPP_H727730819e_bool=1. hAPP_H1421470952a_bool=1. hAPP_H248360617l_bool=1. hAPP_pname_bool=1. hAPP_p905327722e_bool=1. hAPP_H513860823e_bool=1. hAPP_s1806633685e_bool=1. plus_plus_nat=1. hAPP_f271130963a_bool=1. hAPP_c408625258_state=1. hAPP_f1949912908_state=1. hAPP_f588507005_state=1. hAPP_c1407587404iple_a=1. hAPP_f150255961iple_a=1. hAPP_f1807945453iple_a=1. hAPP_f631639356e_bool=1. hAPP_f387058535l_bool=1. hAPP_nat_nat=1. hAPP_pname_com=1. hAPP_f1297739591_pname=1. while=1. hAPP_f961197973l_bool=1. hAPP_f1935102916l_bool=1. hAPP_f124283079iple_a=1. hAPP_f2143211163_state=1. hAPP_p1842370726_state=1. hAPP_p263283121iple_a=1. hAPP_f1402196763l_bool=1. hAPP_f649174806e_bool=1. hAPP_nat_bool=1. hAPP_pname_pname=1. hAPP_a2036067514e_bool=1. hAPP_f1557928608l_bool=1. hAPP_f239102607l_bool=1. hAPP_H1190454433a_bool=1. hAPP_H1645666623e_bool=1. hAPP_H678412245iple_a=1. hAPP_f1203760810a_bool=1. hAPP_f661147897e_bool=1. hAPP_f997599971l_bool=1. hAPP_p61793385e_bool=1. hAPP_H563960305_state=1. hAPP_f1139368540iple_a=1. hAPP_f1504849325iple_a=1. hAPP_f1821846428iple_a=1. hAPP_f773999884iple_a=1. hAPP_f79369369iple_a=1. semi=1. hAPP_f672239281a_bool=1. hAPP_f559147733l_bool=1. hAPP_H1455657330iple_a=1. hAPP_option_com_com=1. hAPP_p799580910on_com=1. hAPP_H521649881_state=1. hAPP_f1296386871_state=1. hAPP_f1777033564_state=1. hAPP_f2136041130_state=1. hAPP_f358330902_state=1. hAPP_f950918952_state=1. hAPP_p1170154830_pname=1. hAPP_f1970439265l_bool=1. hAPP_f960623701l_bool=1. hAPP_b1787118453l_bool=1. hAPP_f1558728829l_bool=1. hAPP_f760664097e_bool=1. hAPP_f1126670547e_bool=1. hAPP_f1262649863e_bool=1. finite1282449217_pname=1. hAPP_f1371755681a_bool=1. hAPP_f22061361e_bool=1. hAPP_f262880489e_bool=1. hAPP_p1637813682e_bool=1. hAPP_p635540397e_bool=1. finite89670078_pname=1. hAPP_f556039215l_bool=1. hAPP_f96342628me_com=1. finite1669978781iple_a=1. finite774711482_state=1. hAPP_b496459037l_bool=1. hAPP_f1172769267l_bool=1. hAPP_f1759915619e_bool=1. finite950012314iple_a=1. hAPP_H676960377_pname=1. hAPP_f105100493l_bool=1. hAPP_f1849264231l_bool=1. hAPP_f1863945078e_bool=1. hAPP_f762886889e_bool=1. finite506823037_state=1. hAPP_H1578029518iple_a=1. hAPP_H1797237070_state=1. hAPP_f1182387808e_bool=1. hAPP_f1283379615l_bool=1. hAPP_f1320879424l_bool=1. hAPP_f1509969235l_bool=1. hAPP_f1556354660l_bool=1. hAPP_f434788991l_bool=1. hAPP_f601642911l_bool=1. hAPP_f75870650a_bool=1. hAPP_s58564346l_bool=1. hAPP_H1017515220l_bool=1. hAPP_H1632039476e_bool=1. hAPP_H1991058245e_bool=1. hAPP_H226398757l_bool=1. hAPP_a849909144l_bool=1. hAPP_b1095269219e_bool=1. hAPP_b2019457360e_bool=1. hAPP_b385840250iple_a=1. hAPP_b540892988e_bool=1. hAPP_b76515610e_bool=1. hAPP_b798484845_state=1. hAPP_f1259673775l_bool=1. hAPP_f1587382801l_bool=1. hAPP_f167292325e_bool=1. hAPP_f1824947087e_bool=1. hAPP_f230953622l_bool=1. hAPP_f340725611e_bool=1. hAPP_f42430548e_bool=1. hAPP_f430043647l_bool=1. hAPP_f644196280e_bool=1. hAPP_f701449317e_bool=1. hAPP_f817621513e_bool=1. hAPP_f