TSTP Solution File: SWW471+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW471+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 01:17:07 EDT 2022
% Result : Timeout 300.02s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW471+3 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 5 06:00:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.61/2.04 ============================== Prover9 ===============================
% 1.61/2.04 Prover9 (32) version 2009-11A, November 2009.
% 1.61/2.04 Process 674 was started by sandbox on n017.cluster.edu,
% 1.61/2.04 Sun Jun 5 06:00:16 2022
% 1.61/2.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_494_n017.cluster.edu".
% 1.61/2.04 ============================== end of head ===========================
% 1.61/2.04
% 1.61/2.04 ============================== INPUT =================================
% 1.61/2.04
% 1.61/2.04 % Reading from file /tmp/Prover9_494_n017.cluster.edu
% 1.61/2.04
% 1.61/2.04 set(prolog_style_variables).
% 1.61/2.04 set(auto2).
% 1.61/2.04 % set(auto2) -> set(auto).
% 1.61/2.04 % set(auto) -> set(auto_inference).
% 1.61/2.04 % set(auto) -> set(auto_setup).
% 1.61/2.04 % set(auto_setup) -> set(predicate_elim).
% 1.61/2.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.61/2.04 % set(auto) -> set(auto_limits).
% 1.61/2.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.61/2.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.61/2.04 % set(auto) -> set(auto_denials).
% 1.61/2.04 % set(auto) -> set(auto_process).
% 1.61/2.04 % set(auto2) -> assign(new_constants, 1).
% 1.61/2.04 % set(auto2) -> assign(fold_denial_max, 3).
% 1.61/2.04 % set(auto2) -> assign(max_weight, "200.000").
% 1.61/2.04 % set(auto2) -> assign(max_hours, 1).
% 1.61/2.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.61/2.04 % set(auto2) -> assign(max_seconds, 0).
% 1.61/2.04 % set(auto2) -> assign(max_minutes, 5).
% 1.61/2.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.61/2.04 % set(auto2) -> set(sort_initial_sos).
% 1.61/2.04 % set(auto2) -> assign(sos_limit, -1).
% 1.61/2.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.61/2.04 % set(auto2) -> assign(max_megs, 400).
% 1.61/2.04 % set(auto2) -> assign(stats, some).
% 1.61/2.04 % set(auto2) -> clear(echo_input).
% 1.61/2.04 % set(auto2) -> set(quiet).
% 1.61/2.04 % set(auto2) -> clear(print_initial_clauses).
% 1.61/2.04 % set(auto2) -> clear(print_given).
% 1.61/2.04 assign(lrs_ticks,-1).
% 1.61/2.04 assign(sos_limit,10000).
% 1.61/2.04 assign(order,kbo).
% 1.61/2.04 set(lex_order_vars).
% 1.61/2.04 clear(print_given).
% 1.61/2.04
% 1.61/2.04 % formulas(sos). % not echoed (1423 formulas)
% 1.61/2.04
% 1.61/2.04 ============================== end of input ==========================
% 1.61/2.04
% 1.61/2.04 % From the command line: assign(max_seconds, 300).
% 1.61/2.04
% 1.61/2.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.61/2.04
% 1.61/2.04 % Formulas that are not ordinary clauses:
% 1.61/2.04 1 (all B_1_1 all B_2_1 all B_3_1 is_bool(big_co2022808324_pname(B_1_1,B_2_1,B_3_1))) # label(gsy_c_Big__Operators_Ocomm__monoid__big_000tc__fun_Itc__Hoare____Mirabelle____uw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 2 (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].
% 1.61/2.04 3 (all B_1_1 all B_2_1 is_bool(finite1753440478iple_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 4 (all B_1_1 all B_2_1 is_bool(finite683959609_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_001) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 5 (all B_1_1 all B_2_1 is_bool(finite988810631ne_nat(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 6 (all B_1_1 all B_2_1 is_bool(finite2103247258a_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 7 (all B_1_1 all B_2_1 is_bool(finite89670078_pname(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 8 (all B_1_1 all B_2_1 is_bool(finite1033474011iple_a(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 9 (all B_1_1 all B_2_1 is_bool(finite416071164_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__O_002) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 10 (all B_1_1 all B_2_1 is_bool(finite795500164em_nat(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 11 (all B_1_1 all B_2_1 is_bool(finite927518301a_bool(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Hoare____Mirabelle____uwgp) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 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].
% 1.61/2.04 22 (all B_1_1 all B_2_1 is_pname(hAPP_H2000557816_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 23 (all B_1_1 all B_2_1 is_bool(hAPP_H1037229737a_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__HOL__) # label(hypothesis) # label(non_clause). [assumption].
% 1.61/2.04 24 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H1078816262e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__fun_I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 25 (all B_1_1 all B_2_1 is_fun_bool_bool(hAPP_H2130837971l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__fun_I_003) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 26 (all B_1_1 all B_2_1 is_bool(hAPP_H242767318e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 27 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_H1776011827e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_004) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 28 (all B_1_1 all B_2_1 is_fun_bool_bool(hAPP_H1270401638l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_005) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 29 (all B_1_1 all B_2_1 is_pname(hAPP_nat_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 30 (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].
% 1.61/2.04 31 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 32 (all B_1_1 all B_2_1 is_fun_bool_bool(hAPP_n1006566506l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 33 (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].
% 1.61/2.04 34 (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].
% 1.61/2.04 35 (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].
% 1.61/2.04 36 (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].
% 1.61/2.04 37 (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].
% 1.61/2.04 38 (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].
% 1.61/2.04 39 (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].
% 1.61/2.04 40 (all B_1_1 all B_2_1 is_pname(hAPP_f1764134762_pname(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 41 (all B_1_1 all B_2_1 is_bool(hAPP_f1695230391l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc_006) # label(hypothesis) # label(non_clause). [assumption].
% 1.61/2.04 42 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f1216026388e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc_007) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 43 (all B_1_1 all B_2_1 is_fun_bool_bool(hAPP_f244528453l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc_008) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 44 (all B_1_1 all B_2_1 is_bool(hAPP_f1378282496l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 45 (all B_1_1 all B_2_1 is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 46 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f654413245e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 47 (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].
% 1.61/2.04 48 (all B_1_1 all B_2_1 (is_fun1661590463l_bool(B_2_1) -> is_fun_pname_bool(hAPP_f674760225e_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_009) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 49 (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_010) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 50 (all B_1_1 all B_2_1 is_bool(hAPP_f2110825313l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 51 (all B_1_1 all B_2_1 is_fun_pname_bool(hAPP_f147139262e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It_011) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 52 (all B_1_1 all B_2_1 is_bool(hAPP_f1410040974l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It_012) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 53 (all B_1_1 all B_2_1 is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 54 (all B_1_1 all B_2_1 is_bool(hAPP_f670355311l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 55 (all Fun1 all Com_1 all Fun2 all Fun1_2 all Com all Fun2_2 (hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1),Com_1),Fun2) = hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1_2),Com),Fun2_2) <-> Fun1 = Fun1_2 & Com_1 = Com & Fun2 = Fun2_2)) # label(fact_0_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 56 (all Fun1 all Com_1 all Fun2 all Fun1_2 all Com all Fun2_2 (hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com_1),Fun2) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_2),Com),Fun2_2) <-> Fun1 = Fun1_2 & Com_1 = Com & Fun2 = Fun2_2)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 57 (all Ga all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(Ga),Ts)) <-> (all N ((all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ga)) -> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N),X)))) -> (all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ts)) -> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N),X)))))))) # label(fact_2_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 58 (all Ga all Ts (hBOOL(hAPP_f1695230391l_bool(hoare_293150257lids_a(Ga),Ts)) <-> (all N ((all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ga)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)))) -> (all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ts)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)))))))) # label(fact_3_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 59 (all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),body)),Qa)),Procsa))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),body)),Qa)),Procsa))))) # label(fact_4_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 60 (all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),body)),Qa)),Procsa))))) # label(fact_5_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 61 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2))))) # label(fact_6_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 62 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) -> (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2))))) # label(fact_7_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 63 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2))))) # label(fact_8_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 64 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2))))) # label(fact_9_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 65 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2))))) # label(fact_10_UnE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 66 (all A_1 all B_2 all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2)) -> (-hBOOL(hAPP_nat_bool(A_1,X_2)) -> hBOOL(hAPP_nat_bool(B_2,X_2))))) # label(fact_11_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 67 (all A_1 all B_2 all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2)) -> (-hBOOL(hAPP_f1695230391l_bool(A_1,X_2)) -> hBOOL(hAPP_f1695230391l_bool(B_2,X_2))))) # label(fact_12_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 68 (all A_1 all B_2 all X_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2)) -> (-hBOOL(hAPP_H242767318e_bool(A_1,X_2)) -> hBOOL(hAPP_H242767318e_bool(B_2,X_2))))) # label(fact_13_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 69 (all A_1 all B_2 all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2)) -> (-hBOOL(hAPP_pname_bool(A_1,X_2)) -> hBOOL(hAPP_pname_bool(B_2,X_2))))) # label(fact_14_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 70 (all A_1 all B_2 all X_2 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2)) -> (-hBOOL(hAPP_H1037229737a_bool(A_1,X_2)) -> hBOOL(hAPP_H1037229737a_bool(B_2,X_2))))) # label(fact_15_sup1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 71 (all A_1 all B_2 all X_2 ((-hBOOL(hAPP_nat_bool(B_2,X_2)) -> hBOOL(hAPP_nat_bool(A_1,X_2))) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2)))) # label(fact_16_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 72 (all A_1 all B_2 all X_2 ((-hBOOL(hAPP_f1695230391l_bool(B_2,X_2)) -> hBOOL(hAPP_f1695230391l_bool(A_1,X_2))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2)))) # label(fact_17_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 73 (all A_1 all B_2 all X_2 ((-hBOOL(hAPP_H242767318e_bool(B_2,X_2)) -> hBOOL(hAPP_H242767318e_bool(A_1,X_2))) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2)))) # label(fact_18_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 74 (all A_1 all B_2 all X_2 ((-hBOOL(hAPP_pname_bool(B_2,X_2)) -> hBOOL(hAPP_pname_bool(A_1,X_2))) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2)))) # label(fact_19_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 75 (all A_1 all B_2 all X_2 ((-hBOOL(hAPP_H1037229737a_bool(B_2,X_2)) -> hBOOL(hAPP_H1037229737a_bool(A_1,X_2))) -> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2)))) # label(fact_20_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 76 (all A_1 all C_2 all B_2 ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))))) # label(fact_21_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 77 (all A_1 all C_2 all B_2 ((-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))))) # label(fact_22_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 78 (all A_1 all C_2 all B_2 ((-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))))) # label(fact_23_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 79 (all A_1 all C_2 all B_2 ((-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))))) # label(fact_24_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 80 (all A_1 all C_2 all B_2 ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))))) # label(fact_25_UnCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 81 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_nat_nat(F,X_2) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1)))))) # label(fact_26_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 82 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_p1751618853_state(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1)))))) # label(fact_27_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 83 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_pname_nat(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f1066163005t_bool(image_pname_nat(F),A_1)))))) # label(fact_28_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 84 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_p1743421830a_bool(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1)))))) # label(fact_29_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 85 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_nat_pname(F,X_2) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f654413245e_bool(image_nat_pname(F),A_1)))))) # label(fact_30_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 86 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_f1764134762_pname(F,X_2) -> (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1)))))) # label(fact_31_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 87 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_H2000557816_pname(F,X_2) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1)))))) # label(fact_32_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 88 (all A_1 all B_1 all F all X_2 (B_1 = hAPP_p346744818iple_a(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)))))) # label(fact_33_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 89 (all F all A_1 all B_2 hAPP_f800510211t_bool(image_nat_nat(F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(image_nat_nat(F),A_1)),hAPP_f800510211t_bool(image_nat_nat(F),B_2))) # label(fact_34_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 90 (all F all A_1 all B_2 hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A_1)),hAPP_f360545851e_bool(image_185131637_state(F),B_2))) # label(fact_35_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 91 (all F all A_1 all B_2 hAPP_f1968395738t_bool(image_48635758_a_nat(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f1968395738t_bool(image_48635758_a_nat(F),A_1)),hAPP_f1968395738t_bool(image_48635758_a_nat(F),B_2))) # label(fact_36_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 92 (all F all A_1 all B_2 hAPP_f1767618879l_bool(image_2034400499a_bool(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f1767618879l_bool(image_2034400499a_bool(F),A_1)),hAPP_f1767618879l_bool(image_2034400499a_bool(F),B_2))) # label(fact_37_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 93 (all F all A_1 all B_2 hAPP_f101573982e_bool(image_1599849618_state(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f101573982e_bool(image_1599849618_state(F),A_1)),hAPP_f101573982e_bool(image_1599849618_state(F),B_2))) # label(fact_38_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 94 (all F all A_1 all B_2 hAPP_f1216026388e_bool(image_1244540328_pname(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1)),hAPP_f1216026388e_bool(image_1244540328_pname(F),B_2))) # label(fact_39_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 95 (all F all A_1 all B_2 hAPP_f420957402a_bool(image_1865589340iple_a(F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f420957402a_bool(image_1865589340iple_a(F),A_1)),hAPP_f420957402a_bool(image_1865589340iple_a(F),B_2))) # label(fact_40_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 96 (all F all A_1 all B_2 hAPP_f258822235a_bool(image_1153683671iple_a(F),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f258822235a_bool(image_1153683671iple_a(F),A_1)),hAPP_f258822235a_bool(image_1153683671iple_a(F),B_2))) # label(fact_41_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 97 (all F all A_1 all B_2 hAPP_f1029392762a_bool(image_299066104iple_a(F),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f1029392762a_bool(image_299066104iple_a(F),A_1)),hAPP_f1029392762a_bool(image_299066104iple_a(F),B_2))) # label(fact_42_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 98 (all F all A_1 all B_2 hAPP_f2034373396a_bool(image_1738210978iple_a(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),B_2))) # label(fact_43_image__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 99 (all F all G all X (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_nat_bool(F,X)),hAPP_nat_bool(G,X))))) # label(fact_44_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 100 (all F all G all X (hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_f1695230391l_bool(F,X)),hAPP_f1695230391l_bool(G,X))))) # label(fact_45_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 101 (all F all G all X (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H242767318e_bool(F,X)),hAPP_H242767318e_bool(G,X))))) # label(fact_46_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 102 (all F all G all X (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X)),hAPP_pname_bool(G,X))))) # label(fact_47_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 103 (all F all G all X (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1037229737a_bool(F,X)),hAPP_H1037229737a_bool(G,X))))) # label(fact_48_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 104 (all F all G all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))))) # label(fact_49_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 105 (all F all G all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_f1695230391l_bool(F,X_2)),hAPP_f1695230391l_bool(G,X_2))))) # label(fact_50_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 106 (all F all G all X_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2))))) # label(fact_51_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 107 (all F all G all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))))) # label(fact_52_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 108 (all F all G all X_2 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F),G),X_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1037229737a_bool(F,X_2)),hAPP_H1037229737a_bool(G,X_2))))) # label(fact_53_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 109 (all Ga all G_1 all Ts (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(G_1),Ts)) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),G_1)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts))))) # label(fact_54_cut) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 110 (all Ga all G_1 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts)) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),G_1)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),Ts))))) # label(fact_55_cut) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 111 (all X_2 all Y_1 all Z_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)),Z_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1))) # label(fact_56_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 112 (all X_20 all Y_17 all Z_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_20),Y_17)),Z_9) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_20),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_17),Z_9))) # label(fact_57_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 113 (all X_2 all Y_1 all Z_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)),Z_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1))) # label(fact_58_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 114 (all X_2 all Y_1 all Z_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)),Z_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1))) # label(fact_59_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 115 (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_60_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 116 (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_61_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 117 (all X_2 all Y_1 all Z_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)),Z_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1))) # label(fact_62_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 118 (all X_2 all Y_1 all Z_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)),Z_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1))) # label(fact_63_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 119 (all X_19 all Y_16 all Z_8 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_19),Y_16)),Z_8) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_16),Z_8))) # label(fact_64_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 120 (all X_2 all Y_1 all Z_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)),Z_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1))) # label(fact_65_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 121 (all X_2 all Y_1 all Z_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)),Z_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1))) # label(fact_66_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 122 (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_67_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 123 (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_68_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 124 (all X_2 all Y_1 all Z_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)),Z_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1))) # label(fact_69_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 125 (all A_2 all B_1 all C_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1)),C_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),C_2))) # label(fact_70_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 126 (all A_13 all B_10 all C_5 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_13),B_10)),C_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_10),C_5))) # label(fact_71_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 127 (all A_2 all B_1 all C_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1)),C_2) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),C_2))) # label(fact_72_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 128 (all A_2 all B_1 all C_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1)),C_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C_2))) # label(fact_73_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 129 (all A_2 all B_1 all C_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1)),C_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_2))) # label(fact_74_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 130 (all A_2 all B_1 all C_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1)),C_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C_2))))) # label(fact_75_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 131 (all A_2 all B_1 all C_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1)),C_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),C_2))) # label(fact_76_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 132 (all X_2 all Y_1 all Z_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Z_1))) # label(fact_77_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 133 (all X_18 all Y_15 all Z_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_15),Z_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_18),Z_7))) # label(fact_78_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 134 (all X_2 all Y_1 all Z_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Z_1))) # label(fact_79_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 135 (all X_2 all Y_1 all Z_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Z_1))) # label(fact_80_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 136 (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_81_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 137 (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_82_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 138 (all X_2 all Y_1 all Z_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Z_1))) # label(fact_83_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 139 (all X_2 all Y_1 all Z_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Z_1))) # label(fact_84_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 140 (all X_17 all Y_14 all Z_6 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_17),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_14),Z_6)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_17),Z_6))) # label(fact_85_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 141 (all X_2 all Y_1 all Z_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Z_1))) # label(fact_86_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 142 (all X_2 all Y_1 all Z_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Z_1))) # label(fact_87_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 143 (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_88_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 144 (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_89_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 145 (all X_2 all Y_1 all Z_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Z_1))) # label(fact_90_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 146 (all B_1 all A_2 all C_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),C_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),C_2))) # label(fact_91_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 147 (all B_9 all A_12 all C_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_12),C_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_9),C_4))) # label(fact_92_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 148 (all B_1 all A_2 all C_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),C_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),C_2))) # label(fact_93_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 149 (all B_1 all A_2 all C_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),C_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C_2))) # label(fact_94_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 150 (all B_1 all A_2 all C_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),C_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_2))) # label(fact_95_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 151 (all B_1 all A_2 all C_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),C_2))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C_2))))) # label(fact_96_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 152 (all B_1 all A_2 all C_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),C_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),C_2))) # label(fact_97_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 153 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)) # label(fact_98_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 154 (all X_16 all Y_13 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_16),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_16),Y_13)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_16),Y_13)) # label(fact_99_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 155 (all X_2 all Y_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)) # label(fact_100_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 156 (all X_2 all Y_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)) # label(fact_101_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 157 (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_102_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 158 (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_103_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 159 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)) # label(fact_104_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 160 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)) # label(fact_105_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 161 (all X_15 all Y_12 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_15),Y_12)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_15),Y_12)) # label(fact_106_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 162 (all X_2 all Y_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)) # label(fact_107_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 163 (all X_2 all Y_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)) # label(fact_108_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 164 (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_109_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 165 (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_110_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 166 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)) # label(fact_111_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 167 (all A_2 all B_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1)) # label(fact_112_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 168 (all A_11 all B_8 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_11),B_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_11),B_8)) # label(fact_113_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 169 (all A_2 all B_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1)) # label(fact_114_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 170 (all A_2 all B_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1)) # label(fact_115_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 171 (all A_2 all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1)) # label(fact_116_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 172 (all A_2 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1)))) # label(fact_117_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 173 (all A_2 all B_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1)) # label(fact_118_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 174 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),X_2)) # label(fact_119_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 175 (all X_14 all Y_11 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_14),Y_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_11),X_14)) # label(fact_120_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 176 (all X_2 all Y_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),X_2)) # label(fact_121_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 177 (all X_2 all Y_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),X_2)) # label(fact_122_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 178 (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_123_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 179 (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_124_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 180 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),X_2)) # label(fact_125_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 181 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),X_2)) # label(fact_126_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 182 (all X_13 all Y_10 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_13),Y_10) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_10),X_13)) # label(fact_127_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 183 (all X_2 all Y_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),X_2)) # label(fact_128_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 184 (all X_2 all Y_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),X_2)) # label(fact_129_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 185 (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_130_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 186 (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_131_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 187 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),X_2)) # label(fact_132_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 188 (all A_2 all B_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),A_2)) # label(fact_133_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 189 (all A_10 all B_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_10),B_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_7),A_10)) # label(fact_134_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 190 (all A_2 all B_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),A_2)) # label(fact_135_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 191 (all A_2 all B_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),A_2)) # label(fact_136_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 192 (all A_2 all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A_2)) # label(fact_137_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 193 (all A_2 all B_1 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),A_2)))) # label(fact_138_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 194 (all A_2 all B_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),A_2)) # label(fact_139_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 195 (all X_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),X_2) = X_2) # label(fact_140_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 196 (all X_12 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_12),X_12) = X_12) # label(fact_141_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 197 (all X_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),X_2) = X_2) # label(fact_142_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 198 (all X_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),X_2) = X_2) # label(fact_143_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 199 (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_144_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 200 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2)) <-> hBOOL(X_2))) # label(fact_145_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 201 (all X_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),X_2) = X_2) # label(fact_146_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 202 (all A_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),A_2) = A_2) # label(fact_147_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 203 (all A_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_9),A_9) = A_9) # label(fact_148_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 204 (all A_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),A_2) = A_2) # label(fact_149_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 205 (all A_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),A_2) = A_2) # label(fact_150_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 206 (all A_2 (is_fun_pname_bool(A_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),A_2) = A_2)) # label(fact_151_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 207 (all A_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),A_2)) <-> hBOOL(A_2))) # label(fact_152_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 208 (all A_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),A_2) = A_2) # label(fact_153_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 209 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> (B_1 = hAPP_nat_nat(F,X_2) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1)))))) # label(fact_154_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 210 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (B_1 = hAPP_p1751618853_state(F,X_2) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1)))))) # label(fact_155_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 211 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (B_1 = hAPP_pname_nat(F,X_2) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f1066163005t_bool(image_pname_nat(F),A_1)))))) # label(fact_156_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 212 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (B_1 = hAPP_p1743421830a_bool(F,X_2) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1)))))) # label(fact_157_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 213 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> (B_1 = hAPP_nat_pname(F,X_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f654413245e_bool(image_nat_pname(F),A_1)))))) # label(fact_158_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 214 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> (B_1 = hAPP_f1764134762_pname(F,X_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1)))))) # label(fact_159_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 215 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) -> (B_1 = hAPP_H2000557816_pname(F,X_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1)))))) # label(fact_160_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 216 (all B_1 all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (B_1 = hAPP_p346744818iple_a(F,X_2) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)))))) # label(fact_161_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 217 (all F all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(F,X_2)),hAPP_f800510211t_bool(image_nat_nat(F),A_1))))) # label(fact_162_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 218 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_2)),hAPP_f360545851e_bool(image_185131637_state(F),A_1))))) # label(fact_163_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 219 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_2)),hAPP_f1066163005t_bool(image_pname_nat(F),A_1))))) # label(fact_164_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 220 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,hAPP_p1743421830a_bool(F,X_2)),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1))))) # label(fact_165_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 221 (all F all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_2)),hAPP_f654413245e_bool(image_nat_pname(F),A_1))))) # label(fact_166_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 222 (all F all X_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1764134762_pname(F,X_2)),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1))))) # label(fact_167_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 223 (all F all X_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H2000557816_pname(F,X_2)),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1))))) # label(fact_168_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.04 224 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_p346744818iple_a(F,X_2)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))))) # label(fact_169_imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 225 (all Z_1 all F all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1))) <-> (exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) & Z_1 = hAPP_nat_nat(F,X))))) # label(fact_170_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 226 (all Z_1 all F all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Z_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & Z_1 = hAPP_p1751618853_state(F,X))))) # label(fact_171_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 227 (all Z_1 all F all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Z_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & Z_1 = hAPP_p346744818iple_a(F,X))))) # label(fact_172_image__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 228 (all A_1 all C_2 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))))) # label(fact_173_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 229 (all A_1 all C_2 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))))) # label(fact_174_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 230 (all A_1 all C_2 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))))) # label(fact_175_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 231 (all A_1 all C_2 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))))) # label(fact_176_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 232 (all A_1 all C_2 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))))) # label(fact_177_UnI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 233 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))))) # label(fact_178_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 234 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))))) # label(fact_179_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 235 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))))) # label(fact_180_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 236 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))))) # label(fact_181_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 237 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))))) # label(fact_182_UnI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 238 (all A_1 all B_2 all X_2 (hBOOL(hAPP_nat_bool(B_2,X_2)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2)))) # label(fact_183_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 239 (all A_1 all B_2 all X_2 (hBOOL(hAPP_f1695230391l_bool(B_2,X_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2)))) # label(fact_184_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 240 (all A_1 all B_2 all X_2 (hBOOL(hAPP_H242767318e_bool(B_2,X_2)) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2)))) # label(fact_185_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 241 (all A_1 all B_2 all X_2 (hBOOL(hAPP_pname_bool(B_2,X_2)) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2)))) # label(fact_186_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 242 (all A_1 all B_2 all X_2 (hBOOL(hAPP_H1037229737a_bool(B_2,X_2)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2)))) # label(fact_187_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 243 (all B_2 all A_1 all X_2 (hBOOL(hAPP_nat_bool(A_1,X_2)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2)))) # label(fact_188_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 244 (all B_2 all A_1 all X_2 (hBOOL(hAPP_f1695230391l_bool(A_1,X_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2)))) # label(fact_189_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 245 (all B_2 all A_1 all X_2 (hBOOL(hAPP_H242767318e_bool(A_1,X_2)) -> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2)))) # label(fact_190_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 246 (all B_2 all A_1 all X_2 (hBOOL(hAPP_pname_bool(A_1,X_2)) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2)))) # label(fact_191_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 247 (all B_2 all A_1 all X_2 (hBOOL(hAPP_H1037229737a_bool(A_1,X_2)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2)))) # label(fact_192_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 248 (all Pa all A_1 all B_2 ((all X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) -> hBOOL(hAPP_nat_bool(Pa,X)))) <-> (all X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) -> hBOOL(hAPP_nat_bool(Pa,X)))) & (all X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),B_2)) -> hBOOL(hAPP_nat_bool(Pa,X)))))) # label(fact_193_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 249 (all Pa all A_1 all B_2 ((all X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) -> hBOOL(hAPP_f1695230391l_bool(Pa,X)))) <-> (all X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1)) -> hBOOL(hAPP_f1695230391l_bool(Pa,X)))) & (all X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),B_2)) -> hBOOL(hAPP_f1695230391l_bool(Pa,X)))))) # label(fact_194_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 250 (all Pa all A_1 all B_2 ((all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) -> hBOOL(hAPP_H242767318e_bool(Pa,X)))) <-> (all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1)) -> hBOOL(hAPP_H242767318e_bool(Pa,X)))) & (all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),B_2)) -> hBOOL(hAPP_H242767318e_bool(Pa,X)))))) # label(fact_195_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 251 (all Pa all A_1 all B_2 ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) -> hBOOL(hAPP_pname_bool(Pa,X))))) <-> (all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) -> hBOOL(hAPP_pname_bool(Pa,X))))) & (all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_2)) -> hBOOL(hAPP_pname_bool(Pa,X))))))) # label(fact_196_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 252 (all Pa all A_1 all B_2 ((all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) -> hBOOL(hAPP_H1037229737a_bool(Pa,X)))) <-> (all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1)) -> hBOOL(hAPP_H1037229737a_bool(Pa,X)))) & (all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),B_2)) -> hBOOL(hAPP_H1037229737a_bool(Pa,X)))))) # label(fact_197_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 253 (all Pa all A_1 all B_2 ((exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) & hBOOL(hAPP_nat_bool(Pa,X)))) <-> (exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) & hBOOL(hAPP_nat_bool(Pa,X)))) | (exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),B_2)) & hBOOL(hAPP_nat_bool(Pa,X)))))) # label(fact_198_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 254 (all Pa all A_1 all B_2 ((exists X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) & hBOOL(hAPP_f1695230391l_bool(Pa,X)))) <-> (exists X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1)) & hBOOL(hAPP_f1695230391l_bool(Pa,X)))) | (exists X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),B_2)) & hBOOL(hAPP_f1695230391l_bool(Pa,X)))))) # label(fact_199_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 255 (all Pa all A_1 all B_2 ((exists X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) & hBOOL(hAPP_H242767318e_bool(Pa,X)))) <-> (exists X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1)) & hBOOL(hAPP_H242767318e_bool(Pa,X)))) | (exists X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),B_2)) & hBOOL(hAPP_H242767318e_bool(Pa,X)))))) # label(fact_200_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 256 (all Pa all A_1 all B_2 ((exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) & hBOOL(hAPP_pname_bool(Pa,X)))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & hBOOL(hAPP_pname_bool(Pa,X)))) | (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_2)) & hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_201_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 257 (all Pa all A_1 all B_2 ((exists X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) & hBOOL(hAPP_H1037229737a_bool(Pa,X)))) <-> (exists X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1)) & hBOOL(hAPP_H1037229737a_bool(Pa,X)))) | (exists X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),B_2)) & hBOOL(hAPP_H1037229737a_bool(Pa,X)))))) # label(fact_202_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 258 (all A_1 all B_2 all C_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)),C_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1))) # label(fact_203_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 259 (all A_1 all B_2 all C_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)),C_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1))) # label(fact_204_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 260 (all A_1 all B_2 all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1))) # label(fact_205_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 261 (all A_1 all B_2 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1))) # label(fact_206_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 262 (all A_1 all B_2 all C_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)),C_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1))) # label(fact_207_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 263 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)))) # label(fact_208_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 264 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) <-> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) | hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)))) # label(fact_209_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 265 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1)) | hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2)))) # label(fact_210_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 266 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) | hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)))) # label(fact_211_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 267 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)))) # label(fact_212_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 268 (all A_1 all B_2 all C_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),C_1))) # label(fact_213_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 269 (all A_1 all B_2 all C_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),C_1))) # label(fact_214_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 270 (all A_1 all B_2 all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),C_1))) # label(fact_215_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 271 (all A_1 all B_2 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),C_1))) # label(fact_216_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 272 (all A_1 all B_2 all C_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),C_1))) # label(fact_217_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 273 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) # label(fact_218_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 274 (all A_1 all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) # label(fact_219_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 275 (all A_1 all B_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) # label(fact_220_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 276 (all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) # label(fact_221_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 277 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) # label(fact_222_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 278 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),A_1)) # label(fact_223_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 279 (all A_1 all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),A_1)) # label(fact_224_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 280 (all A_1 all B_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),A_1)) # label(fact_225_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 281 (all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),A_1)) # label(fact_226_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 282 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),A_1)) # label(fact_227_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 283 (all A_1 all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2)))) # label(fact_228_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 284 (all A_1 all B_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A_1))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B_2)))) # label(fact_229_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 285 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2)))) # label(fact_230_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 286 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2)))) # label(fact_231_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 287 (all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2)))) # label(fact_232_Un__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 288 (all A_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),A_1) = A_1) # label(fact_233_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 289 (all A_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),A_1) = A_1) # label(fact_234_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 290 (all A_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),A_1) = A_1) # label(fact_235_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 291 (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_236_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 292 (all A_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),A_1) = A_1) # label(fact_237_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 293 (all Y_9 hAPP_f800510211t_bool(image_nat_nat(cOMBI_nat),Y_9) = Y_9) # label(fact_238_image__ident) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 294 (all F all G all A_1 hAPP_f101573982e_bool(image_1599849618_state(F),hAPP_f2034373396a_bool(image_1738210978iple_a(G),A_1)) = hAPP_f360545851e_bool(image_185131637_state(hAPP_f922567064_state(cOMBB_452540923_pname(F),G)),A_1)) # label(fact_239_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 295 (all F all G all A_1 hAPP_f1029392762a_bool(image_299066104iple_a(F),hAPP_f360545851e_bool(image_185131637_state(G),A_1)) = hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f1273628548iple_a(cOMBB_1824120853_pname(F),G)),A_1)) # label(fact_240_image__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 296 (all R_1 all S_2 all X (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_2)),X)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,R_1),S_2))))) # label(fact_241_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 297 (all R_1 all S_2 all X (hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),R_1)),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),S_2)),X)) <-> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,R_1),S_2))))) # label(fact_242_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 298 (all R_1 all S_2 all X (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),R_1)),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),S_2)),X)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,R_1),S_2))))) # label(fact_243_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 299 (all R_1 all S_2 all X (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),R_1)),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_2)),X)) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,R_1),S_2))))) # label(fact_244_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 300 (all R_1 all S_2 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_2)),X)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S_2))))) # label(fact_245_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 301 (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_246_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 302 (all Pa all Qa hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),Pa)),Qa)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(collec999179778a_bool,Pa)),hAPP_f396832789l_bool(collec999179778a_bool,Qa))) # label(fact_247_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 303 (all Pa all Qa hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),Pa)),Qa)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(collec637225377_state,Pa)),hAPP_f806699093e_bool(collec637225377_state,Qa))) # label(fact_248_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 304 (all Pa all Qa hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),Pa)),Qa)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(collec351493750iple_a,Pa)),hAPP_f20753329a_bool(collec351493750iple_a,Qa))) # label(fact_249_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 305 (all Pa all Qa hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),Pa)),Qa)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(collect_nat,Pa)),hAPP_f800510211t_bool(collect_nat,Qa))) # label(fact_250_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 306 (all B_1 all F all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1))) -> -(all X (B_1 = hAPP_nat_nat(F,X) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)))))) # label(fact_251_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 307 (all B_1 all F all A_1 (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f654413245e_bool(image_nat_pname(F),A_1))) -> -(all X (B_1 = hAPP_nat_pname(F,X) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))))))) # label(fact_252_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 308 (all B_1 all F all A_1 (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1))) -> -(all X (B_1 = hAPP_f1764134762_pname(F,X) -> -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))))))) # label(fact_253_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 309 (all B_1 all F all A_1 (is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1))) -> -(all X (B_1 = hAPP_H2000557816_pname(F,X) -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))))))) # label(fact_254_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 310 (all B_1 all F all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1))) -> -(all X (is_pname(X) -> (B_1 = hAPP_p1751618853_state(F,X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))))))) # label(fact_255_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 311 (all B_1 all F all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f1066163005t_bool(image_pname_nat(F),A_1))) -> -(all X (is_pname(X) -> (B_1 = hAPP_pname_nat(F,X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))))))) # label(fact_256_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 312 (all B_1 all F all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1))) -> -(all X (is_pname(X) -> (B_1 = hAPP_p1743421830a_bool(F,X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))))))) # label(fact_257_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 313 (all B_1 all F all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))) -> -(all X (is_pname(X) -> (B_1 = hAPP_p346744818iple_a(F,X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))))))) # label(fact_258_imageE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 314 (all N_1 all Pa all Pn_1 all Qa (hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_1),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa))) <-> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,hAPP_nat_nat(suc,N_1)),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa))))) # label(fact_259_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 315 (all N_1 all Pa all Pn_1 all Qa (hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_1),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa))) <-> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,hAPP_nat_nat(suc,N_1)),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))))) # label(fact_260_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 316 (all Y_1 -(all Fun1_1 all Com_2 all Fun2_1 Y_1 != hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1_1),Com_2),Fun2_1))) # label(fact_261_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 317 (all Y_1 -(all Fun1_1 all Com_2 all Fun2_1 Y_1 != hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_1),Com_2),Fun2_1))) # label(fact_262_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 318 (all Pn_1 all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),body)),Qa)),Procsa))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_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_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p1637813682e_bool(Qa,Pn_1))),bot_bo784226126e_bool)))))) # label(fact_263_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 319 (all Pn_1 all Ga all Pa all Qa all Procsa (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_p635540397e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p635540397e_bool(Qa,Pn_1))),bot_bo797238721a_bool)))))) # label(fact_264_Body1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 320 (all F all G all M_5 all N_3 (M_5 = N_3 -> ((all X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),N_3)) -> hAPP_nat_nat(F,X) = hAPP_nat_nat(G,X))) -> hAPP_f800510211t_bool(image_nat_nat(F),M_5) = hAPP_f800510211t_bool(image_nat_nat(G),N_3)))) # label(fact_265_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 321 (all F all G all M_5 all N_3 (M_5 = N_3 -> ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3)) -> hAPP_p1751618853_state(F,X) = hAPP_p1751618853_state(G,X)))) -> hAPP_f360545851e_bool(image_185131637_state(F),M_5) = hAPP_f360545851e_bool(image_185131637_state(G),N_3)))) # label(fact_266_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 322 (all F all G all M_5 all N_3 (M_5 = N_3 -> ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3)) -> hAPP_p346744818iple_a(F,X) = hAPP_p346744818iple_a(G,X)))) -> hAPP_f2034373396a_bool(image_1738210978iple_a(F),M_5) = hAPP_f2034373396a_bool(image_1738210978iple_a(G),N_3)))) # label(fact_267_image__cong) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 323 (all Pa all Pn_1 all Qa hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,zero_zero_nat),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)))) # label(fact_268_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 324 (all Pa all Pn_1 all Qa hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,zero_zero_nat),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)))) # label(fact_269_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 325 (all Pname_3 all Pname (is_pname(Pname_3) & is_pname(Pname) -> (hAPP_pname_com(body,Pname_3) = hAPP_pname_com(body,Pname) <-> Pname_3 = Pname))) # label(fact_270_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 326 (all Pn all S0 all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn))),S0),S1_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,Pn)),S0),S1_2)))) # label(fact_271_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 327 (all P all S all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,P)),S),S1_2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P))),S),S1_2)))) # label(fact_272_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 328 (all X_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),X_2) = X_2) # label(fact_273_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 329 (all X_11 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_11),X_11) = X_11) # label(fact_274_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 330 (all X_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),X_2) = X_2) # label(fact_275_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 331 (all X_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),X_2) = X_2) # label(fact_276_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 332 (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_277_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 333 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2)) <-> hBOOL(X_2))) # label(fact_278_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 334 (all X_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),X_2) = X_2) # label(fact_279_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 335 (all N_1 all Ts ((all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ts)) -> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,hAPP_nat_nat(suc,N_1)),X)))) -> (all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ts)) -> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_1),X)))))) # label(fact_280_triples__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 336 (all N_1 all Ts ((all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ts)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,hAPP_nat_nat(suc,N_1)),X)))) -> (all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ts)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_1),X)))))) # label(fact_281_triples__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 337 (all A_2 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),bot_bot_fun_nat_bool))) # label(fact_282_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 338 (all A_2 -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),bot_bo332163887l_bool))) # label(fact_283_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 339 (all A_2 -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),bot_bo797238721a_bool))) # label(fact_284_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 340 (all A_2 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),bot_bo784226126e_bool))) # label(fact_285_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 341 (all A_2 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool))) # label(fact_286_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 342 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),A_1))) -> (A_2 != B_1 -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1))))) # label(fact_287_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 343 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),A_1))) -> (A_2 != B_1 -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1))))) # label(fact_288_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 344 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),A_1))) -> (A_2 != B_1 -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1))))) # label(fact_289_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 345 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A_1))) -> (A_2 != B_1 -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1))))) # label(fact_290_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 346 (all A_2 all B_1 all A_1 (is_pname(A_2) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1))) -> (A_2 != B_1 -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)))))) # label(fact_291_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 347 (all B_1 all A_2 all B_2 ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B_2)) -> A_2 = B_1) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),B_2))))) # label(fact_292_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 348 (all B_1 all A_2 all B_2 ((-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),B_2)) -> A_2 = B_1) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),B_2))))) # label(fact_293_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 349 (all B_1 all A_2 all B_2 ((-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),B_2)) -> A_2 = B_1) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),B_2))))) # label(fact_294_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 350 (all B_1 all A_2 all B_2 ((-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),B_2)) -> A_2 = B_1) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B_2))))) # label(fact_295_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 351 (all B_1 all A_2 all B_2 ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B_2)) -> A_2 = B_1) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B_2))))) # label(fact_296_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 352 (all A_2 all A_1 bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1)) # label(fact_297_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 353 (all A_2 all A_1 bot_bo332163887l_bool != hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1)) # label(fact_298_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 354 (all A_2 all A_1 bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1)) # label(fact_299_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 355 (all A_2 all A_1 bot_bo797238721a_bool != hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1)) # label(fact_300_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 356 (all A_2 all A_1 bot_bo784226126e_bool != hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1)) # label(fact_301_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 357 (all A_2 all A_1 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1) != bot_bot_fun_nat_bool) # label(fact_302_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 358 (all A_2 all A_1 hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1) != bot_bo332163887l_bool) # label(fact_303_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 359 (all A_2 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1) != bot_bo844097828e_bool) # label(fact_304_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 360 (all A_2 all A_1 hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1) != bot_bo797238721a_bool) # label(fact_305_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 361 (all A_2 all A_1 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1) != bot_bo784226126e_bool) # label(fact_306_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 362 (all X (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),bot_bot_fun_nat_bool)))) # label(fact_307_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 363 (all X (hBOOL(hAPP_f1695230391l_bool(bot_bo332163887l_bool,X)) <-> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),bot_bo332163887l_bool)))) # label(fact_308_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 364 (all X (hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X)) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),bot_bo797238721a_bool)))) # label(fact_309_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 365 (all X (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X)) <-> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),bot_bo784226126e_bool)))) # label(fact_310_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 366 (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_311_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 367 (all A_2 all B_2 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2)))) # label(fact_317_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 368 (all A_2 all B_2 hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2)))) # label(fact_318_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 369 (all A_2 all B_2 hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2)))) # label(fact_319_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 370 (all A_2 all B_2 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2)))) # label(fact_320_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 371 (all A_2 all B_2 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)))) # label(fact_321_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 372 (all A_1 ((all X -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))) <-> A_1 = bot_bot_fun_nat_bool)) # label(fact_322_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 373 (all A_1 ((all X -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))) <-> A_1 = bot_bo332163887l_bool)) # label(fact_323_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 374 (all A_1 ((all X -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))) <-> A_1 = bot_bo797238721a_bool)) # label(fact_324_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 375 (all A_1 ((all X -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1))) <-> A_1 = bot_bo784226126e_bool)) # label(fact_325_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 376 (all A_1 (is_fun_pname_bool(A_1) -> ((all X (is_pname(X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)))) <-> A_1 = bot_bo844097828e_bool))) # label(fact_326_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 377 (all A_2 hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f1767618879l_bool(fequal874423448a_bool,A_2)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)) # label(fact_327_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 378 (all A_2 hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)) # label(fact_328_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 379 (all A_2 hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(fequal963300192iple_a,A_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)) # label(fact_329_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 380 (all A_2 hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(fequal1440809015_state,A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)) # label(fact_330_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 381 (all A_2 hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(fequal_nat,A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) # label(fact_331_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 382 (all A_1 ((exists X hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))) <-> A_1 != bot_bot_fun_nat_bool)) # label(fact_332_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 383 (all A_1 ((exists X hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))) <-> A_1 != bot_bo332163887l_bool)) # label(fact_333_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 384 (all A_1 ((exists X hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))) <-> A_1 != bot_bo797238721a_bool)) # label(fact_334_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 385 (all A_1 ((exists X hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1))) <-> A_1 != bot_bo784226126e_bool)) # label(fact_335_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 386 (all A_1 (is_fun_pname_bool(A_1) -> ((exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)))) <-> A_1 != bot_bo844097828e_bool))) # label(fact_336_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 387 (all A_2 hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)) # label(fact_337_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 388 (all A_2 hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)) # label(fact_338_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 389 (all A_2 hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)) # label(fact_339_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 390 (all A_2 hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)) # label(fact_340_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 391 (all A_2 hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) # label(fact_341_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 392 (all Pa all A_2 ((hBOOL(hAPP_f1695230391l_bool(Pa,A_2)) -> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(fequal874423448a_bool,A_2))),Pa)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)) & (-hBOOL(hAPP_f1695230391l_bool(Pa,A_2)) -> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(fequal874423448a_bool,A_2))),Pa)) = bot_bo332163887l_bool))) # label(fact_342_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 393 (all Pa all A_2 ((hBOOL(hAPP_pname_bool(Pa,A_2)) -> 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_2))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_2)) -> 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_2))),Pa)) = bot_bo844097828e_bool))) # label(fact_343_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 394 (all Pa all A_2 ((hBOOL(hAPP_H1037229737a_bool(Pa,A_2)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(fequal963300192iple_a,A_2))),Pa)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)) & (-hBOOL(hAPP_H1037229737a_bool(Pa,A_2)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(fequal963300192iple_a,A_2))),Pa)) = bot_bo797238721a_bool))) # label(fact_344_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 395 (all Pa all A_2 ((hBOOL(hAPP_H242767318e_bool(Pa,A_2)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(fequal1440809015_state,A_2))),Pa)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)) & (-hBOOL(hAPP_H242767318e_bool(Pa,A_2)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(fequal1440809015_state,A_2))),Pa)) = bot_bo784226126e_bool))) # label(fact_345_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 396 (all Pa all A_2 ((hBOOL(hAPP_nat_bool(Pa,A_2)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(fequal_nat,A_2))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_2)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(fequal_nat,A_2))),Pa)) = bot_bot_fun_nat_bool))) # label(fact_346_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 397 (all Pa all A_2 ((hBOOL(hAPP_f1695230391l_bool(Pa,A_2)) -> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),Pa)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)) & (-hBOOL(hAPP_f1695230391l_bool(Pa,A_2)) -> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),Pa)) = bot_bo332163887l_bool))) # label(fact_347_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 398 (all Pa all A_2 ((hBOOL(hAPP_pname_bool(Pa,A_2)) -> 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_2))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_2)) -> 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_2))),Pa)) = bot_bo844097828e_bool))) # label(fact_348_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 399 (all Pa all A_2 ((hBOOL(hAPP_H1037229737a_bool(Pa,A_2)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),Pa)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)) & (-hBOOL(hAPP_H1037229737a_bool(Pa,A_2)) -> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),Pa)) = bot_bo797238721a_bool))) # label(fact_349_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 400 (all Pa all A_2 ((hBOOL(hAPP_H242767318e_bool(Pa,A_2)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),Pa)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)) & (-hBOOL(hAPP_H242767318e_bool(Pa,A_2)) -> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),Pa)) = bot_bo784226126e_bool))) # label(fact_350_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 401 (all Pa all A_2 ((hBOOL(hAPP_nat_bool(Pa,A_2)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)) & (-hBOOL(hAPP_nat_bool(Pa,A_2)) -> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),Pa)) = bot_bot_fun_nat_bool))) # label(fact_351_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 402 (all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) <-> hBOOL(hAPP_nat_bool(A_1,X_2)))) # label(fact_352_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 403 (all X_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) <-> hBOOL(hAPP_f1695230391l_bool(A_1,X_2)))) # label(fact_353_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 404 (all X_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) <-> hBOOL(hAPP_H1037229737a_bool(A_1,X_2)))) # label(fact_354_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 405 (all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) <-> hBOOL(hAPP_pname_bool(A_1,X_2)))) # label(fact_355_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 406 (all Pa (is_fun_pname_bool(Pa) -> hAPP_f759274231e_bool(collect_pname,Pa) = Pa)) # label(fact_356_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 407 (all Pa hAPP_f20753329a_bool(collec351493750iple_a,Pa) = Pa) # label(fact_357_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 408 (all Pa hAPP_f800510211t_bool(collect_nat,Pa) = Pa) # label(fact_358_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 409 (all Pa (bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,Pa) <-> (all X (is_pname(X) -> -hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_359_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 410 (all Pa (bot_bo797238721a_bool = hAPP_f20753329a_bool(collec351493750iple_a,Pa) <-> (all X -hBOOL(hAPP_H1037229737a_bool(Pa,X))))) # label(fact_360_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 411 (all Pa (bot_bo332163887l_bool = hAPP_f396832789l_bool(collec999179778a_bool,Pa) <-> (all X -hBOOL(hAPP_f1695230391l_bool(Pa,X))))) # label(fact_361_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 412 (all Pa (bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,Pa) <-> (all X -hBOOL(hAPP_H242767318e_bool(Pa,X))))) # label(fact_362_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 413 (all Pa (bot_bot_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,Pa) <-> (all X -hBOOL(hAPP_nat_bool(Pa,X))))) # label(fact_363_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 414 (all C_2 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),bot_bot_fun_nat_bool))) # label(fact_364_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 415 (all C_2 -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),bot_bo332163887l_bool))) # label(fact_365_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 