854625363l_bool=1. hAPP_f873506917e_bool=1. hAPP_f997688506l_bool=1. hAPP_p2127663045a_bool=1. hAPP_p393069232l_bool=1. hAPP_p877885514e_bool=1. hAPP_s2001034685l_bool=1. hAPP_a1200519163e_bool=1. hAPP_a723219176e_bool=1. hAPP_b119575286a_bool=1. hAPP_b1245957081e_bool=1. hAPP_f1026488024_state=1. hAPP_f1044063253iple_a=1. hAPP_f113652738iple_a=1. hAPP_f1138284024e_bool=1. hAPP_f1191449183e_bool=1. hAPP_f1261923407e_bool=1. hAPP_f1311175287a_bool=1. hAPP_f137248406_state=1. hAPP_f1401255196iple_a=1. hAPP_f1405979047_state=1. hAPP_f1456107715e_bool=1. hAPP_f1505732693e_bool=1. hAPP_f1646799884a_bool=1. hAPP_f1661207211_state=1. hAPP_f1665407592a_bool=1. hAPP_f167506745e_bool=1. hAPP_f1728520198a_bool=1. hAPP_f180827860e_bool=1. hAPP_f2022238777a_bool=1. hAPP_f2101567797_state=1. hAPP_f428084316iple_a=1. hAPP_f549683569a_bool=1. hAPP_f621094798e_bool=1. hAPP_f653022294iple_a=1. hAPP_f687460073e_bool=1. hAPP_f698292281e_bool=1. hAPP_f762269719e_bool=1. hAPP_f772297704a_bool=1. hAPP_f866544818iple_a=1. hAPP_f915354021e_bool=1. hAPP_f939130838_state=1. hAPP_f963367678e_bool=1. hAPP_f964290431e_bool=1. hAPP_f998786331e_bool=1. hAPP_p1263586117iple_a=1. hAPP_p1682965390e_bool=1. hAPP_p1712839024_state=1. hAPP_p2032835427_state=1. hAPP_p321057131iple_a=1. hAPP_p344936018iple_a=1. hAPP_p363087182iple_a=1. hAPP_p54391842a_bool=1. hAPP_p80247908_state=1. hAPP_p964374716_state=1. hAPP_s1226857760e_bool=1. hAPP_s1874344717e_bool=1. fun=1. hAPP_H1600811558iple_a=1. hAPP_H928324994_state=1. hoare_1674107620_state=1. hoare_953425885size_a=1. f2=1. f3=1. f5=1. f6=1. f50=1. f51=1. f71=1. f72=1. f93=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. f100=1. f109=1. f110=1. f111=1. f112=1. f113=1. f114=1. f115=1. f116=1. f117=1. f131=1. f132=1. f133=1. f134=1. f135=1. f136=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f156=1. f157=1. f158=1. f159=1. f160=1. f161=1. semila1635148844e_bool=1. semila310582991f_bool=1. semila671163144a_bool=1. suc=1. semila2145357127e_bool=1. image_1654749281iple_a=1. big_la1480321694n_bool=1. hoare_606018542rivs_a=1. hoare_659004819_state=1. image_275883510_state=1. evalc=1. minus_minus_nat=1. big_la841148155e_bool=1. hoare_560051114alid_a=1. big_la1640362552e_bool=1. big_la1993344855a_bool=1. cOMBB_675860798_pname=1. hoare_592710359_state=1. cOMBB_1782929690iple_a=1. cOMBB_109684016_pname=1. cOMBB_2123334001_pname=1. cOMBB_1382207997_state=1. minus_1015773161e_bool=1. size_size_com=1. image_2068426537_pname=1. image_bool_bool=1. minus_469558085a_bool=1. cOMBB_188601460_state=1. cOMBB_923936821_pname=1. com_size=1. image_pname_pname=1. semila1551573549l_bool=1. hoare_1065416081_state=1. hoare_943851888lids_a=1. minus_2076558538e_bool=1. cOMBB_1355796797bool_a=1. cOMBB_1759179140_state=1. cOMBB_647938656_pname=1. image_129517430iple_a=1. image_1604514514_state=1. big_la472677547n_bool=1. cOMBB_1348041619bool_a=1. cOMBB_160679318_state=1. cOMBB_1757942702_state=1. image_2063528359e_bool=1. semila1130628874l_bool=1. semila