416 (all C_2 -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),bot_bo797238721a_bool))) # label(fact_366_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 417 (all C_2 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),bot_bo784226126e_bool))) # label(fact_367_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 418 (all C_2 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),bot_bo844097828e_bool))) # label(fact_368_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 419 (all A_2 all B_2 hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2)))) # label(fact_369_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 420 (all A_2 all B_2 hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2)))) # label(fact_370_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 421 (all A_2 all B_2 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B_2)))) # label(fact_371_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 422 (all A_2 all B_2 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2)))) # label(fact_372_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 423 (all A_2 all B_2 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2) = 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_2))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2)))) # label(fact_373_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 424 (all A_2 all Pa hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(collec999179778a_bool,Pa)) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fimplies),hAPP_f396832789l_bool(cOMBB_193631803a_bool(fNot),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2)))),Pa))) # label(fact_374_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 425 (all A_2 all Pa hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),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_2)))),Pa))) # label(fact_375_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 426 (all A_2 all Pa hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(collec351493750iple_a,Pa)) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fimplies),hAPP_f20753329a_bool(cOMBB_1882975613iple_a(fNot),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2)))),Pa))) # label(fact_376_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.05 427 (all A_2 all Pa hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(collec637225377_state,Pa)) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fimplies),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2)))),Pa))) # label(fact_377_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 428 (all A_2 all Pa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(collect_nat,Pa)) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fimplies),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2)))),Pa))) # label(fact_378_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 429 (all B_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) <-> B_1 = A_2)) # label(fact_379_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 430 (all B_1 all A_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool))) <-> B_1 = A_2)) # label(fact_380_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 431 (all B_1 all A_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool))) <-> B_1 = A_2)) # label(fact_381_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 432 (all B_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool))) <-> B_1 = A_2)) # label(fact_382_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 433 (all B_1 all A_2 (is_pname(B_1) & is_pname(A_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) <-> B_1 = A_2))) # label(fact_383_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 434 (all X_2 all A_1 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) # label(fact_384_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 435 (all X_2 all A_1 hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) # label(fact_385_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 436 (all X_2 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) # label(fact_386_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 437 (all X_2 all A_1 hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) # label(fact_387_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 438 (all X_2 all A_1 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) # label(fact_388_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 439 (all X_2 all Y_1 all A_1 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1))) # label(fact_389_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 440 (all X_2 all Y_1 all A_1 hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_1),A_1)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1))) # label(fact_390_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 441 (all X_2 all Y_1 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1))) # label(fact_391_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 442 (all X_2 all Y_1 all A_1 hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),A_1)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1))) # label(fact_392_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 443 (all X_2 all Y_1 all A_1 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1))) # label(fact_393_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 444 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),A_1))) <-> A_2 = B_1 | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)))) # label(fact_394_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 445 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),A_1))) <-> A_2 = B_1 | hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)))) # label(fact_395_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 446 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),A_1))) <-> A_2 = B_1 | hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1)))) # label(fact_396_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 447 (all A_2 all B_1 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A_1))) <-> A_2 = B_1 | hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1)))) # label(fact_397_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 448 (all A_2 all B_1 all A_1 (is_pname(A_2) & is_pname(B_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1))) <-> A_2 = B_1 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1))))) # label(fact_398_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 449 (all Pa (hAPP_f759274231e_bool(collect_pname,Pa) = bot_bo844097828e_bool <-> (all X (is_pname(X) -> -hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_399_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 450 (all Pa (hAPP_f20753329a_bool(collec351493750iple_a,Pa) = bot_bo797238721a_bool <-> (all X -hBOOL(hAPP_H1037229737a_bool(Pa,X))))) # label(fact_400_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 451 (all Pa (hAPP_f396832789l_bool(collec999179778a_bool,Pa) = bot_bo332163887l_bool <-> (all X -hBOOL(hAPP_f1695230391l_bool(Pa,X))))) # label(fact_401_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 452 (all Pa (hAPP_f806699093e_bool(collec637225377_state,Pa) = bot_bo784226126e_bool <-> (all X -hBOOL(hAPP_H242767318e_bool(Pa,X))))) # label(fact_402_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 453 (all Pa (hAPP_f800510211t_bool(collect_nat,Pa) = bot_bot_fun_nat_bool <-> (all X -hBOOL(hAPP_nat_bool(Pa,X))))) # label(fact_403_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 454 (all A_2 all B_1 all C_2 all D (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D),bot_bot_fun_nat_bool)) <-> A_2 = C_2 & B_1 = D | A_2 = D & B_1 = C_2)) # label(fact_404_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 455 (all A_2 all B_1 all C_2 all D (hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),bot_bo332163887l_bool)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,D),bot_bo332163887l_bool)) <-> A_2 = C_2 & B_1 = D | A_2 = D & B_1 = C_2)) # label(fact_405_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 456 (all A_2 all B_1 all C_2 all D (is_pname(A_2) & is_pname(B_1) & is_pname(C_2) & is_pname(D) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D),bot_bo844097828e_bool)) <-> A_2 = C_2 & B_1 = D | A_2 = D & B_1 = C_2))) # label(fact_406_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 457 (all A_2 all B_1 all C_2 all D (hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),bot_bo797238721a_bool)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,C_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,D),bot_bo797238721a_bool)) <-> A_2 = C_2 & B_1 = D | A_2 = D & B_1 = C_2)) # label(fact_407_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 458 (all A_2 all B_1 all C_2 all D (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,D),bot_bo784226126e_bool)) <-> A_2 = C_2 & B_1 = D | A_2 = D & B_1 = C_2)) # label(fact_408_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 459 (all Y_1 all A_1 all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_1),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_nat_bool(A_1,X_2)))) # label(fact_409_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 460 (all Y_1 all A_1 all X_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_1),A_1),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_f1695230391l_bool(A_1,X_2)))) # label(fact_410_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 461 (all Y_1 all A_1 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_1),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_pname_bool(A_1,X_2))))) # label(fact_411_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 462 (all Y_1 all A_1 all X_2 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),A_1),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_H1037229737a_bool(A_1,X_2)))) # label(fact_412_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 463 (all Y_1 all A_1 all X_2 (hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_1),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_H242767318e_bool(A_1,X_2)))) # label(fact_413_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 464 (all B_2 all X_2 all A_1 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_2)) -> (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_2) <-> A_1 = B_2)))) # label(fact_414_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 465 (all B_2 all X_2 all A_1 (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),B_2)) -> (hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),B_2) <-> A_1 = B_2)))) # label(fact_415_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 466 (all B_2 all X_2 all A_1 (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B_2)) -> (hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),B_2) <-> A_1 = B_2)))) # label(fact_416_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 467 (all B_2 all X_2 all A_1 (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_2)) -> (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_2) <-> A_1 = B_2)))) # label(fact_417_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 468 (all B_2 all X_2 all A_1 (is_fun_pname_bool(B_2) & is_fun_pname_bool(A_1) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2)) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2) <-> A_1 = B_2))))) # label(fact_418_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 469 (all A_2 all A_1 (A_1 = bot_bot_fun_nat_bool -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)))) # label(fact_419_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 470 (all A_2 all A_1 (A_1 = bot_bo332163887l_bool -> -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)))) # label(fact_420_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 471 (all A_2 all A_1 (A_1 = bot_bo797238721a_bool -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1)))) # label(fact_421_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 472 (all A_2 all A_1 (A_1 = bot_bo784226126e_bool -> -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1)))) # label(fact_422_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 473 (all A_2 all A_1 (A_1 = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)))) # label(fact_423_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 474 (all B_1 all A_2 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),B_2))))) # label(fact_424_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 475 (all B_1 all A_2 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),B_2)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),B_2))))) # label(fact_425_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 476 (all B_1 all A_2 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),B_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),B_2))))) # label(fact_426_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 477 (all B_1 all A_2 all B_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),B_2)) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B_2))))) # label(fact_427_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 478 (all B_1 all A_2 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B_2))))) # label(fact_428_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 479 (all A_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1) = A_1)) # label(fact_429_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 480 (all A_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)) -> hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1) = A_1)) # label(fact_430_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 481 (all A_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1)) -> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1) = A_1)) # label(fact_431_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 482 (all A_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1) = A_1)) # label(fact_432_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 483 (all A_2 all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1) = A_1))) # label(fact_433_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 484 (all B_1 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) -> B_1 = A_2)) # label(fact_434_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 485 (all B_1 all A_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool))) -> B_1 = A_2)) # label(fact_435_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 486 (all B_1 all A_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool))) -> B_1 = A_2)) # label(fact_436_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 487 (all B_1 all A_2 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool))) -> B_1 = A_2)) # label(fact_437_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 488 (all B_1 all A_2 (is_pname(B_1) & is_pname(A_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) -> B_1 = A_2))) # label(fact_438_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 489 (all A_2 all B_1 (hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),bot_bot_fun_nat_bool) -> A_2 = B_1)) # label(fact_439_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 490 (all A_2 all B_1 (hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),bot_bo332163887l_bool) -> A_2 = B_1)) # label(fact_440_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 491 (all A_2 all B_1 (is_pname(A_2) & is_pname(B_1) -> (hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool) -> A_2 = B_1))) # label(fact_441_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 492 (all A_2 all B_1 (hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),bot_bo797238721a_bool) -> A_2 = B_1)) # label(fact_442_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 493 (all A_2 all B_1 (hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool) -> A_2 = B_1)) # label(fact_443_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 494 (all U_1 all C all S all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),T)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),U_1)) -> U_1 = T))) # label(fact_444_com__det) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 495 (all A_2 all A_1 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)),A_1)) # label(fact_445_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 496 (all A_2 all A_1 hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)),A_1)) # label(fact_446_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 497 (all A_2 all A_1 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)),A_1)) # label(fact_447_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 498 (all A_2 all A_1 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)),A_1)) # label(fact_448_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 499 (all A_2 all A_1 hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)),A_1)) # label(fact_449_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 500 (all X all Xa hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),Xa) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),X))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),Xa)))) # label(fact_450_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 501 (all X all Xa hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),Xa) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),X))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),Xa)))) # label(fact_451_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 502 (all X all Xa hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),Xa) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),X))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),Xa)))) # label(fact_452_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 503 (all X all Xa hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),Xa) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),Xa)))) # label(fact_453_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 504 (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_454_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 505 (all Ga all T_1 all Ts (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),Ts))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),bot_bo797238721a_bool))) & hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts)))) # label(fact_455_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 506 (all Ga all T_1 all Ts (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool))) & hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),Ts)))) # label(fact_456_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 507 (all Ts all Ga all T_1 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),bot_bo797238721a_bool))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),Ts)))))) # label(fact_457_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 508 (all Ts all Ga all T_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),Ts)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts)))))) # label(fact_458_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 509 (all C_2 all A_1 ((A_1 = bot_bot_fun_nat_bool -> hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,C_2)),A_1) = bot_bot_fun_nat_bool) & (A_1 != bot_bot_fun_nat_bool -> hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,C_2)),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),bot_bot_fun_nat_bool)))) # label(fact_459_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 510 (all C_2 all A_1 (is_fun_pname_bool(A_1) -> (A_1 = bot_bo844097828e_bool -> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C_2)),A_1) = bot_bo784226126e_bool) & (A_1 != bot_bo844097828e_bool -> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C_2)),A_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C_2),bot_bo784226126e_bool)))) # label(fact_460_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 511 (all C_2 all A_1 (is_fun_pname_bool(A_1) -> (A_1 = bot_bo844097828e_bool -> hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,C_2)),A_1) = bot_bo797238721a_bool) & (A_1 != bot_bo844097828e_bool -> hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,C_2)),A_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,C_2),bot_bo797238721a_bool)))) # label(fact_461_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 512 (all C_2 all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,C_2)),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),bot_bot_fun_nat_bool))) # label(fact_462_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 513 (all C_2 all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C_2)),A_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C_2),bot_bo784226126e_bool))) # label(fact_463_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 514 (all C_2 all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f1066163005t_bool(image_pname_nat(hAPP_n362732366me_nat(cOMBK_nat_pname,C_2)),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),bot_bot_fun_nat_bool))) # label(fact_464_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 515 (all C_2 all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f290545180l_bool(image_2016317142a_bool(hAPP_f624861966a_bool(cOMBK_1667642481_pname,C_2)),A_1) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,C_2),bot_bo332163887l_bool))) # label(fact_465_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 516 (all C_2 all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f759274231e_bool(image_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,C_2)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C_2),bot_bo844097828e_bool))) # label(fact_466_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 517 (all C_2 all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,C_2)),A_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,C_2),bot_bo797238721a_bool))) # label(fact_467_image__constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 518 (all F all A_2 all B_2 hAPP_f800510211t_bool(image_nat_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_nat_nat(F,A_2)),hAPP_f800510211t_bool(image_nat_nat(F),B_2))) # label(fact_468_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 519 (all F all A_2 all B_2 hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,A_2)),hAPP_f360545851e_bool(image_185131637_state(F),B_2))) # label(fact_469_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 520 (all F all A_2 all B_2 hAPP_f2034373396a_bool(image_1738210978iple_a(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_p346744818iple_a(F,A_2)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),B_2))) # label(fact_470_image__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 521 (all F all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_nat_nat(F,X_2)),hAPP_f800510211t_bool(image_nat_nat(F),A_1)) = hAPP_f800510211t_bool(image_nat_nat(F),A_1))) # label(fact_471_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 522 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,X_2)),hAPP_f360545851e_bool(image_185131637_state(F),A_1)) = hAPP_f360545851e_bool(image_185131637_state(F),A_1))) # label(fact_472_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 523 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_pname_nat(F,X_2)),hAPP_f1066163005t_bool(image_pname_nat(F),A_1)) = hAPP_f1066163005t_bool(image_pname_nat(F),A_1))) # label(fact_473_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 524 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,hAPP_p1743421830a_bool(F,X_2)),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1)) = hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1))) # label(fact_474_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 525 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_pname_pname(F,X_2)),hAPP_f759274231e_bool(image_pname_pname(F),A_1)) = hAPP_f759274231e_bool(image_pname_pname(F),A_1))) # label(fact_475_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 526 (all F all X_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_p346744818iple_a(F,X_2)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)) = hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))) # label(fact_476_insert__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 527 (all A_1 all A_2 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) # label(fact_477_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 528 (all A_1 all A_2 all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) # label(fact_478_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 529 (all A_1 all A_2 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) # label(fact_479_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 530 (all A_1 all A_2 all B_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) # label(fact_480_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 531 (all A_1 all A_2 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) # label(fact_481_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 532 (all A_2 all B_2 all C_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2)),C_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1))) # label(fact_482_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 533 (all A_2 all B_2 all C_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2)),C_1) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1))) # label(fact_483_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 534 (all A_2 all B_2 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1))) # label(fact_484_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 535 (all A_2 all B_2 all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1))) # label(fact_485_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 536 (all A_2 all B_2 all C_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2)),C_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1))) # label(fact_486_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 537 (all F all A_1 (bot_bot_fun_nat_bool = hAPP_f800510211t_bool(image_nat_nat(F),A_1) <-> A_1 = bot_bot_fun_nat_bool)) # label(fact_487_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 538 (all F all A_1 (is_fun_pname_bool(A_1) -> (bot_bo784226126e_bool = hAPP_f360545851e_bool(image_185131637_state(F),A_1) <-> A_1 = bot_bo844097828e_bool))) # label(fact_488_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 539 (all F all A_1 (is_fun_pname_bool(A_1) -> (bot_bo797238721a_bool = hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1) <-> A_1 = bot_bo844097828e_bool))) # label(fact_489_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 540 (all F hAPP_f800510211t_bool(image_nat_nat(F),bot_bot_fun_nat_bool) = bot_bot_fun_nat_bool) # label(fact_490_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 541 (all F hAPP_f360545851e_bool(image_185131637_state(F),bot_bo844097828e_bool) = bot_bo784226126e_bool) # label(fact_491_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 542 (all F hAPP_f2034373396a_bool(image_1738210978iple_a(F),bot_bo844097828e_bool) = bot_bo797238721a_bool) # label(fact_492_image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 543 (all F all A_1 (hAPP_f800510211t_bool(image_nat_nat(F),A_1) = bot_bot_fun_nat_bool <-> A_1 = bot_bot_fun_nat_bool)) # label(fact_493_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 544 (all F all A_1 (is_fun_pname_bool(A_1) -> (hAPP_f360545851e_bool(image_185131637_state(F),A_1) = bot_bo784226126e_bool <-> A_1 = bot_bo844097828e_bool))) # label(fact_494_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 545 (all F all A_1 (is_fun_pname_bool(A_1) -> (hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1) = bot_bo797238721a_bool <-> A_1 = bot_bo844097828e_bool))) # label(fact_495_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 546 (all Pa all X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),bot_bot_fun_nat_bool)) -> hBOOL(hAPP_nat_bool(Pa,X)))) # label(fact_496_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 547 (all Pa all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),bot_bo797238721a_bool)) -> hBOOL(hAPP_H1037229737a_bool(Pa,X)))) # label(fact_497_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 548 (all Pa all X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),bot_bo332163887l_bool)) -> hBOOL(hAPP_f1695230391l_bool(Pa,X)))) # label(fact_498_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 549 (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_499_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 550 (all Pa all X (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),bot_bo784226126e_bool)) -> hBOOL(hAPP_H242767318e_bool(Pa,X)))) # label(fact_500_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 551 (all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,bot_bot_fun_nat_bool),B_2) = B_2) # label(fact_501_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 552 (all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,bot_bo332163887l_bool),B_2) = B_2) # label(fact_502_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 553 (all B_2 (is_fun_pname_bool(B_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B_2) = B_2)) # label(fact_503_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 554 (all B_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),B_2) = B_2) # label(fact_504_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 555 (all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,bot_bo797238721a_bool),B_2) = B_2) # label(fact_505_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 556 (all A_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),bot_bot_fun_nat_bool) = A_1) # label(fact_506_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 557 (all A_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),bot_bo332163887l_bool) = A_1) # label(fact_507_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 558 (all A_1 (is_fun_pname_bool(A_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),bot_bo844097828e_bool) = A_1)) # label(fact_508_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 559 (all A_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),bot_bo784226126e_bool) = A_1) # label(fact_509_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 560 (all A_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),bot_bo797238721a_bool) = A_1) # label(fact_510_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 561 (all A_1 all B_2 (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2) = bot_bot_fun_nat_bool <-> A_1 = bot_bot_fun_nat_bool & B_2 = bot_bot_fun_nat_bool)) # label(fact_511_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 562 (all A_1 all B_2 (hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2) = bot_bo332163887l_bool <-> A_1 = bot_bo332163887l_bool & B_2 = bot_bo332163887l_bool)) # label(fact_512_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 563 (all A_1 all B_2 (is_fun_pname_bool(A_1) & is_fun_pname_bool(B_2) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2) = bot_bo844097828e_bool <-> A_1 = bot_bo844097828e_bool & B_2 = bot_bo844097828e_bool))) # label(fact_513_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 564 (all A_1 all B_2 (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2) = bot_bo784226126e_bool <-> A_1 = bot_bo784226126e_bool & B_2 = bot_bo784226126e_bool)) # label(fact_514_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 565 (all A_1 all B_2 (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2) = bot_bo797238721a_bool <-> A_1 = bot_bo797238721a_bool & B_2 = bot_bo797238721a_bool)) # label(fact_515_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 566 (all Ga all Pa all C_2 all Qa all C_1 ((hBOOL(C_1) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool)))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_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_2),Qa)),bot_bo797238721a_bool))))) # label(fact_516_constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 567 (all Ga all Pa all C_2 all Qa all C_1 ((hBOOL(C_1) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_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_2),Qa)),bot_bo784226126e_bool))))) # label(fact_517_constant) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 568 (all Ga hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),bot_bo797238721a_bool))) # label(fact_518_empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 569 (all Ga hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),bot_bo784226126e_bool))) # label(fact_519_empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 570 (all X_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,bot_bot_fun_nat_bool),X_2) = X_2) # label(fact_520_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 571 (all X_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,bot_bo332163887l_bool),X_2) = X_2) # label(fact_521_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 572 (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_522_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 573 (all X_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),X_2) = X_2) # label(fact_523_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 574 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,bot_bot_bool),X_2)) <-> hBOOL(X_2))) # label(fact_524_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 575 (all X_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,bot_bo797238721a_bool),X_2) = X_2) # label(fact_525_sup__bot__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 576 (all X_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),bot_bot_fun_nat_bool) = X_2) # label(fact_526_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 577 (all X_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),bot_bo332163887l_bool) = X_2) # label(fact_527_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 578 (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_528_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 579 (all X_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),bot_bo784226126e_bool) = X_2) # label(fact_529_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 580 (all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),bot_bot_bool)) <-> hBOOL(X_2))) # label(fact_530_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 581 (all X_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),bot_bo797238721a_bool) = X_2) # label(fact_531_sup__bot__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 582 (all X_2 all Y_1 (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) = bot_bot_fun_nat_bool <-> X_2 = bot_bot_fun_nat_bool & Y_1 = bot_bot_fun_nat_bool)) # label(fact_532_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 583 (all X_2 all Y_1 (hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) = bot_bo332163887l_bool <-> X_2 = bot_bo332163887l_bool & Y_1 = bot_bo332163887l_bool)) # label(fact_533_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 584 (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_534_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 585 (all X_2 all Y_1 (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) = bot_bo784226126e_bool <-> X_2 = bot_bo784226126e_bool & Y_1 = bot_bo784226126e_bool)) # label(fact_535_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 586 (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_536_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 587 (all X_2 all Y_1 (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) = bot_bo797238721a_bool <-> X_2 = bot_bo797238721a_bool & Y_1 = bot_bo797238721a_bool)) # label(fact_537_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 588 (all N_4 all T_2 (hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,hAPP_nat_nat(suc,N_4)),T_2)) -> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_4),T_2)))) # label(fact_538_triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 589 (all N_4 all T_2 (hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,hAPP_nat_nat(suc,N_4)),T_2)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_4),T_2)))) # label(fact_539_triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 590 (all A_2 all B_2 hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),B_2)) # label(fact_540_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 591 (all A_2 all B_2 hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2) = 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_2))),B_2)) # label(fact_541_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 592 (all A_2 all B_2 hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),B_2)) # label(fact_542_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 593 (all A_2 all B_2 hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),B_2)) # label(fact_543_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 594 (all A_2 all B_2 hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),B_2)) # label(fact_544_insert__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 595 (all Ga all Pa all Pn_1 all Qa (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo797238721a_bool))))) # label(fact_545_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 596 (all Ga all Pa all Pn_1 all Qa (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo784226126e_bool))))) # label(fact_546_weak__Body) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 597 (all Pa all Pn_1 all Qa all Ga (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo797238721a_bool))))) # label(fact_547_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 598 (all Pa all Pn_1 all Qa all Ga (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo784226126e_bool))))) # label(fact_548_BodyN) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 599 (all Ga all C_2 all Qa all Pa ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3)) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C_2),hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(Qa,Z_4)))),bot_bo797238721a_bool))))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool))))) # label(fact_549_escape) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 600 (all Ga all C_2 all Qa all Pa ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3)) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C_2),hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Qa,Z_4)))),bot_bo784226126e_bool))))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool))))) # label(fact_550_escape) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 601 (all Pa all Ga all P_1 all C_2 all Qa (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,P_1),C_2),Qa)),bot_bo797238721a_bool))) -> ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_4),S_3)))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool)))))) # label(fact_551_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 602 (all Pa all Ga all P_1 all C_2 all Qa (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C_2),Qa)),bot_bo784226126e_bool))) -> ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_4),S_3)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool)))))) # label(fact_552_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 603 (all Qa all Ga all Pa all C_2 all Q_1 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Q_1)),bot_bo797238721a_bool))) -> ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_4),S_3)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_4),S_3)))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool)))))) # label(fact_553_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 604 (all Qa all Ga all Pa all C_2 all Q_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Q_1)),bot_bo784226126e_bool))) -> ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_4),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_4),S_3)))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool)))))) # label(fact_554_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 605 (all Fa all Fun1 all Com_1 all Fun2 hAPP_H592031934_a_nat(hoare_571935964size_a(Fa),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1),Com_1),Fun2)) = zero_zero_nat) # label(fact_555_triple_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 606 (all Fa all Fun1 all Com_1 all Fun2 hAPP_H175283793te_nat(hoare_163978021_state(Fa),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com_1),Fun2)) = zero_zero_nat) # label(fact_556_triple_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 607 (all C_2 hoare_Mirabelle_MGT(C_2) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,fequal_state),C_2),evalc(C_2))) # label(fact_557_MGT__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 608 (all Fun1 all Com_1 all Fun2 hAPP_H592031934_a_nat(size_s399404919iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1),Com_1),Fun2)) = zero_zero_nat) # label(fact_558_triple_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 609 (all Fun1 all Com_1 all Fun2 hAPP_H175283793te_nat(size_s255495008_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com_1),Fun2)) = zero_zero_nat) # label(fact_559_triple_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 610 (all Qa all Pa all Ga all P_1 all C_2 all Q_1 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,P_1),C_2),Q_1)),bot_bo797238721a_bool))) -> ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3)) -> (all S_4 ((all Z_5 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_5),S_3)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_5),S_4)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_4),S_4)))))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool)))))) # label(fact_560_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 611 (all Qa all Pa all Ga all P_1 all C_2 all Q_1 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C_2),Q_1)),bot_bo784226126e_bool))) -> ((all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3)) -> (all S_4 ((all Z_5 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_5),S_3)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_5),S_4)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_4),S_4)))))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool)))))) # label(fact_561_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 612 (all X_2 hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) = X_2) # label(fact_562_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 613 (all X_2 hAPP_f258822235a_bool(the_el979963640a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) = X_2) # label(fact_563_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 614 (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_564_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 615 (all X_2 hAPP_f1693662087iple_a(the_el1519802624iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) = X_2) # label(fact_565_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 616 (all X_2 hAPP_f718417177_state(the_el2080696983_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) = X_2) # label(fact_566_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 617 (all M_2 hAPP_nat_nat(suc,M_2) != zero_zero_nat) # label(fact_567_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 618 (all N_2 N_2 != hAPP_nat_nat(suc,N_2)) # label(fact_569_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 619 (all N_2 hAPP_nat_nat(suc,N_2) != N_2) # label(fact_570_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 620 (all Nat_4 all Nat_3 (hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3) <-> Nat_4 = Nat_3)) # label(fact_571_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 621 (all X_1 all Y (hAPP_nat_nat(suc,X_1) = hAPP_nat_nat(suc,Y) -> X_1 = Y)) # label(fact_572_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 622 (all M_2 zero_zero_nat != hAPP_nat_nat(suc,M_2)) # label(fact_573_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 623 (all Nat_2 zero_zero_nat != hAPP_nat_nat(suc,Nat_2)) # label(fact_574_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 624 (all M_2 hAPP_nat_nat(suc,M_2) != zero_zero_nat) # label(fact_575_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 625 (all Nat_1 hAPP_nat_nat(suc,Nat_1) != zero_zero_nat) # label(fact_576_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 626 (all M_2 zero_zero_nat != hAPP_nat_nat(suc,M_2)) # label(fact_577_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 627 (all N_2 (N_2 != zero_zero_nat -> (exists M_1 N_2 = hAPP_nat_nat(suc,M_1)))) # label(fact_578_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 628 (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,hAPP_nat_nat(suc,N))))) -> hBOOL(hAPP_nat_bool(Pa,N_1))))) # label(fact_579_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 629 (all Pa all K_1 (hBOOL(hAPP_nat_bool(Pa,K_1)) -> ((all N (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))) -> hBOOL(hAPP_nat_bool(Pa,N)))) -> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))))) # label(fact_580_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 630 (all Y (Y != zero_zero_nat -> -(all Nat Y != hAPP_nat_nat(suc,Nat)))) # label(fact_581_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 631 (all X (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_582_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 632 (all X (hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_583_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.06 633 (all X (hBOOL(hAPP_f1695230391l_bool(bot_bo332163887l_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_584_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 634 (all X (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_585_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 635 (all X (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X)) <-> hBOOL(bot_bot_bool))) # label(fact_586_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 636 (all X_2 (hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_587_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 637 (all X_2 (hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_588_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 638 (all X_2 (hBOOL(hAPP_f1695230391l_bool(bot_bo332163887l_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_589_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 639 (all X_2 (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_590_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 640 (all X_2 (hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_591_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 641 (all Pn all S0 all N_2 all S1_2 (hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn)),S0,N_2),S1_2)) -> hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,Pn),S0,hAPP_nat_nat(suc,N_2)),S1_2)))) # label(fact_592_evaln_OBody) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 642 (all Ga all Pa hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),skip),Pa)),bot_bo797238721a_bool)))) # label(fact_593_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 643 (all Ga all Pa hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),skip),Pa)),bot_bo784226126e_bool)))) # label(fact_594_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 644 (all Ga all Pa all B_1 all C_2 hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_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_1))),while(B_1,C_2)),Pa)),bot_bo797238721a_bool)))) # label(fact_595_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 645 (all Ga all Pa all B_1 all C_2 hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_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_1))),while(B_1,C_2)),Pa)),bot_bo784226126e_bool)))) # label(fact_596_LoopF) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 646 (all C_2 all N_1 all B_1 all S_1 (-hBOOL(hAPP_state_bool(B_1,S_1)) -> hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S_1,N_1),S_1)))) # label(fact_597_evaln_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 647 (all S2_1 all C_2 all N_1 all S1 all B_1 all S0_1 (hBOOL(hAPP_state_bool(B_1,S0_1)) -> (hBOOL(hAPP_state_bool(evaln(C_2,S0_1,N_1),S1)) -> (hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S1,N_1),S2_1)) -> hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S0_1,N_1),S2_1)))))) # label(fact_598_evaln_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 648 (all S2_1 all C_2 all S1 all B_1 all S0_1 (hBOOL(hAPP_state_bool(B_1,S0_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S0_1),S1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S1),S2_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S0_1),S2_1)))))) # label(fact_599_evalc_OWhileTrue) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 649 (all C_2 all B_1 all S_1 (-hBOOL(hAPP_state_bool(B_1,S_1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S_1),S_1)))) # label(fact_600_evalc_OWhileFalse) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 650 (all S all N_2 hBOOL(hAPP_state_bool(evaln(skip,S,N_2),S))) # label(fact_601_evaln_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 651 (all S all N_2 all T (hBOOL(hAPP_state_bool(evaln(skip,S,N_2),T)) -> T = S)) # label(fact_602_evaln__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 652 (all S all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S),T)) -> T = S)) # label(fact_603_evalc__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 653 (all S hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S),S))) # label(fact_604_evalc_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 654 (all Fun all Com skip != while(Fun,Com)) # label(fact_605_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 655 (all Fun all Com while(Fun,Com) != skip) # label(fact_606_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 656 (all Fun_1 all Com_1 all Fun all Com (while(Fun_1,Com_1) = while(Fun,Com) <-> Fun_1 = Fun & Com_1 = Com)) # label(fact_607_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 657 (all C all S all N_2 all S_5 (hBOOL(hAPP_state_bool(evaln(C,S,N_2),S_5)) -> hBOOL(hAPP_state_bool(evaln(C,S,hAPP_nat_nat(suc,N_2)),S_5)))) # label(fact_608_evaln__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 658 (all C all S all N_2 all T (hBOOL(hAPP_state_bool(evaln(C,S,N_2),T)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),T)))) # label(fact_609_evaln__evalc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 659 (all C_2 all S_1 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),T_1)) <-> (exists N hBOOL(hAPP_state_bool(evaln(C_2,S_1,N),T_1))))) # label(fact_610_eval__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 660 (all Pname all Fun_1 all Com_1 hAPP_pname_com(body,Pname) != while(Fun_1,Com_1)) # label(fact_611_com_Osimps_I59_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 661 (all Fun_1 all Com_1 all Pname while(Fun_1,Com_1) != hAPP_pname_com(body,Pname)) # label(fact_612_com_Osimps_I58_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 662 (all Pname_2 skip != hAPP_pname_com(body,Pname_2)) # label(fact_613_com_Osimps_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 663 (all Pname_2 hAPP_pname_com(body,Pname_2) != skip) # label(fact_614_com_Osimps_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 664 (all N_1 all Pa all C_2 all Qa (hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_1),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa))) <-> (all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3)) -> (all S_4 (hBOOL(hAPP_state_bool(evaln(C_2,S_3,N_1),S_4)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_4),S_4)))))))) # label(fact_615_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 665 (all N_1 all Pa all C_2 all Qa (hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_1),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa))) <-> (all Z_4 all S_3 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3)) -> (all S_4 (hBOOL(hAPP_state_bool(evaln(C_2,S_3,N_1),S_4)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_4),S_4)))))))) # label(fact_616_triple__valid__def2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 666 (all P all S all N_2 all S1_2 (hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,P),S,N_2),S1_2)) -> -(all N (N_2 = hAPP_nat_nat(suc,N) -> -hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P)),S,N),S1_2)))))) # label(fact_617_evaln__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 667 (all B_1 all C_2 all S_1 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S_1),T_1)) -> ((T_1 = S_1 -> hBOOL(hAPP_state_bool(B_1,S_1))) -> -(hBOOL(hAPP_state_bool(B_1,S_1)) -> (all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),S1_1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S1_1),T_1)))))))) # label(fact_618_evalc__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 668 (all B_1 all C_2 all S_1 all N_1 all T_1 (hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S_1,N_1),T_1)) -> ((T_1 = S_1 -> hBOOL(hAPP_state_bool(B_1,S_1))) -> -(hBOOL(hAPP_state_bool(B_1,S_1)) -> (all S1_1 (hBOOL(hAPP_state_bool(evaln(C_2,S_1,N_1),S1_1)) -> -hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S1_1,N_1),T_1)))))))) # label(fact_619_evaln__WHILE__case) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 669 (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_620_evalc__evaln) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 670 (all D all R_1 all Ga all Pa all C_2 all Qa (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Qa),D),R_1)),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),semi(C_2,D)),R_1)),bot_bo797238721a_bool)))))) # label(fact_621_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 671 (all D all R_1 all Ga all Pa all C_2 all Qa (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Qa),D),R_1)),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),semi(C_2,D)),R_1)),bot_bo784226126e_bool)))))) # label(fact_622_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 672 (all X_10 hAPP_f22106695ol_nat(the_elem_nat,X_10) = hAPP_f22106695ol_nat(the_nat,hAPP_f158894502t_bool(cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_10)),hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,insert_nat),bot_bot_fun_nat_bool)))) # label(fact_623_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 673 (all X_10 hAPP_f258822235a_bool(the_el979963640a_bool,X_10) = hAPP_f258822235a_bool(the_fu1555441254a_bool,hAPP_f536631715l_bool(cOMBB_1575464575a_bool(hAPP_f1303207443l_bool(fequal1455900568l_bool,X_10)),hAPP_f759941367l_bool(hAPP_f254338943l_bool(cOMBC_1324894996l_bool,insert1421434205a_bool),bot_bo332163887l_bool)))) # label(fact_624_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 674 (all X_10 hAPP_f1297739591_pname(the_elem_pname,X_10) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_10)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool)))) # label(fact_625_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 675 (all X_10 hAPP_f1693662087iple_a(the_el1519802624iple_a,X_10) = hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_f1194757675a_bool(cOMBB_1610959875iple_a(hAPP_f1767618879l_bool(fequal874423448a_bool,X_10)),hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,insert956547291iple_a),bot_bo797238721a_bool)))) # label(fact_626_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 676 (all X_10 hAPP_f718417177_state(the_el2080696983_state,X_10) = hAPP_f718417177_state(the_Ho2067184133_state,hAPP_f1900156034e_bool(cOMBB_1282391997_state(hAPP_f849457489l_bool(fequal1475827639e_bool,X_10)),hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,insert1744391420_state),bot_bo784226126e_bool)))) # label(fact_627_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 677 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,U_2)) -> ((all P_2 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_H1893885264e_bool(P_1,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H1893885264e_bool(Q_1,P_2))),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_H1893885264e_bool(Pa,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H1893885264e_bool(Qa,P_2))),bot_bo797238721a_bool))))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(image_533441733iple_a(hAPP_f1766326554iple_a(hAPP_f2004506425iple_a(cOMBS_1744968921iple_a,hAPP_f524917645iple_a(hAPP_f51865337iple_a(cOMBS_1597898188iple_a,hAPP_f338450734iple_a(cOMBB_1799328076iple_a(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(image_533441733iple_a(hAPP_f1766326554iple_a(hAPP_f2004506425iple_a(cOMBS_1744968921iple_a,hAPP_f524917645iple_a(hAPP_f51865337iple_a(cOMBS_1597898188iple_a,hAPP_f338450734iple_a(cOMBB_1799328076iple_a(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))))))) # label(fact_628_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 678 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,U_2)) -> ((all P_2 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_f477771714e_bool(P_1,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f477771714e_bool(Q_1,P_2))),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_f477771714e_bool(Pa,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f477771714e_bool(Qa,P_2))),bot_bo797238721a_bool))))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f258822235a_bool(image_1153683671iple_a(hAPP_f1255935540iple_a(hAPP_f410259831iple_a(cOMBS_1097875753iple_a,hAPP_f159541635iple_a(hAPP_f2023640211iple_a(cOMBS_1949899292iple_a,hAPP_f1787234632iple_a(cOMBB_1013749676a_bool(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f258822235a_bool(image_1153683671iple_a(hAPP_f1255935540iple_a(hAPP_f410259831iple_a(cOMBS_1097875753iple_a,hAPP_f159541635iple_a(hAPP_f2023640211iple_a(cOMBS_1949899292iple_a,hAPP_f1787234632iple_a(cOMBB_1013749676a_bool(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))))))) # label(fact_629_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 679 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2)) -> ((all P_2 (is_pname(P_2) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Q_1,P_2))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Qa,P_2))),bot_bo784226126e_bool)))))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))))))) # label(fact_630_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 680 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,U_2)) -> ((all P_2 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_H838560847e_bool(P_1,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H838560847e_bool(Q_1,P_2))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_H838560847e_bool(Pa,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H838560847e_bool(Qa,P_2))),bot_bo784226126e_bool))))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f101573982e_bool(image_1599849618_state(hAPP_f1551299824_state(hAPP_f461066925_state(cOMBS_1860286139_state,hAPP_f1573424489_state(hAPP_f1527065593_state(cOMBS_1436317352_state,hAPP_f1874377965_state(cOMBB_1269509967iple_a(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f101573982e_bool(image_1599849618_state(hAPP_f1551299824_state(hAPP_f461066925_state(cOMBS_1860286139_state,hAPP_f1573424489_state(hAPP_f1527065593_state(cOMBS_1436317352_state,hAPP_f1874377965_state(cOMBB_1269509967iple_a(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))))))) # label(fact_631_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 681 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,U_2)) -> ((all P_2 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1246524253e_bool(P_1,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f1246524253e_bool(Q_1,P_2))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1246524253e_bool(Pa,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f1246524253e_bool(Qa,P_2))),bot_bo784226126e_bool))))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f1513075764e_bool(image_821490176_state(hAPP_f582141064_state(hAPP_f1784570101_state(cOMBS_988488459_state,hAPP_f1235235423_state(hAPP_f1151038867_state(cOMBS_1113512696_state,hAPP_f868277077_state(cOMBB_989249001a_bool(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f1513075764e_bool(image_821490176_state(hAPP_f582141064_state(hAPP_f1784570101_state(cOMBS_988488459_state,hAPP_f1235235423_state(hAPP_f1151038867_state(cOMBS_1113512696_state,hAPP_f868277077_state(cOMBB_989249001a_bool(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))))))) # label(fact_632_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 682 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2)) -> ((all P_2 (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_n1063102567e_bool(P_1,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1063102567e_bool(Q_1,P_2))),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_n1063102567e_bool(Pa,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1063102567e_bool(Qa,P_2))),bot_bo797238721a_bool))))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f420957402a_bool(image_1865589340iple_a(hAPP_f817035994iple_a(hAPP_f311800994iple_a(cOMBS_1417107330iple_a,hAPP_f1857794253iple_a(hAPP_f803745506iple_a(cOMBS_519355893iple_a,hAPP_f1921807086iple_a(cOMBB_1443236341_a_nat(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f420957402a_bool(image_1865589340iple_a(hAPP_f817035994iple_a(hAPP_f311800994iple_a(cOMBS_1417107330iple_a,hAPP_f1857794253iple_a(hAPP_f803745506iple_a(cOMBS_519355893iple_a,hAPP_f1921807086iple_a(cOMBB_1443236341_a_nat(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))))))) # label(fact_633_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 683 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2)) -> ((all P_2 (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_n1252169848e_bool(P_1,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1252169848e_bool(Q_1,P_2))),bot_bo784226126e_bool))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_n1252169848e_bool(Pa,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1252169848e_bool(Qa,P_2))),bot_bo784226126e_bool))))) -> (hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f375948533e_bool(image_1730813499_state(hAPP_f634763074_state(hAPP_f1172439208_state(cOMBS_1390821348_state,hAPP_f1158791849_state(hAPP_f459571426_state(cOMBS_183256401_state,hAPP_f432895259_state(cOMBB_1531938296te_nat(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f375948533e_bool(image_1730813499_state(hAPP_f634763074_state(hAPP_f1172439208_state(cOMBS_1390821348_state,hAPP_f1158791849_state(hAPP_f459571426_state(cOMBS_183256401_state,hAPP_f432895259_state(cOMBB_1531938296te_nat(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))))))) # label(fact_634_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 684 (all Pa all Qa all Ga all P_1 all C0 all Q_1 all U_2 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2)) -> ((all P_2 (is_pname(P_2) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_p635540397e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Q_1,P_2))),bot_bo797238721a_bool))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_p635540397e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Qa,P_2))),bot_bo797238721a_bool)))))) -> (hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2))) -> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))))))) # label(fact_635_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 685 (all C2_1 all S2 all N2 all T2 all C1_1 all S1_2 all N1 all T1 (hBOOL(hAPP_state_bool(evaln(C1_1,S1_2,N1),T1)) -> (hBOOL(hAPP_state_bool(evaln(C2_1,S2,N2),T2)) -> (exists N (hBOOL(hAPP_state_bool(evaln(C1_1,S1_2,N),T1)) & hBOOL(hAPP_state_bool(evaln(C2_1,S2,N),T2))))))) # label(fact_636_evaln__max2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 686 (all A_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) -> (exists B_6 (A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_6) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B_6)))))) # label(fact_637_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 687 (all A_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)) -> (exists B_6 (A_1 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_6) & -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),B_6)))))) # label(fact_638_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 688 (all A_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1)) -> (exists B_6 (A_1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_6) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),B_6)))))) # label(fact_639_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 689 (all A_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1)) -> (exists B_6 (A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_6) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),B_6)))))) # label(fact_640_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 690 (all A_2 all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)) -> (exists B_6 (is_fun_pname_bool(B_6) & A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_6) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B_6))))))) # label(fact_641_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 691 (all C1_1 all S2 all C0_1 all S0 all N_2 all S1_2 (hBOOL(hAPP_state_bool(evaln(C0_1,S0,N_2),S1_2)) -> (hBOOL(hAPP_state_bool(evaln(C1_1,S1_2,N_2),S2)) -> hBOOL(hAPP_state_bool(evaln(semi(C0_1,C1_1),S0,N_2),S2))))) # label(fact_642_evaln_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 692 (all C1_1 all S2 all C0_1 all S0 all S1_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0_1),S0),S1_2)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S1_2),S2)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0_1,C1_1)),S0),S2))))) # label(fact_643_evalc_OSemi) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 693 (all Com1_1 all Com2_1 all Com1 all Com2 (semi(Com1_1,Com2_1) = semi(Com1,Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_644_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 694 (all Com1_2 all Com2_2 all Pname_2 semi(Com1_2,Com2_2) != hAPP_pname_com(body,Pname_2)) # label(fact_645_com_Osimps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 695 (all Pname_2 all Com1_2 all Com2_2 hAPP_pname_com(body,Pname_2) != semi(Com1_2,Com2_2)) # label(fact_646_com_Osimps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 696 (all Fun all Com all Com1_1 all Com2_1 while(Fun,Com) != semi(Com1_1,Com2_1)) # label(fact_647_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 697 (all Com1_1 all Com2_1 all Fun all Com semi(Com1_1,Com2_1) != while(Fun,Com)) # label(fact_648_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 698 (all Com1_3 all Com2_3 semi(Com1_3,Com2_3) != skip) # label(fact_649_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 699 (all Com1_3 all Com2_3 skip != semi(Com1_3,Com2_3)) # label(fact_650_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 700 (all C1_1 all C2_1 all S all T (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1_1,C2_1)),S),T)) -> -(all S1_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S),S1_1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2_1),S1_1),T)))))) # label(fact_651_evalc__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 701 (all C1_1 all C2_1 all S all N_2 all T (hBOOL(hAPP_state_bool(evaln(semi(C1_1,C2_1),S,N_2),T)) -> -(all S1_1 (hBOOL(hAPP_state_bool(evaln(C1_1,S,N_2),S1_1)) -> -hBOOL(hAPP_state_bool(evaln(C2_1,S1_1,N_2),T)))))) # label(fact_652_evaln__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 702 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(H),F_1))))) # label(fact_653_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 703 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f420957402a_bool(image_1865589340iple_a(H),F_1))))) # label(fact_654_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 704 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f1098153174l_bool(image_1590538908a_bool(H),F_1))))) # label(fact_655_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 705 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f654413245e_bool(image_nat_pname(H),F_1))))) # label(fact_656_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 706 (all H all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(image_nat_nat(H),F_1))))) # label(fact_657_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 707 (all H all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1968395738t_bool(image_48635758_a_nat(H),F_1))))) # label(fact_658_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 708 (all H all F_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1900748420t_bool(image_1769043840ol_nat(H),F_1))))) # label(fact_659_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 709 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1066163005t_bool(image_pname_nat(H),F_1))))) # label(fact_660_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 710 (all H all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f2034373396a_bool(image_1738210978iple_a(H),F_1))))) # label(fact_661_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 711 (all A_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1))))) # label(fact_662_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 712 (all A_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1))))) # label(fact_663_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 713 (all A_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1))))) # label(fact_664_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 714 (all A_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1))))) # label(fact_665_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 715 (all A_2 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1))))) # label(fact_666_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 716 (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_672_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 717 (all Qa all Pa (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Pa))) | hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Qa))) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),Pa)),Qa)))))) # label(fact_673_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 718 (all Qa all Pa (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Pa))) | hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Qa))) -> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),Pa)),Qa)))))) # label(fact_674_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 719 (all Qa all Pa (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Pa))) | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Qa))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),Qa)))))) # label(fact_675_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 720 (all F_1 all Ga (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F_1),Ga))) <-> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1)) & hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,Ga)))) # label(fact_676_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 721 (all F_1 all Ga (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),Ga))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)))) # label(fact_677_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 722 (all F_1 all Ga (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F_1),Ga))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1)) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Ga)))) # label(fact_678_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 723 (all F_1 all Ga (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F_1),Ga))) <-> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) & hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,Ga)))) # label(fact_679_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 724 (all F_1 all Ga (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F_1),Ga))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)))) # label(fact_680_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 725 (all Ga all F_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,Ga)) -> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F_1),Ga)))))) # label(fact_681_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 726 (all Ga all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),Ga)))))) # label(fact_682_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 727 (all Ga all F_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Ga)) -> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F_1),Ga)))))) # label(fact_683_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 728 (all Ga all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,Ga)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F_1),Ga)))))) # label(fact_684_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 729 (all Ga all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F_1),Ga)))))) # label(fact_685_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 730 (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_686_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 731 (all Pa all Qa (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),Pa)),Qa)))) <-> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Pa))) & hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Qa))))) # label(fact_687_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 732 (all Pa all Qa (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),Pa)),Qa)))) <-> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Pa))) & hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Qa))))) # label(fact_688_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 733 (all Pa all Qa (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),Pa)),Qa)))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Pa))) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Qa))))) # label(fact_689_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 734 (all A_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1))) <-> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)))) # label(fact_690_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 735 (all A_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1))) <-> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)))) # label(fact_691_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 736 (all A_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1))) <-> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)))) # label(fact_692_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 737 (all A_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1))) <-> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)))) # label(fact_693_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 738 (all A_2 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1))) <-> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)))) # label(fact_694_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 739 (all Pa all F_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(Pa,bot_bo332163887l_bool)) -> ((all X all F_2 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_2)) -> (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),F_2)) -> (hBOOL(hAPP_f2110825313l_bool(Pa,F_2)) -> hBOOL(hAPP_f2110825313l_bool(Pa,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),F_2))))))) -> hBOOL(hAPP_f2110825313l_bool(Pa,F_1)))))) # label(fact_695_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 740 (all Pa all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,bot_bo797238721a_bool)) -> ((all X all F_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_2)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),F_2)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,F_2)) -> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),F_2))))))) -> hBOOL(hAPP_f1695230391l_bool(Pa,F_1)))))) # label(fact_696_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 741 (all Pa all F_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool)) -> ((all X all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,F_2)) -> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),F_2))))))) -> hBOOL(hAPP_f1378282496l_bool(Pa,F_1)))))) # label(fact_697_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 742 (all Pa all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) -> ((all X all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),F_2))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1)))))) # label(fact_698_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 743 (all Pa all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (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_1)))))) # label(fact_699_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 744 (all A_2 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_2)) <-> A_2 = bot_bo332163887l_bool | (exists A_8 exists A_7 (A_2 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_7),A_8) & hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_8)))))) # label(fact_700_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 745 (all A_2 (is_fun_pname_bool(A_2) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_2)) <-> A_2 = bot_bo844097828e_bool | (exists A_8 exists A_7 (is_fun_pname_bool(A_8) & is_pname(A_7) & A_2 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_7),A_8) & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_8))))))) # label(fact_701_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 746 (all A_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_2)) <-> A_2 = bot_bo797238721a_bool | (exists A_8 exists A_7 (A_2 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_7),A_8) & hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_8)))))) # label(fact_702_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 747 (all A_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2)) <-> A_2 = bot_bo784226126e_bool | (exists A_8 exists A_7 (A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_7),A_8) & hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_8)))))) # label(fact_703_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 748 (all A_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) <-> A_2 = bot_bot_fun_nat_bool | (exists A_8 exists A_7 (A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_7),A_8) & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_8)))))) # label(fact_704_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 749 (all F all A_1 (-hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1900748420t_bool(image_1769043840ol_nat(F),A_1))) -> (exists X (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1)) & -hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_n37219812l_bool(hAPP_f1852971749l_bool(cOMBC_594836627t_bool,hAPP_f1144745493t_bool(cOMBB_85437587a_bool(fequal_nat),F)),hAPP_f2097660464ol_nat(F,X))))))))))) # label(fact_705_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 750 (all F all A_1 (-hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1968395738t_bool(image_48635758_a_nat(F),A_1))) -> (exists X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1)) & -hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_n1919155532a_bool(hAPP_f228417655a_bool(cOMBC_364739t_bool,hAPP_f1872860171t_bool(cOMBB_1391527205iple_a(fequal_nat),F)),hAPP_H592031934_a_nat(F,X))))))))))) # label(fact_706_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 751 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1066163005t_bool(image_pname_nat(F),A_1))) -> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_n1025906991e_bool(hAPP_f1715247037e_bool(cOMBC_pname_nat_bool,hAPP_f1358769483t_bool(cOMBB_523834888_pname(fequal_nat),F)),hAPP_pname_nat(F,X))))))))))) # label(fact_707_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 752 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(image_nat_nat(F),A_1))) -> (exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(fequal_nat),F)),hAPP_nat_nat(F,X))))))))))) # label(fact_708_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 753 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f420957402a_bool(image_1865589340iple_a(F),A_1))) -> (exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_H144868812t_bool(hAPP_f1886543991t_bool(cOMBC_533513393a_bool,hAPP_f260875897a_bool(cOMBB_1063143712ol_nat(fequal963300192iple_a),F)),hAPP_n261501868iple_a(F,X))))))))))) # label(fact_709_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 754 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f1098153174l_bool(image_1590538908a_bool(F),A_1))) -> (exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f1968395738t_bool(hAPP_f2110185157t_bool(cOMBC_805992879l_bool,hAPP_f635381775l_bool(cOMBB_1370228356ol_nat(fequal874423448a_bool),F)),hAPP_n1919155532a_bool(F,X))))))))))) # label(fact_710_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 755 (all F all A_1 (-hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f654413245e_bool(image_nat_pname(F),A_1))) -> (exists X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) & -hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_p1499970991t_bool(hAPP_f998021053t_bool(cOMBC_nat_pname_bool,hAPP_f414474559e_bool(cOMBB_1212655066ol_nat(fequal_pname),F)),hAPP_nat_pname(F,X))))))))))) # label(fact_711_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 756 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(F),A_1))) -> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_H1776011827e_bool(hAPP_f343137017e_bool(cOMBC_19854728e_bool,hAPP_f472107739e_bool(cOMBB_181781758_pname(fequal1440809015_state),F)),hAPP_p1751618853_state(F,X))))))))))) # label(fact_712_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 757 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1))) -> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f1216026388e_bool(hAPP_f1415030585e_bool(cOMBC_173670761l_bool,hAPP_f1577042203l_bool(cOMBB_1363536318_pname(fequal874423448a_bool),F)),hAPP_p1743421830a_bool(F,X))))))))))) # label(fact_713_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 758 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A_1))) -> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X))))))))))) # label(fact_714_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 759 (all F all A_1 (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))) -> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) & -hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_H1078816262e_bool(hAPP_f421895915e_bool(cOMBC_1309726071a_bool,hAPP_f2085416313a_bool(cOMBB_1388879450_pname(fequal963300192iple_a),F)),hAPP_p346744818iple_a(F,X))))))))))) # label(fact_715_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 760 (all A_1 (A_1 != bot_bot_fun_nat_bool <-> (exists X exists B_6 (A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),B_6) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),B_6)))))) # label(fact_716_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 761 (all A_1 (A_1 != bot_bo332163887l_bool <-> (exists X exists B_6 (A_1 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),B_6) & -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),B_6)))))) # label(fact_717_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 762 (all A_1 (A_1 != bot_bo797238721a_bool <-> (exists X exists B_6 (A_1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),B_6) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),B_6)))))) # label(fact_718_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 763 (all A_1 (A_1 != bot_bo784226126e_bool <-> (exists X exists B_6 (A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),B_6) & -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),B_6)))))) # label(fact_719_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 764 (all A_1 (is_fun_pname_bool(A_1) -> (A_1 != bot_bo844097828e_bool <-> (exists X exists B_6 (is_pname(X) & is_fun_pname_bool(B_6) & A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),B_6) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_6))))))) # label(fact_720_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 765 (all B_2 all A_1 all F all F_1 (hBOOL(finite927518301a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (A_1 != bot_bo332163887l_bool -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2)) -> (B_2 != bot_bo332163887l_bool -> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,A_1)),hAPP_f258822235a_bool(F_1,B_2)))))))) # label(fact_721_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 766 (all B_2 all A_1 all F all F_1 (is_fun_pname_bool(B_2) & is_fun_pname_bool(A_1) -> (hBOOL(finite89670078_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_2)) -> (B_2 != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,A_1)),hAPP_f1297739591_pname(F_1,B_2))))))))) # label(fact_722_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 767 (all B_2 all A_1 all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> (A_1 != bot_bo784226126e_bool -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_2)) -> (B_2 != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,A_1)),hAPP_f718417177_state(F_1,B_2)))))))) # label(fact_723_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 768 (all B_2 all A_1 all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (A_1 != bot_bo797238721a_bool -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B_2)) -> (B_2 != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,A_1)),hAPP_f1693662087iple_a(F_1,B_2)))))))) # label(fact_724_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 769 (all B_2 all A_1 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (A_1 != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2)) -> (B_2 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,A_1)),hAPP_f22106695ol_nat(F_1,B_2)))))))) # label(fact_725_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 770 (all X_2 all A_1 all F all F_1 (hBOOL(finite927518301a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (A_1 != bot_bo332163887l_bool -> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,A_1)))))) # label(fact_726_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 771 (all X_2 all A_1 all F all F_1 (is_fun_pname_bool(A_1) -> (hBOOL(finite89670078_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,A_1))))))) # label(fact_727_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 772 (all X_2 all A_1 all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (A_1 != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,A_1)))))) # label(fact_728_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 773 (all X_2 all A_1 all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> (A_1 != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),hAPP_f718417177_state(F_1,A_1)))))) # label(fact_729_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 774 (all X_2 all A_1 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (A_1 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,A_1)))))) # label(fact_730_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 775 (all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hAPP_f360545851e_bool(image_185131637_state(F),A_1) = hAPP_f360545851e_bool(hAPP_f447027986e_bool(finite1443934175_pname(semila176469292e_bool,hAPP_f103229774e_bool(hAPP_f376349141e_bool(cOMBC_59067399e_bool,hAPP_f2028971360e_bool(cOMBB_667059641_pname(insert1744391420_state),F)),bot_bo784226126e_bool)),bot_bo784226126e_bool),A_1))) # label(fact_731_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 776 (all F all A_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> hAPP_f20753329a_bool(image_533441733iple_a(F),A_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(finite1750867337iple_a(semila1114547555a_bool,hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,hAPP_f181951559a_bool(cOMBB_1722563443iple_a(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1))) # label(fact_732_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 777 (all F all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> hAPP_f258822235a_bool(image_1153683671iple_a(F),A_1) = hAPP_f258822235a_bool(hAPP_f1748906467a_bool(finite576419631a_bool(semila1114547555a_bool,hAPP_f1706700729a_bool(hAPP_f957014749a_bool(cOMBC_288844080a_bool,hAPP_f2116512939a_bool(cOMBB_734913733a_bool(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1))) # label(fact_733_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 778 (all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hAPP_f800510211t_bool(image_nat_nat(F),A_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(finite2098682953ol_nat(semila465093516t_bool,hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,hAPP_f934069744t_bool(cOMBB_1141542387ol_nat(insert_nat),F)),bot_bot_fun_nat_bool)),bot_bot_fun_nat_bool),A_1))) # label(fact_734_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 779 (all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hAPP_f1098153174l_bool(image_1590538908a_bool(F),A_1) = hAPP_f1098153174l_bool(hAPP_f1659318414l_bool(finite183661956ol_nat(semila834425101l_bool,hAPP_f924569416l_bool(hAPP_f1384990677l_bool(cOMBC_1645572109l_bool,hAPP_f992030835l_bool(cOMBB_1467678496ol_nat(insert1421434205a_bool),F)),bot_bo332163887l_bool)),bot_bo332163887l_bool),A_1))) # label(fact_735_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 780 (all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hAPP_f654413245e_bool(image_nat_pname(F),A_1) = hAPP_f654413245e_bool(hAPP_f1319825314e_bool(finite491497871ol_nat(semila278973382e_bool,hAPP_f1501416730e_bool(hAPP_f883303749e_bool(cOMBC_1771919087e_bool,hAPP_f446737578e_bool(cOMBB_1209446585ol_nat(insert_pname),F)),bot_bo844097828e_bool)),bot_bo844097828e_bool),A_1))) # label(fact_736_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 781 (all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hAPP_f420957402a_bool(image_1865589340iple_a(F),A_1) = hAPP_f420957402a_bool(hAPP_f1023496418a_bool(finite658192434ol_nat(semila1114547555a_bool,hAPP_f1938783956a_bool(hAPP_f816688069a_bool(cOMBC_1584660393a_bool,hAPP_f1402630535a_bool(cOMBB_2115959324ol_nat(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1))) # label(fact_737_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 782 (all F all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hAPP_f375948533e_bool(image_1730813499_state(F),A_1) = hAPP_f375948533e_bool(hAPP_f1502860876e_bool(finite1171393829ol_nat(semila176469292e_bool,hAPP_f1718442376e_bool(hAPP_f1696618965e_bool(cOMBC_1048264781e_bool,hAPP_f953597140e_bool(cOMBB_1524346879ol_nat(insert1744391420_state),F)),bot_bo784226126e_bool)),bot_bo784226126e_bool),A_1))) # label(fact_738_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 783 (all F all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1) = hAPP_f2034373396a_bool(hAPP_f490436380a_bool(finite1174086764_pname(semila1114547555a_bool,hAPP_f624861966a_bool(hAPP_f843217465a_bool(cOMBC_2103945827a_bool,hAPP_f682420871a_bool(cOMBB_1481150806_pname(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1))) # label(fact_739_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 784 (all Pa all F_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1)) -> (F_1 != bot_bo332163887l_bool -> ((all X hBOOL(hAPP_f2110825313l_bool(Pa,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),bot_bo332163887l_bool)))) -> ((all X all F_2 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_2)) -> (F_2 != bot_bo332163887l_bool -> (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),F_2)) -> (hBOOL(hAPP_f2110825313l_bool(Pa,F_2)) -> hBOOL(hAPP_f2110825313l_bool(Pa,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),F_2)))))))) -> hBOOL(hAPP_f2110825313l_bool(Pa,F_1))))))) # label(fact_740_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 785 (all Pa all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) -> (F_1 != bot_bo797238721a_bool -> ((all X hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),bot_bo797238721a_bool)))) -> ((all X all F_2 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_2)) -> (F_2 != bot_bo797238721a_bool -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),F_2)) -> (hBOOL(hAPP_f1695230391l_bool(Pa,F_2)) -> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),F_2)))))))) -> hBOOL(hAPP_f1695230391l_bool(Pa,F_1))))))) # label(fact_741_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 786 (all Pa all F_1 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1)) -> (F_1 != bot_bo784226126e_bool -> ((all X hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),bot_bo784226126e_bool)))) -> ((all X all F_2 (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2)) -> (F_2 != bot_bo784226126e_bool -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),F_2)) -> (hBOOL(hAPP_f1378282496l_bool(Pa,F_2)) -> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),F_2)))))))) -> hBOOL(hAPP_f1378282496l_bool(Pa,F_1))))))) # label(fact_742_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 787 (all Pa all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) -> (F_1 != bot_bot_fun_nat_bool -> ((all X hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),bot_bot_fun_nat_bool)))) -> ((all X all F_2 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) -> (F_2 != bot_bot_fun_nat_bool -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),F_2)) -> (hBOOL(hAPP_f54304608l_bool(Pa,F_2)) -> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),F_2)))))))) -> hBOOL(hAPP_f54304608l_bool(Pa,F_1))))))) # label(fact_743_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 788 (all Pa all F_1 (is_fun_pname_bool(F_1) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) -> (F_1 != 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_1)))))))) # label(fact_744_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.07 789 (all X_2 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),X_2) = X_2)) # label(fact_745_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 790 (all X_2 all F all F_1 (is_pname(X_2) -> (hBOOL(finite89670078_pname(F,F_1)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),X_2) = X_2))) # label(fact_746_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 791 (all X_2 all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),X_2) = X_2)) # label(fact_747_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 792 (all F all G all Z_1 hAPP_f2034373396a_bool(hAPP_f490436380a_bool(finite1174086764_pname(F,G),Z_1),bot_bo844097828e_bool) = Z_1) # label(fact_748_fold__image__empty) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 793 (all X_2 all A_1 all F all F_1 (hBOOL(finite927518301a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,A_1)) = hAPP_f258822235a_bool(F_1,A_1))))) # label(fact_749_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 794 (all X_2 all A_1 all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) -> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,A_1)) = hAPP_f1693662087iple_a(F_1,A_1))))) # label(fact_750_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 795 (all X_2 all A_1 all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,A_1)) = hAPP_f22106695ol_nat(F_1,A_1))))) # label(fact_751_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 796 (all X_2 all A_1 all F all F_1 (hBOOL(finite89670078_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,A_1)) = hAPP_f1297739591_pname(F_1,A_1))))) # label(fact_752_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 797 (all N_3 all H all F all F_1 (hBOOL(finite1033474011iple_a(F,F_1)) -> ((all X all Y_8 hAPP_H905846293iple_a(H,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X),Y_8)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_H905846293iple_a(H,X)),hAPP_H905846293iple_a(H,Y_8))) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,N_3)) -> (N_3 != bot_bo797238721a_bool -> hAPP_H905846293iple_a(H,hAPP_f1693662087iple_a(F_1,N_3)) = hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(image_533441733iple_a(H),N_3))))))) # label(fact_753_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 798 (all N_3 all H all F all F_1 (hBOOL(finite927518301a_bool(F,F_1)) -> ((all X all Y_8 hAPP_f20753329a_bool(H,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X),Y_8)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f20753329a_bool(H,X)),hAPP_f20753329a_bool(H,Y_8))) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,N_3)) -> (N_3 != bot_bo332163887l_bool -> hAPP_f20753329a_bool(H,hAPP_f258822235a_bool(F_1,N_3)) = hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(image_696316513a_bool(H),N_3))))))) # label(fact_754_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 799 (all N_3 all H all F all F_1 (is_fun_pname_bool(N_3) -> (hBOOL(finite89670078_pname(F,F_1)) -> ((all X all Y_8 (is_pname(X) & is_pname(Y_8) -> hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F,X),Y_8)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H,X)),hAPP_pname_pname(H,Y_8)))) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N_3)) -> (N_3 != bot_bo844097828e_bool -> hAPP_pname_pname(H,hAPP_f1297739591_pname(F_1,N_3)) = hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(image_pname_pname(H),N_3)))))))) # label(fact_755_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 800 (all N_3 all H all F all F_1 (hBOOL(finite416071164_state(F,F_1)) -> ((all X all Y_8 hAPP_H574424047_state(H,hAPP_H574424047_state(hAPP_H280516760_state(F,X),Y_8)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_H574424047_state(H,X)),hAPP_H574424047_state(H,Y_8))) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,N_3)) -> (N_3 != bot_bo784226126e_bool -> hAPP_H574424047_state(H,hAPP_f718417177_state(F_1,N_3)) = hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(image_661047967_state(H),N_3))))))) # label(fact_756_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 801 (all N_3 all H all F all F_1 (hBOOL(finite795500164em_nat(F,F_1)) -> ((all X all Y_8 hAPP_nat_nat(H,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X),Y_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_nat_nat(H,X)),hAPP_nat_nat(H,Y_8))) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) -> (N_3 != bot_bot_fun_nat_bool -> hAPP_nat_nat(H,hAPP_f22106695ol_nat(F_1,N_3)) = hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(image_nat_nat(H),N_3))))))) # label(fact_757_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 802 (all G all A_1 all F all Z_1 all F_1 (hBOOL(big_co2022808324_pname(F,Z_1,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hAPP_f2034373396a_bool(hAPP_f1234324863a_bool(F_1,G),A_1) = hAPP_f2034373396a_bool(hAPP_f490436380a_bool(finite1174086764_pname(F,G),Z_1),A_1)) & (-hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hAPP_f2034373396a_bool(hAPP_f1234324863a_bool(F_1,G),A_1) = Z_1))) # label(fact_758_comm__monoid__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 803 (all X_2 all A_1 all F all F_1 (hBOOL(finite2103247258a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> (A_1 != bot_bo332163887l_bool -> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,A_1))))))) # label(fact_759_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 804 (all X_2 all A_1 all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) -> (A_1 != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,A_1))))))) # label(fact_760_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 805 (all X_2 all A_1 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> (-hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1)) -> (A_1 != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),hAPP_f718417177_state(F_1,A_1))))))) # label(fact_761_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 806 (all X_2 all A_1 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> (A_1 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,A_1))))))) # label(fact_762_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 807 (all X_2 all A_1 all F all F_1 (is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> (A_1 != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,A_1)))))))) # label(fact_763_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 808 (all X_2 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) = X_2)) # label(fact_764_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 809 (all X_2 all F all F_1 (hBOOL(finite2103247258a_bool(F,F_1)) -> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) = X_2)) # label(fact_765_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 810 (all X_2 all F all F_1 (is_pname(X_2) -> (hBOOL(finite1282449217_pname(F,F_1)) -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = X_2))) # label(fact_766_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 811 (all X_2 all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) = X_2)) # label(fact_767_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 812 (all X_2 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) = X_2)) # label(fact_768_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 813 (all A_1 all F all F_1 (hBOOL(finite2103247258a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (A_1 != bot_bo332163887l_bool -> ((all X all Y_8 hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X),Y_8)),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_8),bot_bo332163887l_bool))))) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,hAPP_f258822235a_bool(F_1,A_1)),A_1))))))) # label(fact_769_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 814 (all A_1 all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (A_1 != bot_bo797238721a_bool -> ((all X all Y_8 hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X),Y_8)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_8),bot_bo797238721a_bool))))) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_f1693662087iple_a(F_1,A_1)),A_1))))))) # label(fact_770_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 815 (all A_1 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> (A_1 != bot_bo784226126e_bool -> ((all X all Y_8 hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_H574424047_state(hAPP_H280516760_state(F,X),Y_8)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_8),bot_bo784226126e_bool))))) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_f718417177_state(F_1,A_1)),A_1))))))) # label(fact_771_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 816 (all A_1 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (A_1 != bot_bot_fun_nat_bool -> ((all X all Y_8 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X),Y_8)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_8),bot_bot_fun_nat_bool))))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A_1)),A_1))))))) # label(fact_772_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 817 (all A_1 all F all F_1 (is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> ((all X all Y_8 (is_pname(X) & is_pname(Y_8) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X),Y_8)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_8),bot_bo844097828e_bool)))))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(F_1,A_1)),A_1)))))))) # label(fact_773_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 818 (all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> -(all B_6 (A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_6) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_6)))))) # label(fact_774_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 819 (all X_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> -(all B_6 (A_1 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),B_6) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),B_6)))))) # label(fact_775_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 820 (all X_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) -> -(all B_6 (A_1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),B_6) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B_6)))))) # label(fact_776_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 821 (all X_2 all A_1 (hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1)) -> -(all B_6 (A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_6) -> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_6)))))) # label(fact_777_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 822 (all X_2 all A_1 (is_fun_pname_bool(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) -> -(all B_6 (is_fun_pname_bool(B_6) -> (A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_6) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_6)))))))) # label(fact_778_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 823 (all A_1 ((all Y_8 -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_8),A_1))) -> A_1 = bot_bot_fun_nat_bool)) # label(fact_779_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 824 (all A_1 ((all Y_8 -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,Y_8),A_1))) -> A_1 = bot_bo332163887l_bool)) # label(fact_780_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 825 (all A_1 ((all Y_8 -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Y_8),A_1))) -> A_1 = bot_bo797238721a_bool)) # label(fact_781_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 826 (all A_1 ((all Y_8 -hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_8),A_1))) -> A_1 = bot_bo784226126e_bool)) # label(fact_782_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 827 (all A_1 (is_fun_pname_bool(A_1) -> ((all Y_8 (is_pname(Y_8) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_8),A_1)))) -> A_1 = bot_bo844097828e_bool))) # label(fact_783_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 828 (all B_2 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (A_1 != bot_bo1701429464l_bool -> (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_2)) -> (B_2 != bot_bo1701429464l_bool -> hAPP_f582319405t_bool(big_la1704749377t_bool,hAPP_f1246832597l_bool(hAPP_f540020688l_bool(semila653644470l_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f582319405t_bool(big_la1704749377t_bool,A_1)),hAPP_f582319405t_bool(big_la1704749377t_bool,B_2))))))) # label(fact_784_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 829 (all B_2 all A_1 (hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,A_1)) -> (A_1 != bot_bo156414585l_bool -> (hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,B_2)) -> (B_2 != bot_bo156414585l_bool -> hAPP_f2060061063l_bool(big_la914314008l_bool,hAPP_f1841260065l_bool(hAPP_f1120848625l_bool(semila1803437851l_bool,A_1),B_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f2060061063l_bool(big_la914314008l_bool,A_1)),hAPP_f2060061063l_bool(big_la914314008l_bool,B_2))))))) # label(fact_785_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 830 (all B_2 all A_1 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_1)) -> (A_1 != bot_bo942947096l_bool -> (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B_2)) -> (B_2 != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(big_la1369269047e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f1216288071e_bool(big_la1369269047e_bool,A_1)),hAPP_f1216288071e_bool(big_la1369269047e_bool,B_2))))))) # label(fact_786_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 831 (all B_2 all A_1 (is_fun1661590463l_bool(B_2) & is_fun1661590463l_bool(A_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_2)) -> (B_2 != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(big_la841148155e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f674760225e_bool(big_la841148155e_bool,A_1)),hAPP_f674760225e_bool(big_la841148155e_bool,B_2)))))))) # label(fact_787_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 832 (all B_2 all A_1 (is_fun_bool_bool(B_2) & is_fun_bool_bool(A_1) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A_1)) -> (A_1 != bot_bo806936373l_bool -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_2)) -> (B_2 != bot_bo806936373l_bool -> (hBOOL(hAPP_f387058535l_bool(big_la1480321694n_bool,hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A_1),B_2))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_f387058535l_bool(big_la1480321694n_bool,A_1)),hAPP_f387058535l_bool(big_la1480321694n_bool,B_2)))))))))) # label(fact_788_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 833 (all B_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (A_1 != bot_bo332163887l_bool -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2)) -> (B_2 != bot_bo332163887l_bool -> hAPP_f258822235a_bool(big_la1609103640a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f258822235a_bool(big_la1609103640a_bool,A_1)),hAPP_f258822235a_bool(big_la1609103640a_bool,B_2))))))) # label(fact_789_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 834 (all B_2 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (A_1 != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2)) -> (B_2 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_f22106695ol_nat(big_la43341705in_nat,A_1)),hAPP_f22106695ol_nat(big_la43341705in_nat,B_2))))))) # label(fact_790_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 835 (all X_2 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (-hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A_1)) -> (A_1 != bot_bo1701429464l_bool -> hAPP_f582319405t_bool(big_la1704749377t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_2),A_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f582319405t_bool(big_la1704749377t_bool,A_1)))))) # label(fact_791_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 836 (all X_2 all A_1 (hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,A_1)) -> (-hBOOL(hAPP_f670355311l_bool(hAPP_f21712077l_bool(member38210668l_bool,X_2),A_1)) -> (A_1 != bot_bo156414585l_bool -> hAPP_f2060061063l_bool(big_la914314008l_bool,hAPP_f1841260065l_bool(hAPP_f1499754623l_bool(insert2046103699l_bool,X_2),A_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f2060061063l_bool(big_la914314008l_bool,A_1)))))) # label(fact_792_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 837 (all X_2 all A_1 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_1)) -> (-hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A_1)) -> (A_1 != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(big_la1369269047e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),A_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f1216288071e_bool(big_la1369269047e_bool,A_1)))))) # label(fact_793_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 838 (all X_2 all A_1 (is_fun1661590463l_bool(A_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (-hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1)) -> (A_1 != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(big_la841148155e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f674760225e_bool(big_la841148155e_bool,A_1))))))) # label(fact_794_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 839 (all X_2 all A_1 (is_fun_bool_bool(A_1) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A_1)) -> (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) -> (A_1 != bot_bo806936373l_bool -> (hBOOL(hAPP_f387058535l_bool(big_la1480321694n_bool,hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_f387058535l_bool(big_la1480321694n_bool,A_1))))))))) # label(fact_795_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 840 (all X_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) -> (A_1 != bot_bo332163887l_bool -> hAPP_f258822235a_bool(big_la1609103640a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f258822235a_bool(big_la1609103640a_bool,A_1)))))) # label(fact_796_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 841 (all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) -> (A_1 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_2),hAPP_f22106695ol_nat(big_la43341705in_nat,A_1)))))) # label(fact_797_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 842 (all X_2 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (A_1 != bot_bo1701429464l_bool -> hAPP_f582319405t_bool(big_la1704749377t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_2),A_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f582319405t_bool(big_la1704749377t_bool,A_1))))) # label(fact_798_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 843 (all X_2 all A_1 (hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,A_1)) -> (A_1 != bot_bo156414585l_bool -> hAPP_f2060061063l_bool(big_la914314008l_bool,hAPP_f1841260065l_bool(hAPP_f1499754623l_bool(insert2046103699l_bool,X_2),A_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f2060061063l_bool(big_la914314008l_bool,A_1))))) # label(fact_799_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 844 (all X_2 all A_1 (hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_1)) -> (A_1 != bot_bo942947096l_bool -> hAPP_f1216288071e_bool(big_la1369269047e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),A_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f1216288071e_bool(big_la1369269047e_bool,A_1))))) # label(fact_800_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 845 (all X_2 all A_1 (is_fun1661590463l_bool(A_1) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (A_1 != bot_bo1649642514l_bool -> hAPP_f674760225e_bool(big_la841148155e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f674760225e_bool(big_la841148155e_bool,A_1)))))) # label(fact_801_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 846 (all X_2 all A_1 (is_fun_bool_bool(A_1) -> (hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A_1)) -> (A_1 != bot_bo806936373l_bool -> (hBOOL(hAPP_f387058535l_bool(big_la1480321694n_bool,hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A_1))) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_f387058535l_bool(big_la1480321694n_bool,A_1)))))))) # label(fact_802_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 847 (all X_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (A_1 != bot_bo332163887l_bool -> hAPP_f258822235a_bool(big_la1609103640a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f258822235a_bool(big_la1609103640a_bool,A_1))))) # label(fact_803_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 848 (all X_2 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (A_1 != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_2),hAPP_f22106695ol_nat(big_la43341705in_nat,A_1))))) # label(fact_804_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 849 (all B_2 all A_1 all F all F_1 (hBOOL(finite2103247258a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (A_1 != bot_bo332163887l_bool -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2)) -> (B_2 != bot_bo332163887l_bool -> (hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2) = bot_bo332163887l_bool -> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,A_1)),hAPP_f258822235a_bool(F_1,B_2))))))))) # label(fact_805_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 850 (all B_2 all A_1 all F all F_1 (is_fun_pname_bool(B_2) & is_fun_pname_bool(A_1) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (A_1 != bot_bo844097828e_bool -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_2)) -> (B_2 != bot_bo844097828e_bool -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,A_1)),hAPP_f1297739591_pname(F_1,B_2)))))))))) # label(fact_806_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 851 (all B_2 all A_1 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> (A_1 != bot_bo784226126e_bool -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_2)) -> (B_2 != bot_bo784226126e_bool -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2) = bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,A_1)),hAPP_f718417177_state(F_1,B_2))))))))) # label(fact_807_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 852 (all B_2 all A_1 all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (A_1 != bot_bo797238721a_bool -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B_2)) -> (B_2 != bot_bo797238721a_bool -> (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) = bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,A_1)),hAPP_f1693662087iple_a(F_1,B_2))))))))) # label(fact_808_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 853 (all B_2 all A_1 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (A_1 != bot_bot_fun_nat_bool -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2)) -> (B_2 != bot_bot_fun_nat_bool -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,A_1)),hAPP_f22106695ol_nat(F_1,B_2))))))))) # label(fact_809_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 854 (all B_2 all A_1 all F all F_1 (hBOOL(finite2103247258a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2)) -> (hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2) != bot_bo332163887l_bool -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))),hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2))) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,A_1)),hAPP_f258822235a_bool(F_1,B_2))))))) # label(fact_810_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 855 (all B_2 all A_1 all F all F_1 (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_2)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) != bot_bo844097828e_bool -> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,A_1)),hAPP_f1297739591_pname(F_1,B_2))))))) # label(fact_811_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 856 (all B_2 all A_1 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_2)) -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2) != bot_bo784226126e_bool -> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2))) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,A_1)),hAPP_f718417177_state(F_1,B_2))))))) # label(fact_812_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 857 (all B_2 all A_1 all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B_2)) -> (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) != bot_bo797238721a_bool -> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))),hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2))) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,A_1)),hAPP_f1693662087iple_a(F_1,B_2))))))) # label(fact_813_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 858 (all B_2 all A_1 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) != bot_bot_fun_nat_bool -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,A_1)),hAPP_f22106695ol_nat(F_1,B_2))))))) # label(fact_814_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 859 (all X_2 all A_1 all F all F_1 (hBOOL(finite2103247258a_bool(F,F_1)) -> (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) = bot_bo332163887l_bool -> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = X_2) & (hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) != bot_bo332163887l_bool -> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)))))))) # label(fact_815_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 860 (all X_2 all A_1 all F all F_1 (is_pname(X_2) -> (hBOOL(finite1282449217_pname(F,F_1)) -> (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = X_2) & (hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) != bot_bo844097828e_bool -> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool))))))))) # label(fact_816_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 861 (all X_2 all A_1 all F all F_1 (hBOOL(finite1753440478iple_a(F,F_1)) -> (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) = bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = X_2) & (hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) != bot_bo797238721a_bool -> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)))))))) # label(fact_817_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 862 (all X_2 all A_1 all F all F_1 (hBOOL(finite683959609_state(F,F_1)) -> (hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) -> (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) = bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = X_2) & (hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) != bot_bo784226126e_bool -> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)))))))) # label(fact_818_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 863 (all X_2 all A_1 all F all F_1 (hBOOL(finite988810631ne_nat(F,F_1)) -> (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = X_2) & (hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool -> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))))))) # label(fact_819_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 864 (all B_2 all A_1 all X_2 (hBOOL(hAPP_nat_bool(A_1,X_2)) -> (hBOOL(hAPP_nat_bool(B_2,X_2)) -> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2),X_2))))) # label(fact_820_inf1I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 865 (all B_2 all A_1 all X_2 (hBOOL(hAPP_H1037229737a_bool(A_1,X_2)) -> (hBOOL(hAPP_H1037229737a_bool(B_2,X_2)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2),X_2))))) # label(fact_821_inf1I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 866 (all B_2 all A_1 all X_2 (hBOOL(hAPP_pname_bool(A_1,X_2)) -> (hBOOL(hAPP_pname_bool(B_2,X_2)) -> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2),X_2))))) # label(fact_822_inf1I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 867 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)))))) # label(fact_823_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 868 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) -> (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2)))))) # label(fact_824_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 869 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) -> (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)))))) # label(fact_825_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 870 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)))))) # label(fact_826_IntI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 871 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2))))) # label(fact_827_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 872 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2))) -> -(hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) -> -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2))))) # label(fact_828_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 873 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2))) -> -(hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) -> -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2))))) # label(fact_829_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 874 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2))))) # label(fact_830_IntE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 875 (all A_1 all B_2 all X_2 (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2),X_2)) -> -(hBOOL(hAPP_nat_bool(A_1,X_2)) -> -hBOOL(hAPP_nat_bool(B_2,X_2))))) # label(fact_831_inf1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 876 (all A_1 all B_2 all X_2 (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2),X_2)) -> -(hBOOL(hAPP_H1037229737a_bool(A_1,X_2)) -> -hBOOL(hAPP_H1037229737a_bool(B_2,X_2))))) # label(fact_832_inf1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 877 (all A_1 all B_2 all X_2 (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2),X_2)) -> -(hBOOL(hAPP_pname_bool(A_1,X_2)) -> -hBOOL(hAPP_pname_bool(B_2,X_2))))) # label(fact_833_inf1E) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 878 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)))))) # label(fact_834_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 