1410775201l_bool=1. semila1746965734l_bool=1. big_la28065288e_bool=1. cOMBB_1191710871_pname=1. cOMBB_145932198bool_a=1. cOMBB_1501709507iple_a=1. cOMBB_1653402815_state=1. cOMBB_1799513916iple_a=1. cOMBB_1916528323_pname=1. cOMBB_2015474199_pname=1. cOMBB_20296667_state=1. cOMBB_2118237115_pname=1. cOMBB_416661851_state=1. cOMBB_530759491_pname=1. cOMBB_557071226_pname=1. cOMBB_707293872_pname=1. cOMBB_799949246_pname=1. cOMBB_858699740_pname=1. big_la1164677860a_bool=1. big_la508066411e_bool=1. hoare_Mirabelle_MGT=1. image_119931871a_bool=1. image_306007685iple_a=1. image_505022149e_bool=1. image_650584225_state=1. size_s315943222iple_a=1. size_s346246881_state=1. undefi17486888e_bool=1. undefined_bool=1. undefined_pname=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f70=1. f73=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f137=1. f138=1. f139=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f187=1. evaln=1. cond=1. nat_case_nat=1. f1=1. f4=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. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f74=1. f82=1. f124=1. f125=1. f126=1. f127=1. f128=1. f129=1. f162=1. f163=1. f164=1. f165=1. f166=1. f167=1. f168=1. f169=1. f170=1. f171=1. f172=1. f173=1. f174=1. f175=1. f176=1. f177=1. f178=1. f179=1. f180=1. f181=1. f182=1. f183=1. f184=1. f185=1. f186=1. finite216774046_pname=1. finite979333485_pname=1. f36=1. f37=1. f52=1. f53=1. f54=1. f55=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f85=1. f101=1. f118=1. f119=1. f120=1. f121=1. f122=1. f123=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f86=1. f102=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f83=1. f84=1. f130=1.
% 4.51/4.76
% 4.51/4.76 ============================== end of process initial clauses ========
% 4.51/4.76
% 4.51/4.76 ============================== CLAUSES FOR SEARCH ====================
% 4.51/4.76
% 4.51/4.76 ============================== end of clauses for search =============
% 4.51/4.76
% 4.51/4.76 ============================== SEARCH ================================
% 4.51/4.76
% 4.51/4.76 % Starting search at 0.86 seconds.
% 4.51/4.76
% 4.51/4.76 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 2.57 sec).
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=45.000, iters=3530
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=43.000, iters=3517
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=39.000, iters=3386
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=36.000, iters=3348
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=35.000, iters=3348
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=34.000, iters=3438
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=33.000, iters=3354
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=32.000, iters=3380
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=31.000, iters=3358
% 4.51/4.76
% 4.51/4.76 Low Water (keep): wt=30.000, iters=337Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------