879 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) -> (-hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)))))) # label(fact_835_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 880 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) -> (-hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)))))) # label(fact_836_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 881 (all B_2 all C_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)))))) # label(fact_837_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 882 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2))))) # label(fact_838_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 883 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2))) -> -(hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) -> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2))))) # label(fact_839_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 884 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2))) -> -(hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) -> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2))))) # label(fact_840_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 885 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2))) -> -(hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2))))) # label(fact_841_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 886 (all Ga all F_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1)) | hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,Ga)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,F_1),Ga))))) # label(fact_842_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 887 (all Ga all F_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1)) | hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,Ga)) -> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,F_1),Ga))))) # label(fact_843_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 888 (all Ga all F_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,F_1),Ga))))) # label(fact_844_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 889 (all Ga all F_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,F_1),Ga))))) # label(fact_845_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 890 (all B_2 all A_1 (hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) -> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2))))) # label(fact_846_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 891 (all B_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2))))) # label(fact_847_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 892 (all B_2 all A_1 (hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) -> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2))))) # label(fact_848_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 893 (all B_2 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2))))) # label(fact_849_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 894 (all A_2 all A_1 (hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) -> (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)) -> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),hAPP_f258822235a_bool(big_la1609103640a_bool,A_1)) = A_2))) # label(fact_850_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 895 (all A_2 all A_1 (hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) -> (hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),A_1)) -> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),hAPP_f582319405t_bool(big_la1704749377t_bool,A_1)) = A_2))) # label(fact_851_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 896 (all A_2 all A_1 (is_fun_pname_bool(A_2) -> (hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) -> (hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_1)) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),hAPP_f674760225e_bool(big_la841148155e_bool,A_1)) = A_2)))) # label(fact_852_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 897 (all A_2 all A_1 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_2),hAPP_f22106695ol_nat(big_la43341705in_nat,A_1)) = A_2))) # label(fact_853_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 898 (all A_1 all B_2 all C_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),C_1))) # label(fact_854_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 899 (all A_1 all B_2 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),C_1))) # label(fact_855_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 900 (all A_1 all B_2 all C_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,B_2),C_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),C_1))) # label(fact_856_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 901 (all A_1 all B_2 all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B_2),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),B_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),C_1))) # label(fact_857_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 902 (all A_1 all B_2 all C_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),C_1))) # label(fact_858_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 903 (all A_1 all B_2 all C_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),C_1))) # label(fact_859_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 904 (all A_1 all B_2 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),C_1))) # label(fact_860_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 905 (all A_1 all B_2 all C_1 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),C_1))) # label(fact_861_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 906 (all A_1 all B_2 all C_1 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),B_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),C_1))) # label(fact_862_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 907 (all A_1 all B_2 all C_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),C_1))) # label(fact_863_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 908 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)) = A_1) # label(fact_864_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 909 (all A_1 all B_2 (is_fun_pname_bool(A_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)) = A_1)) # label(fact_865_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 910 (all A_1 all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2)) = A_1) # label(fact_866_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 911 (all A_1 all B_2 hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),B_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2)) = A_1) # label(fact_867_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 912 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)) = A_1) # label(fact_868_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 913 (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(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(collect_pname,Pa)),hAPP_f759274231e_bool(collect_pname,Qa))) # label(fact_869_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 914 (all Pa all Qa hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),Pa)),Qa)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,hAPP_f20753329a_bool(collec351493750iple_a,Pa)),hAPP_f20753329a_bool(collec351493750iple_a,Qa))) # label(fact_870_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 915 (all Pa all Qa hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),Qa)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(collect_nat,Pa)),hAPP_f800510211t_bool(collect_nat,Qa))) # label(fact_871_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 916 (all X_2 all A_1 all Pa (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),hAPP_f396832789l_bool(collec999179778a_bool,Pa)))) <-> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1)) & hBOOL(hAPP_f1695230391l_bool(Pa,X_2)))) # label(fact_872_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 917 (all X_2 all A_1 all Pa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),hAPP_f800510211t_bool(collect_nat,Pa)))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1)) & hBOOL(hAPP_nat_bool(Pa,X_2)))) # label(fact_873_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 918 (all X_2 all A_1 all Pa (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),hAPP_f20753329a_bool(collec351493750iple_a,Pa)))) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1)) & hBOOL(hAPP_H1037229737a_bool(Pa,X_2)))) # label(fact_874_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 919 (all X_2 all A_1 all Pa (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,Pa)))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) & hBOOL(hAPP_pname_bool(Pa,X_2)))) # label(fact_875_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 920 (all R_1 all S_2 all X (hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),R_1)),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),S_2)),X)) <-> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,R_1),S_2))))) # label(fact_876_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 921 (all R_1 all S_2 all X (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_2)),X)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,R_1),S_2))))) # label(fact_877_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 922 (all R_1 all S_2 all X (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),R_1)),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_2)),X)) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,R_1),S_2))))) # label(fact_878_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 923 (all R_1 all S_2 all X (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S_2)),X)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,R_1),S_2))))) # label(fact_879_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 924 (all A_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),A_1) = A_1) # label(fact_880_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 925 (all A_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),A_1) = A_1) # label(fact_881_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 926 (all A_1 (is_fun_pname_bool(A_1) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),A_1) = A_1)) # label(fact_882_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 927 (all A_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),A_2) = A_2) # label(fact_883_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 928 (all A_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),A_2) = A_2) # label(fact_884_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 929 (all A_6 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_6),A_6) = A_6) # label(fact_885_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 930 (all A_2 (is_fun_pname_bool(A_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),A_2) = A_2)) # label(fact_886_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 931 (all X_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),X_2) = X_2) # label(fact_887_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 932 (all X_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),X_2) = X_2) # label(fact_888_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 933 (all X_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_9),X_9) = X_9) # label(fact_889_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 934 (all X_2 (is_fun_pname_bool(X_2) -> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),X_2) = X_2)) # label(fact_890_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 935 (all A_1 all B_2 all X (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H1037229737a_bool(A_1,X)),hAPP_H1037229737a_bool(B_2,X))))) # label(fact_891_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 936 (all A_1 all B_2 all X (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_pname_bool(A_1,X)),hAPP_pname_bool(B_2,X))))) # label(fact_892_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 937 (all A_1 all B_2 all X (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A_1,X)),hAPP_nat_bool(B_2,X))))) # label(fact_893_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 938 (all F all G all X (hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_nat_bool(F,X)),hAPP_nat_bool(G,X))))) # label(fact_894_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 939 (all F all G all X (hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_H1037229737a_bool(F,X)),hAPP_H1037229737a_bool(G,X))))) # label(fact_895_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 940 (all F all G all X (hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,F),G),X)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_pname_bool(F,X)),hAPP_pname_bool(G,X))))) # label(fact_896_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 941 (all A_1 all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_f396832789l_bool(cOMBB_193631803a_bool(fNot),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2))))) # label(fact_897_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 942 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2))))) # label(fact_898_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 943 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_f20753329a_bool(cOMBB_1882975613iple_a(fNot),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2))))) # label(fact_899_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 944 (all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2))))) # label(fact_900_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 945 (all A_1 all B_2 hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2)))) # label(fact_901_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 946 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2)))) # label(fact_902_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 947 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2)))) # label(fact_903_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 948 (all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2)))) # label(fact_904_Int__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 949 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),A_1)) # label(fact_905_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.08 950 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),A_1)) # label(fact_906_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 951 (all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),A_1)) # label(fact_907_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 952 (all A_2 all B_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),B_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_1),A_2)) # label(fact_908_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 953 (all A_2 all B_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),B_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_1),A_2)) # label(fact_909_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 954 (all A_5 all B_5 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_5),B_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,B_5),A_5)) # label(fact_910_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 955 (all A_2 all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),A_2)) # label(fact_911_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 956 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),X_2)) # label(fact_912_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 957 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),X_2)) # label(fact_913_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 958 (all X_8 all Y_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_8),Y_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_7),X_8)) # label(fact_914_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 959 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),X_2)) # label(fact_915_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 960 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),X_2)) # label(fact_916_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 961 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),X_2)) # label(fact_917_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 962 (all X_7 all Y_6 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_7),Y_6) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_6),X_7)) # label(fact_918_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 963 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),X_2)) # label(fact_919_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 964 (all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)) # label(fact_920_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 965 (all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)) # label(fact_921_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 966 (all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)) # label(fact_922_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 967 (all A_2 all B_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),B_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),B_1)) # label(fact_923_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 968 (all A_2 all B_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),B_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),B_1)) # label(fact_924_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 969 (all A_4 all B_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_4),B_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_4),B_4)) # label(fact_925_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 970 (all A_2 all B_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),B_1)) # label(fact_926_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 971 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1)) # label(fact_927_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 972 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1)) # label(fact_928_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 973 (all X_6 all Y_5 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_6),Y_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_6),Y_5)) # label(fact_929_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 974 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1)) # label(fact_930_inf__sup__aci_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 975 (all X_2 all Y_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1)) # label(fact_931_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 976 (all X_2 all Y_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1)) # label(fact_932_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 977 (all X_5 all Y_4 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_5),Y_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_5),Y_4)) # label(fact_933_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 978 (all X_2 all Y_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1)) # label(fact_934_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 979 (all A_1 all B_2 all C_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),C_1))) # label(fact_935_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 980 (all A_1 all B_2 all C_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),C_1))) # label(fact_936_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 981 (all A_1 all B_2 all C_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),C_1))) # label(fact_937_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 982 (all B_1 all A_2 all C_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),C_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_1),C_2))) # label(fact_938_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 983 (all B_1 all A_2 all C_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),C_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_1),C_2))) # label(fact_939_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 984 (all B_3 all A_3 all C_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,B_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_3),C_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,B_3),C_3))) # label(fact_940_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 985 (all B_1 all A_2 all C_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),C_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),C_2))) # label(fact_941_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 986 (all X_2 all Y_1 all Z_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Z_1))) # label(fact_942_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 987 (all X_2 all Y_1 all Z_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Z_1))) # label(fact_943_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 988 (all X_4 all Y_3 all Z_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_3),Z_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_4),Z_3))) # label(fact_944_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 989 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Z_1))) # label(fact_945_inf__sup__aci_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 990 (all X_2 all Y_1 all Z_1 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Z_1))) # label(fact_946_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 991 (all X_2 all Y_1 all Z_1 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Z_1))) # label(fact_947_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 992 (all X_3 all Y_2 all Z_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_2),Z_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_3),Z_2))) # label(fact_948_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 993 (all X_2 all Y_1 all Z_1 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Z_1))) # label(fact_949_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 994 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2))) <-> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) & -hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)))) # label(fact_950_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 995 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)))) # label(fact_951_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 996 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2))) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) & -hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)))) # label(fact_952_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 997 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) & -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)))) # label(fact_953_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 998 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2))) <-> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) & hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)))) # label(fact_954_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 999 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)))) # label(fact_955_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1000 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2))) <-> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) & hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)))) # label(fact_956_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1001 (all C_2 all A_1 all B_2 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)))) # label(fact_957_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1002 (all C_1 all A_1 all B_2 hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,C_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,C_1),A_1)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,C_1),B_2))) # label(fact_958_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1003 (all C_1 all A_1 all B_2 hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),B_2))) # label(fact_959_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1004 (all C_1 all A_1 all B_2 hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,C_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,C_1),A_1)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,C_1),B_2))) # label(fact_960_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1005 (all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N_2) = zero_zero_nat) # label(fact_961_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1006 (all M_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),zero_zero_nat) = M_2) # label(fact_962_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1007 (all M_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),M_2) = zero_zero_nat) # label(fact_963_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1008 (all M_2 all N_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) = zero_zero_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),M_2) = zero_zero_nat -> M_2 = N_2))) # label(fact_964_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1009 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) # label(fact_965_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1010 (all M_2 all N_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_2)),N_2)),hAPP_nat_nat(suc,K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),K_2)) # label(fact_966_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1011 (all I all J_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),K_2)),J_1)) # label(fact_967_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1012 (all I_1 all Pa all K_1 (hBOOL(hAPP_nat_bool(Pa,K_1)) -> ((all N (hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))) -> hBOOL(hAPP_nat_bool(Pa,N)))) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_1),I_1)))))) # label(fact_968_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1013 (all M all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_1))) # label(fact_969_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1014 (all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N_2)),one_one_nat) = N_2) # label(fact_971_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1015 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),one_one_nat)),N_2)) # label(fact_972_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1016 (all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_2) = N_2) # label(fact_973_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1017 (all M_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2) # label(fact_974_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1018 (all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1) = zero_zero_nat <-> M = zero_zero_nat & N_1 = zero_zero_nat)) # label(fact_975_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1019 (all M_2 all N_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = M_2 -> N_2 = zero_zero_nat)) # label(fact_976_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1020 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2))) # label(fact_977_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1021 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2))) # label(fact_978_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1022 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_2))) # label(fact_979_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1023 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)) # label(fact_980_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1024 (all X_1 all Y all Z hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),Z))) # label(fact_981_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1025 (all M_2 all N_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),K_2))) # label(fact_982_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1026 (all K_1 all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1) <-> M = N_1)) # label(fact_983_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1027 (all M all K_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1) <-> M = N_1)) # label(fact_984_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1028 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)),N_2) = M_2) # label(fact_985_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1029 (all N_2 all M_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)),N_2) = M_2) # label(fact_986_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1030 (all I all J_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) # label(fact_987_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1031 (all K_2 all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) # label(fact_988_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1032 (all M_2 all K_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) # label(fact_989_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1033 (all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N_1 = zero_zero_nat | M = zero_zero_nat & N_1 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_990_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1034 (all M all N_1 (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N_1 = zero_zero_nat | M = zero_zero_nat & N_1 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_991_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1035 (all N_2 all M_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)) = zero_zero_nat) # label(fact_992_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1036 (all N_2 hAPP_nat_nat(suc,N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),one_one_nat)) # label(fact_993_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1037 (all N_2 hAPP_nat_nat(suc,N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_2)) # label(fact_994_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1038 (all N_2 all M_2 ((M_2 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = N_2) & (M_2 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),one_one_nat)),N_2))))) # label(fact_995_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1039 (all Com1_2 all Com2_2 com_size(semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1_2)),com_size(Com2_2))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_996_com_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1040 (all Fun_1 all Com_1 com_size(while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_997_com_Osize_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1041 (all Pname_1 com_size(hAPP_pname_com(body,Pname_1)) = zero_zero_nat) # label(fact_998_com_Osize_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1042 (all Com1_2 all Com2_2 hAPP_com_nat(size_size_com,semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_com_nat(size_size_com,Com1_2)),hAPP_com_nat(size_size_com,Com2_2))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1000_com_Osize_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1043 (all Fun_1 all Com_1 hAPP_com_nat(size_size_com,while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_com_nat(size_size_com,Com_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1001_com_Osize_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1044 (all K_2 all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_2))) # label(fact_1002_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1045 (all M_2 all N_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),K_2))) # label(fact_1003_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1046 (all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1) = one_one_nat <-> M = one_one_nat & N_1 = one_one_nat)) # label(fact_1004_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1047 (all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),one_one_nat) = N_2) # label(fact_1005_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1048 (all M all N_1 (one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1) <-> M = one_one_nat & N_1 = one_one_nat)) # label(fact_1006_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1049 (all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N_2) = N_2) # label(fact_1007_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1050 (all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N_2) = zero_zero_nat) # label(fact_1008_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1051 (all M_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),zero_zero_nat) = zero_zero_nat) # label(fact_1009_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1052 (all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1) = zero_zero_nat <-> M = zero_zero_nat | N_1 = zero_zero_nat)) # label(fact_1010_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1053 (all K_1 all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1) <-> M = N_1 | K_1 = zero_zero_nat)) # label(fact_1011_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1054 (all M all K_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1) <-> M = N_1 | K_1 = zero_zero_nat)) # label(fact_1012_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1055 (all K_1 all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N_1) <-> M = N_1)) # label(fact_1013_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1056 (all M_2 all N_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),K_2))) # label(fact_1014_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1057 (all K_2 all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_2))) # label(fact_1015_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1058 (all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1) = hAPP_nat_nat(suc,zero_zero_nat) <-> M = hAPP_nat_nat(suc,zero_zero_nat) & N_1 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1016_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1059 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2))) # label(fact_1017_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1060 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2))) # label(fact_1018_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1061 (all M_2 all N_2 (M_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2) -> N_2 = one_one_nat | M_2 = zero_zero_nat)) # label(fact_1019_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1062 (all Pname_1 hAPP_com_nat(size_size_com,hAPP_pname_com(body,Pname_1)) = zero_zero_nat) # label(fact_1020_com_Osize_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1063 (all N_2 all M_2 ((M_2 = zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2) = zero_zero_nat) & (M_2 != zero_zero_nat -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),one_one_nat)),N_2))))) # label(fact_1022_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1064 (all M_2 all N_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),M_2)) # label(fact_1023_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1065 (all M_2 all N_2 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),K_2))) # label(fact_1024_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1066 (all I all U_1 all J_1 all K_2 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U_1)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),U_1)),K_2)) # label(fact_1025_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1067 (all K_1 all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1) <-> K_1 = zero_zero_nat | M = N_1)) # label(fact_1026_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1068 (all Fun_1 all Com1_1 all Com2_1 hAPP_com_nat(size_size_com,cond(Fun_1,Com1_1,Com2_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_com_nat(size_size_com,Com1_1)),hAPP_com_nat(size_size_com,Com2_1))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1027_com_Osize_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1069 (all Fun_1 all Com1_1 all Com2_1 com_size(cond(Fun_1,Com1_1,Com2_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1_1)),com_size(Com2_1))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_1028_com_Osize_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1070 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K_1))))) # label(fact_1029_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1071 (all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_2))) # label(fact_1030_le0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1072 (all B_1 all C1 all C2 all S_1 all N_1 all T_1 (hBOOL(hAPP_state_bool(evaln(cond(B_1,C1,C2),S_1,N_1),T_1)) -> ((hBOOL(hAPP_state_bool(B_1,S_1)) -> -hBOOL(hAPP_state_bool(evaln(C1,S_1,N_1),T_1))) -> -(-hBOOL(hAPP_state_bool(B_1,S_1)) -> -hBOOL(hAPP_state_bool(evaln(C2,S_1,N_1),T_1)))))) # label(fact_1031_evaln__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1073 (all C1 all C0 all N_1 all S1 all B_1 all S_1 (hBOOL(hAPP_state_bool(B_1,S_1)) -> (hBOOL(hAPP_state_bool(evaln(C0,S_1,N_1),S1)) -> hBOOL(hAPP_state_bool(evaln(cond(B_1,C0,C1),S_1,N_1),S1))))) # label(fact_1032_evaln_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1074 (all C0 all C1 all N_1 all S1 all B_1 all S_1 (-hBOOL(hAPP_state_bool(B_1,S_1)) -> (hBOOL(hAPP_state_bool(evaln(C1,S_1,N_1),S1)) -> hBOOL(hAPP_state_bool(evaln(cond(B_1,C0,C1),S_1,N_1),S1))))) # label(fact_1033_evaln_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1075 (all C0 all C1 all S1 all B_1 all S_1 (-hBOOL(hAPP_state_bool(B_1,S_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_1),S1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B_1,C0,C1)),S_1),S1))))) # label(fact_1034_evalc_OIfFalse) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1076 (all C1 all C0 all S1 all B_1 all S_1 (hBOOL(hAPP_state_bool(B_1,S_1)) -> (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S_1),S1)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B_1,C0,C1)),S_1),S1))))) # label(fact_1035_evalc_OIfTrue) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1077 (all B_1 all C1 all C2 all S_1 all T_1 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B_1,C1,C2)),S_1),T_1)) -> ((hBOOL(hAPP_state_bool(B_1,S_1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_1),T_1))) -> -(-hBOOL(hAPP_state_bool(B_1,S_1)) -> -hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S_1),T_1)))))) # label(fact_1036_evalc__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1078 (all Pname all Fun_1 all Com1_1 all Com2_1 hAPP_pname_com(body,Pname) != cond(Fun_1,Com1_1,Com2_1)) # label(fact_1037_com_Osimps_I55_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1079 (all Fun_1 all Com1_1 all Com2_1 all Pname cond(Fun_1,Com1_1,Com2_1) != hAPP_pname_com(body,Pname)) # label(fact_1038_com_Osimps_I54_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1080 (all Fun_1 all Com1_1 all Com2_1 all Fun all Com1 all Com2 (cond(Fun_1,Com1_1,Com2_1) = cond(Fun,Com1,Com2) <-> Fun_1 = Fun & Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_1039_com_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1081 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) -> M_2 = N_2))) # label(fact_1040_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1082 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2))))) # label(fact_1041_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1083 (all M_2 all N_2 (M_2 = N_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))) # label(fact_1042_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1084 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)))) # label(fact_1043_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1085 (all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),N_2))) # label(fact_1044_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1086 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))) # label(fact_1045_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1087 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_2))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> M_2 = hAPP_nat_nat(suc,N_2)))) # label(fact_1046_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1088 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_2))))) # label(fact_1047_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1089 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),hAPP_nat_nat(suc,M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)))) # label(fact_1048_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1090 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) | M = hAPP_nat_nat(suc,N_1))) # label(fact_1049_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1091 (all M all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M)))) # label(fact_1050_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1092 (all N_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),N_2))) # label(fact_1051_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1093 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),zero_zero_nat)) <-> N_1 = zero_zero_nat)) # label(fact_1052_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1094 (all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_2))) # label(fact_1053_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1095 (all M_2 all C all S all N_2 all T (hBOOL(hAPP_state_bool(evaln(C,S,N_2),T)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) -> hBOOL(hAPP_state_bool(evaln(C,S,M_2),T))))) # label(fact_1054_evaln__nonstrict) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1096 (all M_2 all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),M_2))) # label(fact_1055_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1097 (all L all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),N_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),M_2))))) # label(fact_1056_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1098 (all L all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),L)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),L))))) # label(fact_1057_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1099 (all I all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),I)) = I)) # label(fact_1058_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1100 (all N_1 all K_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1) <-> M = N_1)))) # label(fact_1059_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1101 (all N_2 all K_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)))) # label(fact_1060_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1102 (all N_1 all K_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))))) # label(fact_1061_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1103 (all M_2 all K_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N_2)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2))))) # label(fact_1062_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1104 (all M_2 all K_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))) # label(fact_1063_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1105 (all M_2 all K_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2)))) # label(fact_1064_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1106 (all K_2 all L all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L)))))) # label(fact_1065_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1107 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))))) # label(fact_1066_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1108 (all M_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))))) # label(fact_1067_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1109 (all M_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))))) # label(fact_1068_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1110 (all K_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_1069_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1111 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) <-> (exists K N_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)))) # label(fact_1070_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1112 (all N_2 all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)))) # label(fact_1071_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1113 (all N_2 all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)))) # label(fact_1072_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1114 (all N_1 hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),N_1))) = hAPP_nat_nat(suc,N_1)) # label(fact_1073_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1115 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N_1)) <-> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M)),N_1)))) # label(fact_1074_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1116 (all K_2 all L all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),L)))))) # label(fact_1075_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1117 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),J_1))))) # label(fact_1076_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1118 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),K_2))))) # label(fact_1077_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1119 (all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),M_2))))) # label(fact_1078_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1120 (all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),M_2)))) # label(fact_1079_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1121 (all Fun_1 all Com1_1 all Com2_1 all Fun all Com cond(Fun_1,Com1_1,Com2_1) != while(Fun,Com)) # label(fact_1080_com_Osimps_I52_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1122 (all Fun all Com all Fun_1 all Com1_1 all Com2_1 while(Fun,Com) != cond(Fun_1,Com1_1,Com2_1)) # label(fact_1081_com_Osimps_I53_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1123 (all Fun all Com1 all Com2 all Com1_1 all Com2_1 cond(Fun,Com1,Com2) != semi(Com1_1,Com2_1)) # label(fact_1082_com_Osimps_I45_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1124 (all Com1_1 all Com2_1 all Fun all Com1 all Com2 semi(Com1_1,Com2_1) != cond(Fun,Com1,Com2)) # label(fact_1083_com_Osimps_I44_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1125 (all Fun all Com1 all Com2 cond(Fun,Com1,Com2) != skip) # label(fact_1084_com_Osimps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1126 (all Fun all Com1 all Com2 skip != cond(Fun,Com1,Com2)) # label(fact_1085_com_Osimps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1127 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) = zero_zero_nat)) # label(fact_1086_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1128 (all M all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_1) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_1087_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1129 (all N_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)))) # label(fact_1088_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1130 (all K_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_1089_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1131 (all I all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),J_1))) # label(fact_1090_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1132 (all J_2 all K_1 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_1)),I_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1))))) # label(fact_1091_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1133 (all M_2 all K_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)),K_2))))) # label(fact_1092_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1134 (all N_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) = M_2)) # label(fact_1093_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1135 (all I all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),K_2))) # label(fact_1094_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1136 (all I_1 all K_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J_2))))) # label(fact_1095_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1137 (all N_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),N_2) = M_2)) # label(fact_1096_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1138 (all K_1 all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_1) = K_1 <-> J_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),I_1)))) # label(fact_1097_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1139 (all I all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)))) # label(fact_1098_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1140 (all I all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)),I) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I)),K_2))) # label(fact_1099_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1141 (all I all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)),I))) # label(fact_1100_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1142 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)))) # label(fact_1101_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1143 (all M_2 all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2))),M_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),M_2)))) # label(fact_1102_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1144 (all M_2 all K_2 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),hAPP_nat_nat(suc,J_1)))) # label(fact_1103_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1145 (all U all M all N_1 all J_2 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J_2)),U)),M)),N_1))))) # label(fact_1104_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1146 (all U_1 all M_2 all N_2 all J_1 all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U_1)),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_1)),U_1)),M_2)),N_2))) # label(fact_1105_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1147 (all U all M all N_1 all J_2 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J_2)),U)),M) = N_1))) # label(fact_1106_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1148 (all U all M all N_1 all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_1)),U)),N_1)))))) # label(fact_1107_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1149 (all U_1 all M_2 all N_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U_1)),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I)),U_1)),N_2)))) # label(fact_1108_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1150 (all U all M all N_1 all I_1 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1) <-> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_1)),U)),N_1)))) # label(fact_1109_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1151 (all N_2 all M_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_4)) -> (exists M_1 M_4 = hAPP_nat_nat(suc,M_1)))) # label(fact_1110_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1152 (all Pa all N_1 all M_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_3)) -> ((all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,M_1))))) -> hBOOL(hAPP_nat_bool(Pa,M_3))))) # label(fact_1111_Suc__le__D__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1153 (all N_3 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) <-> (exists M_1 all X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),M_1)))))) # label(fact_1112_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1154 (all U all F ((all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(F,N)))) -> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U)))))) # label(fact_1113_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1155 (all Z all X_1 all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_1114_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1156 (all Y all X_1 all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_1115_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1157 (all N_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),zero_zero_nat))) # label(fact_1116_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1158 (all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,N_2)))) # label(fact_1117_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1159 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2))))) # label(fact_1118_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1160 (all K_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K_1))))) # label(fact_1119_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1161 (all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_2)))) # label(fact_1120_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1162 (all Pa all I_1 hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))))) # label(fact_1121_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1163 (all N_3 (hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3)) <-> (exists M_1 all X (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),N_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),M_1)))))) # label(fact_1122_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1164 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) | M_2 = N_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))) # label(fact_1123_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1165 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> (M_2 != N_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))))) # label(fact_1124_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1166 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)))) # label(fact_1125_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1167 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) | M = N_1)) # label(fact_1126_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1168 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) & M != N_1)) # label(fact_1127_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1169 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)))) # label(fact_1128_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1170 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M))) <-> N_1 = M))) # label(fact_1129_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1171 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2)))) # label(fact_1130_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1172 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))))) # label(fact_1131_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1173 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1132_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1174 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)))) # label(fact_1133_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1175 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M)))) # label(fact_1134_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1176 (all N_1 all K_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))))) # label(fact_1135_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1177 (all C all A all B (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B),C)))))) # label(fact_1136_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1178 (all I all J_1 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),I))) # label(fact_1137_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1179 (all J_1 all I -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I)),I))) # label(fact_1138_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1180 (all K_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1139_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.09 1181 (all M_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))))) # label(fact_1140_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1182 (all M_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))))) # label(fact_1141_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1183 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))))) # label(fact_1142_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1184 (all K_2 all L all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L)))))) # label(fact_1143_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1185 (all M_2 all N_2 all K_2 all L (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N_2) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))))) # label(fact_1144_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1186 (all I all J_1 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)))) # label(fact_1145_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1187 (all L all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),N_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),M_2)))))) # label(fact_1146_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1188 (all N_2 all J_1 all K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),N_2)),K_2)))) # label(fact_1147_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1189 (all N_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),zero_zero_nat))) # label(fact_1148_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1190 (all N_1 (N_1 != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_1149_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1191 (all N_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),zero_zero_nat))) # label(fact_1150_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1192 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> N_2 != zero_zero_nat)) # label(fact_1151_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1193 (all N_2 (N_2 != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)))) # label(fact_1152_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1194 (all M all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M))))) # label(fact_1153_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1195 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) | M = N_1)) # label(fact_1154_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1196 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1155_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1197 (all N_1 all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M))) <-> N_1 = M))) # label(fact_1156_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1198 (all N_2 all M_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2))) -> M_2 = N_2))) # label(fact_1157_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1199 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))))) # label(fact_1158_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1200 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> (hAPP_nat_nat(suc,M_2) != N_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_2))))) # label(fact_1159_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1201 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_2))))) # label(fact_1160_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1202 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> M_2 = N_2))) # label(fact_1161_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1203 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)))) # label(fact_1162_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1204 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)))) # label(fact_1163_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1205 (all N_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),N_2))) # label(fact_1164_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1206 (all M all N_1 (M != N_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)))) # label(fact_1165_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1207 (all X_1 all Y (X_1 != Y -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X_1))))) # label(fact_1166_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1208 (all N_2 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),N_2))) # label(fact_1167_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1209 (all N_2 all M_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2)) -> M_2 != N_2)) # label(fact_1168_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1210 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_1169_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1211 (all Pa all M all N_1 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M))) -> ((M = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M)))))) # label(fact_1170_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1212 (all I_1 all J_2 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J_2)))) # label(fact_1171_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1213 (all M_2 all N_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) = M_2)) # label(fact_1172_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1214 (all K_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1173_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1215 (all M_2 all N_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),hAPP_nat_nat(suc,M_2)))) # label(fact_1174_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1216 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_1175_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1217 (all K_1 all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1176_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1218 (all M all K_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1177_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1219 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),K_2)))))) # label(fact_1178_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1220 (all K_2 all I all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),J_1)))))) # label(fact_1179_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1221 (all M all N_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1) <-> M = N_1))) # label(fact_1180_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1222 (all M all N_1 all K_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))))) # label(fact_1181_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1223 (all M_2 all N_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),M_2))))) # label(fact_1182_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1224 (all N_1 all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)))) # label(fact_1183_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1225 (all I all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_2))))) # label(fact_1184_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1226 (all I all M_2 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I))))) # label(fact_1185_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1227 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) <-> (exists K N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K))))) # label(fact_1186_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1228 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_1187_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1229 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) <-> (exists M_1 N_1 = hAPP_nat_nat(suc,M_1)))) # label(fact_1188_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1230 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,zero_zero_nat))) <-> N_1 = zero_zero_nat)) # label(fact_1189_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1231 (all M all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1))) <-> M = zero_zero_nat | (exists J (M = hAPP_nat_nat(suc,J) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),N_1)))))) # label(fact_1190_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1232 (all N_1 hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),N_1))) = N_1) # label(fact_1191_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1233 (all X hAPP_n1699378549t_bool(ord_less_nat,X) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X))) # label(fact_1192_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1234 (all Z all X_1 all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_1193_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1235 (all Y all X_1 all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))))) # label(fact_1194_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1236 (all X_1 all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y)))) # label(fact_1195_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1237 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1238 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1239 (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].
% 1.61/2.10 1240 (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].
% 1.61/2.10 1241 (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].
% 1.61/2.10 1242 (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].
% 1.61/2.10 1243 (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].
% 1.61/2.10 1244 (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].
% 1.61/2.10 1245 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1246 (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].
% 1.61/2.10 1247 (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].
% 1.61/2.10 1248 (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].
% 1.61/2.10 1249 (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].
% 1.61/2.10 1250 (all X_1 all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1251 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1252 (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].
% 1.61/2.10 1253 (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].
% 1.61/2.10 1254 (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].
% 1.61/2.10 1255 (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].
% 1.61/2.10 1256 (all P all Q hAPP_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1257 (all P all Q (is_bool(P) -> hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1258 (all P all Q hAPP_pname_nat(hAPP_n362732366me_nat(cOMBK_nat_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1259 (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].
% 1.61/2.10 1260 (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].
% 1.61/2.10 1261 (all X_1 all Y (-hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1262 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1263 (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].
% 1.61/2.10 1264 (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].
% 1.61/2.10 1265 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1266 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(cOMBB_bool_bool_nat(P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1267 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1268 (all P all Q all R hAPP_pname_bool(hAPP_n1025906991e_bool(hAPP_f1715247037e_bool(cOMBC_pname_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_p1499970991t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1269 (all P all Q all R hAPP_nat_bool(hAPP_p1499970991t_bool(hAPP_f998021053t_bool(cOMBC_nat_pname_bool,P),Q),R) = hAPP_pname_bool(hAPP_n1025906991e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1270 (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].
% 1.61/2.10 1271 (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].
% 1.61/2.10 1272 (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].
% 1.61/2.10 1273 (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].
% 1.61/2.10 1274 (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].
% 1.61/2.10 1275 (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].
% 1.61/2.10 1276 (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].
% 1.61/2.10 1277 (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].
% 1.61/2.10 1278 (all X_1 all Y (-hBOOL(hAPP_H1037229737a_bool(hAPP_H426895267a_bool(fequal963300192iple_a,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1279 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_H1037229737a_bool(hAPP_H426895267a_bool(fequal963300192iple_a,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1280 (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].
% 1.61/2.10 1281 (all X_1 all Y (-hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1282 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1283 (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].
% 1.61/2.10 1284 (all P all Q (is_bool(P) -> hAPP_H1037229737a_bool(hAPP_b1882817719a_bool(cOMBK_235286536iple_a,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1285 (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].
% 1.61/2.10 1286 (all P all Q hAPP_p346744818iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1287 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1288 (all P all Q all R hAPP_nat_bool(hAPP_f158894502t_bool(cOMBB_955900739ol_nat(P),Q),R) = hAPP_f54304608l_bool(P,hAPP_n1699378549t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1289 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1290 (all P all Q all R hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_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].
% 1.61/2.10 1291 (all P all Q all R hAPP_p1499970991t_bool(hAPP_f1358769483t_bool(cOMBB_523834888_pname(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_pname_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__013) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1292 (all P all Q all R hAPP_n1025906991e_bool(hAPP_f414474559e_bool(cOMBB_1212655066ol_nat(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_nat_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1293 (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_014) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1294 (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_015) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1295 (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].
% 1.61/2.10 1296 (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].
% 1.61/2.10 1297 (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].
% 1.61/2.10 1298 (all P all Q all R hAPP_p61793385e_bool(hAPP_f1336811455e_bool(cOMBB_542850580_pname(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_016) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1299 (all X_1 all Y (-hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(fequal874423448a_bool,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1300 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(fequal874423448a_bool,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1301 (all P all Q (is_bool(P) -> hAPP_H242767318e_bool(hAPP_b974863576e_bool(cOMBK_988866959_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg___017) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1302 (all P all Q hAPP_p1751618853_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1303 (all P all Q all R hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hAPP_f228417655a_bool(cOMBC_364739t_bool,P),Q),R) = hAPP_nat_bool(hAPP_H144868812t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1304 (all P all Q all R hAPP_nat_bool(hAPP_H144868812t_bool(hAPP_f1886543991t_bool(cOMBC_533513393a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Hoare____Mirabelle____uwgpyvfjxg__O) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1305 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f20753329a_bool(cOMBB_1882975613iple_a(P),Q),R) = hAPP_bool_bool(P,hAPP_H1037229737a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1306 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H2130837971l_bool(P,R),hAPP_H1037229737a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1307 (all P all Q all R hAPP_pname_bool(hAPP_H1078816262e_bool(hAPP_f421895915e_bool(cOMBC_1309726071a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_p1743421830a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1308 (all X_1 all Y (-hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_bool,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_018) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1309 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_bool,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_019) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1310 (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].
% 1.61/2.10 1311 (all P all Q (is_bool(P) -> hAPP_f1695230391l_bool(hAPP_b83765433l_bool(cOMBK_404565488a_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____uwg) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1312 (all P all Q hAPP_p1743421830a_bool(hAPP_f624861966a_bool(cOMBK_1667642481_pname,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1313 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBB_325909978_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H242767318e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel_020) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1314 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1270401638l_bool(P,R),hAPP_H242767318e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1315 (all P all Q all R hAPP_pname_bool(hAPP_H1776011827e_bool(hAPP_f343137017e_bool(cOMBC_19854728e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_p606792009e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__021) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1316 (all P all Q all R hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,P),Q),R) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__022) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1317 (all P all Q all R hAPP_n1025906991e_bool(hAPP_f1501416730e_bool(hAPP_f883303749e_bool(cOMBC_1771919087e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_n60670500e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1318 (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_023) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1319 (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].
% 1.61/2.10 1320 (all X_1 all Y (-hBOOL(hAPP_f2110825313l_bool(hAPP_f1303207443l_bool(fequal1455900568l_bool,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1321 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_f2110825313l_bool(hAPP_f1303207443l_bool(fequal1455900568l_bool,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1322 (all P all Q all R hAPP_H144868812t_bool(hAPP_f1872860171t_bool(cOMBB_1391527205iple_a(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_H592031934_a_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__024) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1323 (all P all Q all R hAPP_nat_bool(hAPP_f1968395738t_bool(hAPP_f2110185157t_bool(cOMBC_805992879l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_n37219812l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1324 (all P all Q all R hAPP_f1695230391l_bool(hAPP_n37219812l_bool(hAPP_f1852971749l_bool(cOMBC_594836627t_bool,P),Q),R) = hAPP_nat_bool(hAPP_f1968395738t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1325 (all P all Q all R hAPP_f1695230391l_bool(hAPP_f396832789l_bool(cOMBB_193631803a_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1695230391l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1326 (all P all Q all R hAPP_H2130837971l_bool(hAPP_f146754017l_bool(cOMBB_1866391387iple_a(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1037229737a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_025) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1327 (all P all Q all R hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f244528453l_bool(P,R),hAPP_f1695230391l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1328 (all P all Q all R hAPP_pname_bool(hAPP_f1216026388e_bool(hAPP_f1415030585e_bool(cOMBC_173670761l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_p1910214954l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1329 (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].
% 1.61/2.10 1330 (all P all Q all R hAPP_H1270401638l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H242767318e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_026) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1331 (all P all Q all R hAPP_n1512601776t_bool(hAPP_f934069744t_bool(cOMBB_1141542387ol_nat(P),Q),R) = hAPP_n1512601776t_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1332 (all P all Q all R hAPP_H1037229737a_bool(hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_H426895267a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_027) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1333 (all P all Q all R hAPP_n60670500e_bool(hAPP_f446737578e_bool(cOMBB_1209446585ol_nat(P),Q),R) = hAPP_p905327722e_bool(P,hAPP_nat_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1334 (all P all Q all R hAPP_n261501868iple_a(hAPP_f817035994iple_a(hAPP_f311800994iple_a(cOMBS_1417107330iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_n83983309iple_a(P,R),hAPP_n1063102567e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1335 (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_028) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1336 (all P all Q all R hAPP_p346744818iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_p1227342867iple_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].
% 1.61/2.10 1337 (all P all Q all R hAPP_p1751618853_state(hAPP_f922567064_state(cOMBB_452540923_pname(P),Q),R) = hAPP_H923660098_state(P,hAPP_p346744818iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1338 (all P all Q all R hAPP_p346744818iple_a(hAPP_f1273628548iple_a(cOMBB_1824120853_pname(P),Q),R) = hAPP_H1770360232iple_a(P,hAPP_p1751618853_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1339 (all P all Q all R hAPP_f1968395738t_bool(hAPP_f1144745493t_bool(cOMBB_85437587a_bool(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_f2097660464ol_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__029) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1340 (all P all Q all R hAPP_f244528453l_bool(hAPP_f1675405437l_bool(cOMBB_703864541a_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1695230391l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_030) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1341 (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].
% 1.61/2.10 1342 (all P all Q all R hAPP_H242767318e_bool(hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_H216526335e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1343 (all P all Q all R hAPP_n1919155532a_bool(hAPP_f260875897a_bool(cOMBB_1063143712ol_nat(P),Q),R) = hAPP_H426895267a_bool(P,hAPP_n261501868iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_031) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1344 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f1194757675a_bool(cOMBB_1610959875iple_a(P),Q),R) = hAPP_f1695230391l_bool(P,hAPP_H426895267a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1345 (all P all Q all R hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_H622608077l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_032) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1346 (all P all Q all R hAPP_n1036200171_state(hAPP_f634763074_state(hAPP_f1172439208_state(cOMBS_1390821348_state,P),Q),R) = hAPP_f497755132_state(hAPP_n766730025_state(P,R),hAPP_n1252169848e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1347 (all P all Q all R hAPP_p1743421830a_bool(hAPP_f2085416313a_bool(cOMBB_1388879450_pname(P),Q),R) = hAPP_H426895267a_bool(P,hAPP_p346744818iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_033) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1348 (all P all Q all R hAPP_p1751618853_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,P),Q),R) = hAPP_f497755132_state(hAPP_p1331349103_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].
% 1.61/2.10 1349 (all P all Q all R hAPP_n83983309iple_a(hAPP_f1857794253iple_a(hAPP_f803745506iple_a(cOMBS_519355893iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_n1753616192iple_a(P,R),hAPP_nat_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__Com__Ocom_000tc__fun_Itc__fun_It__a) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1350 (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_034) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1351 (all P all Q all R hAPP_p1227342867iple_a(hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_p805859462iple_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].
% 1.61/2.10 1352 (all P all Q all R hAPP_H905846293iple_a(hAPP_f1766326554iple_a(hAPP_f2004506425iple_a(cOMBS_1744968921iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_H1401668662iple_a(P,R),hAPP_H1893885264e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_035) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1353 (all P all Q all R hAPP_H242767318e_bool(hAPP_f1900156034e_bool(cOMBB_1282391997_state(P),Q),R) = hAPP_f1378282496l_bool(P,hAPP_H216526335e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_036) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1354 (all P all Q all R hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,P),Q),R) = hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___037) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1355 (all P all Q all R hAPP_p606792009e_bool(hAPP_f472107739e_bool(cOMBB_181781758_pname(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_p1751618853_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___038) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1356 (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_039) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1357 (all P all Q all R hAPP_n1919155532a_bool(hAPP_f1938783956a_bool(hAPP_f816688069a_bool(cOMBC_1584660393a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_n131076574a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp_040) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1358 (all P all Q all R hAPP_n766730025_state(hAPP_f1158791849_state(hAPP_f459571426_state(cOMBS_183256401_state,P),Q),R) = hAPP_c27135337_state(hAPP_n2011101340_state(P,R),hAPP_nat_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1359 (all P all Q all R hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_041) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1360 (all P all Q all R hAPP_p1743421830a_bool(hAPP_f624861966a_bool(hAPP_f843217465a_bool(cOMBC_2103945827a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_p624562724a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw_042) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1361 (all P all Q all R hAPP_p1331349103_state(hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,P),Q),R) = hAPP_c27135337_state(hAPP_p357103842_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].
% 1.61/2.10 1362 (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_043) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1363 (all P all Q all R hAPP_H923660098_state(hAPP_f1551299824_state(hAPP_f461066925_state(cOMBS_1860286139_state,P),Q),R) = hAPP_f497755132_state(hAPP_H1275418130_state(P,R),hAPP_H838560847e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_044) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1364 (all P all Q all R hAPP_H1401668662iple_a(hAPP_f524917645iple_a(hAPP_f51865337iple_a(cOMBS_1597898188iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_H189037865iple_a(P,R),hAPP_H463278718_a_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_045) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1365 (all P all Q all R hAPP_f1693662087iple_a(hAPP_f1255935540iple_a(hAPP_f410259831iple_a(cOMBS_1097875753iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_f1820482984iple_a(P,R),hAPP_f477771714e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_046) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1366 (all P all Q all R hAPP_n1497837059e_bool(hAPP_f1718442376e_bool(hAPP_f1696618965e_bool(cOMBC_1048264781e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_n525995272e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp_047) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1367 (all P all Q all R hAPP_p606792009e_bool(hAPP_f103229774e_bool(hAPP_f376349141e_bool(cOMBC_59067399e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_p105983054e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw_048) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1368 (all P all Q all R hAPP_n37219812l_bool(hAPP_f635381775l_bool(cOMBB_1370228356ol_nat(P),Q),R) = hAPP_f1767618879l_bool(P,hAPP_n1919155532a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_049) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1369 (all P all Q all R hAPP_f1695230391l_bool(hAPP_f536631715l_bool(cOMBB_1575464575a_bool(P),Q),R) = hAPP_f2110825313l_bool(P,hAPP_f1767618879l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1370 (all P all Q all R hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,P),Q),R) = hAPP_f2110825313l_bool(hAPP_f293818473l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_050) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1371 (all P all Q all R hAPP_p1910214954l_bool(hAPP_f1577042203l_bool(cOMBB_1363536318_pname(P),Q),R) = hAPP_f1767618879l_bool(P,hAPP_p1743421830a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_051) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1372 (all P all Q all R hAPP_H426895267a_bool(hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_052) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1373 (all P all Q all R hAPP_H1275418130_state(hAPP_f1573424489_state(hAPP_f1527065593_state(cOMBS_1436317352_state,P),Q),R) = hAPP_c27135337_state(hAPP_H1476318469_state(P,R),hAPP_H463278718_a_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_053) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1374 (all P all Q all R hAPP_f1874848592_state(hAPP_f582141064_state(hAPP_f1784570101_state(cOMBS_988488459_state,P),Q),R) = hAPP_f497755132_state(hAPP_f1310841988_state(P,R),hAPP_f1246524253e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_054) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1375 (all P all Q all R hAPP_f1820482984iple_a(hAPP_f159541635iple_a(hAPP_f2023640211iple_a(cOMBS_1949899292iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_f1784500635iple_a(P,R),hAPP_f1968907248ol_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_055) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1376 (all P all Q all R hAPP_n1753616192iple_a(hAPP_f1921807086iple_a(cOMBB_1443236341_a_nat(P),Q),R) = hAPP_f1350218798iple_a(P,hAPP_n1063102567e_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].
% 1.61/2.10 1377 (all P all Q all R hAPP_p805859462iple_a(hAPP_f854147694iple_a(cOMBB_2054374575_pname(P),Q),R) = hAPP_f1350218798iple_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__056) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1378 (all P all Q all R hAPP_n37219812l_bool(hAPP_f924569416l_bool(hAPP_f1384990677l_bool(cOMBC_1645572109l_bool,P),Q),R) = hAPP_f396832789l_bool(hAPP_n2002774088l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Hoare____Mirabell) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1379 (all P all Q all R hAPP_n131076574a_bool(hAPP_f1402630535a_bool(cOMBB_2115959324ol_nat(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_n261501868iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_057) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1380 (all P all Q all R hAPP_f20753329a_bool(hAPP_f1706700729a_bool(hAPP_f957014749a_bool(cOMBC_288844080a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_058) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1381 (all P all Q all R hAPP_f1310841988_state(hAPP_f1235235423_state(hAPP_f1151038867_state(cOMBS_1113512696_state,P),Q),R) = hAPP_c27135337_state(hAPP_f1439241847_state(P,R),hAPP_f1968907248ol_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_059) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1382 (all P all Q all R hAPP_p624562724a_bool(hAPP_f682420871a_bool(cOMBB_1481150806_pname(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_p346744818iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_060) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1383 (all P all Q all R hAPP_H216526335e_bool(hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___061) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1384 (all P all Q all R hAPP_n2011101340_state(hAPP_f432895259_state(cOMBB_1531938296te_nat(P),Q),R) = hAPP_f274181323_state(P,hAPP_n1252169848e_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].
% 1.61/2.10 1385 (all P all Q all R hAPP_p357103842_state(hAPP_f804744487_state(cOMBB_2084106034_pname(P),Q),R) = hAPP_f274181323_state(P,hAPP_p1637813682e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___062) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1386 (all P all Q all R hAPP_H189037865iple_a(hAPP_f338450734iple_a(cOMBB_1799328076iple_a(P),Q),R) = hAPP_f1350218798iple_a(P,hAPP_H1893885264e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__063) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1387 (all P all Q all R hAPP_n525995272e_bool(hAPP_f953597140e_bool(cOMBB_1524346879ol_nat(P),Q),R) = hAPP_H1902130436e_bool(P,hAPP_n1036200171_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___064) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1388 (all P all Q all R hAPP_p105983054e_bool(hAPP_f2028971360e_bool(cOMBB_667059641_pname(P),Q),R) = hAPP_H1902130436e_bool(P,hAPP_p1751618853_state(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___065) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1389 (all P all Q all R hAPP_H1743777351a_bool(hAPP_f181951559a_bool(cOMBB_1722563443iple_a(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_H905846293iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_066) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1390 (all P all Q all R hAPP_f1784500635iple_a(hAPP_f1787234632iple_a(cOMBB_1013749676a_bool(P),Q),R) = hAPP_f1350218798iple_a(P,hAPP_f477771714e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__067) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1391 (all P all Q all R hAPP_f1767618879l_bool(hAPP_f759941367l_bool(hAPP_f254338943l_bool(cOMBC_1324894996l_bool,P),Q),R) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_068) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1392 (all P all Q all R hAPP_H1476318469_state(hAPP_f1874377965_state(cOMBB_1269509967iple_a(P),Q),R) = hAPP_f274181323_state(P,hAPP_H838560847e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___069) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1393 (all P all Q all R hAPP_f1706700729a_bool(hAPP_f2116512939a_bool(cOMBB_734913733a_bool(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_f1693662087iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_070) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.10 1394 (all P all Q all R hAPP_n2002774088l_bool(hAPP_f992030835l_bool(cOMBB_1467678496ol_nat(P),Q),R) = hAPP_f1376242083l_bool(P,hAPP_n1919155532a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_071) # label(axiom) # label(non_clause). [assumption].
% 3.31/3.55 1395 (all P all Q all R hAPP_f1439241847_state(hAPP_f868277077_state(cOMBB_989249001a_bool(P),Q),R) = hAPP_f274181323_state(P,hAPP_f1246524253e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___072) # label(axiom) # label(non_clause). [assumption].
% 3.31/3.55 1396 (all N ((all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,g),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),p)),body)),q)),procs)))) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)))) -> (all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),p)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),q)),procs))) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption].
% 3.31/3.55 1397 -((all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),g)) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,n),X)))) -> (all X (hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),p)),body)),q)),procs))) -> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,n),X))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.31/3.55
% 3.31/3.55 ============================== end of process non-clausal formulas ===
% 3.31/3.55
% 3.31/3.55 ============================== PROCESS INITIAL CLAUSES ===============
% 3.31/3.55
% 3.31/3.55 ============================== PREDICATE ELIMINATION =================
% 3.31/3.55
% 3.31/3.55 ============================== end predicate elimination =============
% 3.31/3.55
% 3.31/3.55 Auto_denials: (non-Horn, no changes).
% 3.31/3.55
% 3.31/3.55 Term ordering decisions:
% 3.31/3.55 Function symbol KB weights: member_pname=1. ord_less_eq_nat=1. member_nat=1. suc=1. ord_less_nat=1. plus_plus_nat=1. zero_zero_nat=1. member1797258804iple_a=1. bot_bo797238721a_bool=1. bot_bo784226126e_bool=1. member769771716a_bool=1. insert956547291iple_a=1. bot_bo844097828e_bool=1. insert1744391420_state=1. times_times_nat=1. semila1114547555a_bool=1. semila278973382e_bool=1. semila176469292e_bool=1. semila465093516t_bool=1. semila834425101l_bool=1. finite_finite_pname=1. bot_bot_fun_nat_bool=1. semila1168014441p_bool=1. minus_minus_nat=1. finite_finite_nat=1. member1667945571_state=1. bot_bo332163887l_bool=1. insert_nat=1. insert_pname=1. insert1421434205a_bool=1. hoare_1916936827iple_a=1. finite268574148a_bool=1. hoare_1191504582_state=1. finite1738664244iple_a=1. semila1635148844e_bool=1. semila286921929a_bool=1. semila840543986t_bool=1. fconj=1. finite694102371_state=1. collect_nat=1. collect_pname=1. semila972727038up_nat=1. collec351493750iple_a=1. collec999179778a_bool=1. fdisj=1. body=1. bot_bot_bool=1. semila80283416nf_nat=1. one_one_nat=1. cOMBS_568398431l_bool=1. cOMBS_nat_bool_bool=1. hoare_2056833131alid_a=1. cOMBC_1058051404l_bool=1. semila753742375l_bool=1. cOMBC_226598744l_bool=1. minus_1015773161e_bool=1. minus_2067140911t_bool=1. minus_85316870a_bool=1. cOMBS_154988028l_bool=1. hoare_446535894_state=1. body_1=1. cOMBC_1519416966l_bool=1. cOMBC_996544418l_bool=1. cOMBS_824156748l_bool=1. collec637225377_state=1. the_com=1. cOMBS_343917116iple_a=1. cOMBS_839225263iple_a=1. fequal_nat=1. minus_98295210l_bool=1. cOMBC_nat_nat_bool=1. fequal874423448a_bool=1. big_la1480321694n_bool=1. fequal963300192iple_a=1. fequal_pname=1. fNot=1. fequal1440809015_state=1. cOMBS_1020065803_state=1. cOMBS_1524960158_state=1. cOMBS_865875691l_bool=1. minus_1805465033e_bool=1. size_size_com=1. bot_bo806936373l_bool=1. cOMBC_1149511130e_bool=1. cOMBC_538205282l_bool=1. fFalse=1. big_la1609103640a_bool=1. big_la1704749377t_bool=1. big_la43341705in_nat=1. big_la841148155e_bool=1. cOMBC_1940896922a_bool=1. cOMBC_1967329268e_bool=1. cOMBC_627599030l_bool=1. fimplies=1. finite_finite_bool=1. skip=1. big_la1369269047e_bool=1. big_la914314008l_bool=1. minus_minus_bool=1. semila1874263622e_bool=1. semila310582991f_bool=1. bot_bo1649642514l_bool=1. cOMBC_231445413l_bool=1. cOMBS_1097875753iple_a=1. cOMBS_1113512696_state=1. cOMBS_1390821348_state=1. cOMBS_1417107330iple_a=1. cOMBS_1436317352_state=1. cOMBS_1597898188iple_a=1. cOMBS_1744968921iple_a=1. cOMBS_183256401_state=1. cOMBS_1860286139_state=1. cOMBS_1949899292iple_a=1. cOMBS_519355893iple_a=1. cOMBS_988488459_state=1. fequal_state=1. finite2012431853t_bool=1. finite595471783e_bool=1. procs=1. bot_bo156414585l_bool=1. bot_bo1701429464l_bool=1. bot_bo942947096l_bool=1. cOMBK_2086841362_pname=1. cOMBK_523903665_pname=1. cOMBK_nat_nat=1. finite1823766380l_bool=1. finite627955595e_bool=1. insert_bool=1. p=1. q=1. cOMBC_1570214144a_bool=1. cOMBC_178881787t_bool=1. cOMBC_2027030106e_bool=1. cOMBC_41962815e_bool=1. cOMBC_471052088e_bool=1. cOMBI_nat=1. cOMBK_1458035955bool_a=1. cOMBK_631994958_state=1. cOMBS_1378840469l_bool=1. fequal1455900568l_bool=1. fequal1475827639e_bool=1. fequal533582459e_bool=1. fequal_fun_nat_bool=1. cOMBC_1048264781e_bool=1. cOMBC_1123258281e_bool=1. cOMBC_1229155955e_bool=1. cOMBC_1309726071a_bool=1. cOMBC_1324894996l_bool=1. cOMBC_1584660393a_bool=1. cOMBC_1645572109l_bool=1. cOMBC_173670761l_bool=1. cOMBC_1771919087e_bool=1. cOMBC_19854728e_bool=1. cOMBC_2103945827a_bool=1. cOMBC_288844080a_bool=1. cOMBC_364739t_bool=1. cOMBC_533513393a_bool=1. cOMBC_59067399e_bool=1. cOMBC_594836627t_bool=1. cOMBC_805992879l_bool=1. cOMBC_892787026e_bool=1. cOMBC_952831051e_bool=1. cOMBC_nat_pname_bool=1. cOMBC_pname_nat_bool=1. cOMBK_1667642481_pname=1. cOMBK_235286536iple_a=1. cOMBK_404565488a_bool=1. cOMBK_988866959_state=1. cOMBK_bool_nat=1. cOMBK_bool_pname=1. cOMBK_nat_pname=1. cOMBK_pname_pname=1. fTrue=1. finite_card_nat=1. g=1. insert1325755072e_bool=1. insert1720618162e_bool=1. insert2046103699l_bool=1. insert_fun_nat_bool=1. member799430823e_bool=1. member_bool=1. member_fun_nat_bool=1. pname=1. semila1866150931l_bool=1. the_el1519802624iple_a=1. the_el2080696983_state=1. the_el979963640a_bool=1. the_elem_nat=1. the_elem_pname=1. bool=1. bot_bot_nat=1. member131361931e_bool=1. member38210668l_bool=1. n=1. semila1672697786l_bool=1. semila1782091504l_bool=1. semila1803437851l_bool=1. semila653644470l_bool=1. size_s255495008_state=1. size_s399404919iple_a=1. the_Ho2067184133_state=1. the_Ho830102290iple_a=1. the_fu1555441254a_bool=1. the_nat=1. the_pname=1. c1=1. hAPP_nat_nat=1. hAPP_nat_fun_nat_nat=1. hAPP_nat_bool=1. hAPP_f20753329a_bool=1. hAPP_f800510211t_bool=1. hAPP_f759274231e_bool=1. hAPP_f1695230391l_bool=1. hAPP_n1699378549t_bool=1. hAPP_f1664156314l_bool=1. hAPP_f396832789l_bool=1. hAPP_f806699093e_bool=1. hAPP_f54304608l_bool=1. hAPP_f1378282496l_bool=1. hAPP_f2110825313l_bool=1. hAPP_f1706700729a_bool=1. hAPP_f1388330588e_bool=1. hAPP_f1730770594t_bool=1. hAPP_p338031245l_bool=1. hAPP_f1340058745l_bool=1. hAPP_bool_bool=1. hAPP_n215258509l_bool=1. hAPP_state_bool=1. hAPP_b589554111l_bool=1. hAPP_H1743777351a_bool=1. hAPP_H622608077l_bool=1. hAPP_H1902130436e_bool=1. hAPP_f1794460506e_bool=1. hAPP_H1037229737a_bool=1. hAPP_f293818473l_bool=1. hAPP_pname_bool=1. hAPP_n1512601776t_bool=1. hAPP_H242767318e_bool=1. hAPP_H2039996199l_bool=1. hAPP_p905327722e_bool=1. hAPP_f1376242083l_bool=1. hAPP_s1806633685e_bool=1. hAPP_c27135337_state=1. hAPP_f274181323_state=1. hAPP_f497755132_state=1. hAPP_c142510605iple_a=1. hAPP_f1350218798iple_a=1. hAPP_f233717658iple_a=1. hAPP_f2034373396a_bool=1. hAPP_f360545851e_bool=1. hAPP_f258822235a_bool=1. hAPP_f22106695ol_nat=1. hAPP_f1297739591_pname=1. hAPP_pname_com=1. hAPP_n1919155532a_bool=1. while=1. hAPP_f1693662087iple_a=1. hAPP_f387058535l_bool=1. hAPP_f718417177_state=1. hAPP_f1146629647l_bool=1. hAPP_f1402196763l_bool=1. hAPP_f561022312t_bool=1. hAPP_f649174806e_bool=1. hAPP_pname_pname=1. hAPP_f1767618879l_bool=1. hAPP_f661147897e_bool=1. hAPP_f1722879237t_bool=1. hAPP_p61793385e_bool=1. hAPP_n1497837059e_bool=1. hAPP_f146754017l_bool=1. hAPP_f607497069a_bool=1. hAPP_H426895267a_bool=1. hAPP_H905846293iple_a=1. hAPP_a2036067514e_bool=1. hAPP_f1675405437l_bool=1. hAPP_f247708275a_bool=1. hAPP_f288270593l_bool=1. hAPP_f754896967l_bool=1. hAPP_H216526335e_bool=1. hAPP_p1751618853_state=1. hAPP_p346744818iple_a=1. hAPP_f1559918364iple_a=1. hAPP_f316273229iple_a=1. hAPP_f327379420iple_a=1. hAPP_f854147694iple_a=1. hAPP_f961776218iple_a=1. semi=1. hAPP_f229349961t_bool=1. hAPP_H574424047_state=1. hAPP_p1170154830_pname=1. hAPP_f1066163005t_bool=1. hAPP_option_com_com=1. hAPP_p799580910on_com=1. hAPP_H2085992369iple_a=1. hAPP_f1811131990_state=1. hAPP_f1922754332_state=1. hAPP_f290545180l_bool=1. hAPP_f420957402a_bool=1. hAPP_f460309545_state=1. hAPP_f804744487_state=1. hAPP_f914896950_state=1. hAPP_f1216026388e_bool=1. hAPP_f654413245e_bool=1. hAPP_p1743421830a_bool=1. finite1282449217_pname=1. hAPP_H280516760_state=1. hAPP_com_nat=1. hAPP_f1702629984e_bool=1. hAPP_f1968395738t_bool=1. hAPP_f832587837l_bool=1. hAPP_f1184122441e_bool=1. hAPP_f22061361e_bool=1. hAPP_f674760225e_bool=1. finite1753440478iple_a=1. finite2103247258a_bool=1. finite683959609_state=1. finite89670078_pname=1. finite988810631ne_nat=1. hAPP_f101573982e_bool=1. hAPP_f1637334154l_bool=1. hAPP_f1902016361e_bool=1. hAPP_f1935102916l_bool=1. hAPP_f2100528361l_bool=1. hAPP_f582319405t_bool=1. hAPP_f920293029a_bool=1. hAPP_nat_pname=1. hAPP_p1637813682e_bool=1. hAPP_p635540397e_bool=1. hAPP_pname_nat=1. hAPP_f1216288071e_bool=1. hAPP_f2060061063l_bool=1. hAPP_f961197973l_bool=1. hAPP_f96342628me_com=1. finite1033474011iple_a=1. finite795500164em_nat=1. hAPP_H1893885264e_bool=1. hAPP_H463278718_a_com=1. hAPP_H838560847e_bool=1. hAPP_f1246524253e_bool=1. hAPP_f1410040974l_bool=1. hAPP_f147139262e_bool=1. hAPP_f1759915619e_bool=1. hAPP_f1968907248ol_com=1. hAPP_f375948533e_bool=1. hAPP_f477771714e_bool=1. hAPP_f670355311l_bool=1. hAPP_n1025906991e_bool=1. hAPP_n1063102567e_bool=1. hAPP_n1252169848e_bool=1. hAPP_nat_com=1. finite927518301a_bool=1. hAPP_H2000557816_pname=1. hAPP_f1098153174l_bool=1. hAPP_f1151038867_state=1. hAPP_f1158791849_state=1. hAPP_f1172439208_state=1. hAPP_f1235235423_state=1. hAPP_f1255935540iple_a=1. hAPP_f1527065593_state=1. hAPP_f1551299824_state=1. hAPP_f1573424489_state=1. hAPP_f159541635iple_a=1. hAPP_f1764134762_pname=1. hAPP_f1766326554iple_a=1. hAPP_f1784570101_state=1. hAPP_f1787234632iple_a=1. hAPP_f1857794253iple_a=1. hAPP_f1863945078e_bool=1. hAPP_f1874377965_state=1. hAPP_f1921807086iple_a=1. hAPP_f2004506425iple_a=1. hAPP_f2023640211iple_a=1. hAPP_f311800994iple_a=1. hAPP_f338450734iple_a=1. hAPP_f410259831iple_a=1. hAPP_f432895259_state=1. hAPP_f459571426_state=1. hAPP_f461066925_state=1. hAPP_f51865337iple_a=1. hAPP_f524917645iple_a=1. hAPP_f582141064_state=1. hAPP_f634763074_state=1. hAPP_f762886889e_bool=1. hAPP_f803745506iple_a=1. hAPP_f817035994iple_a=1. hAPP_f868277077_state=1. hAPP_n37219812l_bool=1. finite416071164_state=1. hAPP_H144868812t_bool=1. hAPP_H1938877132_state=1. hAPP_H327714446iple_a=1. hAPP_H592031934_a_nat=1. hAPP_b496459037l_bool=1. hAPP_f1029392762a_bool=1. hAPP_f1283379615l_bool=1. hAPP_f1509969235l_bool=1. hAPP_f1513075764e_bool=1. hAPP_f434788991l_bool=1. hAPP_f559147733l_bool=1. hAPP_f624861966a_bool=1. hAPP_n261501868iple_a=1. hAPP_p1499970991t_bool=1. hAPP_s58564346l_bool=1. finite1174086764_pname=1. hAPP_H1078816262e_bool=1. hAPP_H1270401638l_bool=1. hAPP_H1776011827e_bool=1. hAPP_H2130837971l_bool=1. hAPP_a849909144l_bool=1. hAPP_b1095269219e_bool=1. hAPP_b2019457360e_bool=1. hAPP_b540892988e_bool=1. hAPP_b76515610e_bool=1. hAPP_f103356543l_bool=1. hAPP_f1181346091a_bool=1. hAPP_f1246832597l_bool=1. hAPP_f1259673775l_bool=1. hAPP_f1303207443l_bool=1. hAPP_f1570313510t_bool=1. hAPP_f167292325e_bool=1. hAPP_f1824947087e_bool=1. hAPP_f1841260065l_bool=1. hAPP_f1900748420t_bool=1. hAPP_f244528453l_bool=1. hAPP_f340725611e_bool=1. hAPP_f42430548e_bool=1. hAPP_f490436380a_bool=1. hAPP_f571476211a_bool=1. hAPP_f618557131t_bool=1. hAPP_f644196280e_bool=1. hAPP_f688831301t_bool=1. hAPP_f701449317e_bool=1. hAPP_f734420447l_bool=1. hAPP_f817621513e_bool=1. hAPP_f849457489l_bool=1. hAPP_f873506917e_bool=1. hAPP_n1006566506l_bool=1. hAPP_p393069232l_bool=1. hAPP_p606792009e_bool=1. hAPP_s2001034685l_bool=1. hAPP_H1275418130_state=1. hAPP_H1401668662iple_a=1. hAPP_H1476318469_state=1. hAPP_H175283793te_nat=1. hAPP_H189037865iple_a=1. hAPP_H923660098_state=1. hAPP_a1200519163e_bool=1. hAPP_a723219176e_bool=1. hAPP_b1013836512t_bool=1. hAPP_b1787118453l_bool=1. hAPP_b1882817719a_bool=1. hAPP_b83765433l_bool=1. hAPP_b974863576e_bool=1. hAPP_f103229774e_bool=1. hAPP_f1138284024e_bool=1. hAPP_f1144745493t_bool=1. hAPP_f1172769267l_bool=1. hAPP_f1194757675a_bool=1. hAPP_f1234324863a_bool=1. hAPP_f1261923407e_bool=1. hAPP_f1273628548iple_a=1. hAPP_f1310841988_state=1. hAPP_f1320879424l_bool=1. hAPP_f1336811455e_bool=1. hAPP_f1358769483t_bool=1. hAPP_f1384990677l_bool=1. hAPP_f1402630535a_bool=1. hAPP_f1415030585e_bool=1. hAPP_f1439241847_state=1. hAPP_f1472090462l_bool=1. hAPP_f1499754623l_bool=1. hAPP_f1501416730e_bool=1. hAPP_f1577042203l_bool=1. hAPP_f158894502t_bool=1. hAPP_f1696618965e_bool=1. hAPP_f1715247037e_bool=1. hAPP_f1718442376e_bool=1. hAPP_f1784500635iple_a=1. hAPP_f1802364479e_bool=1. hAPP_f180827860e_bool=1. hAPP_f181951559a_bool=1. hAPP_f1820482984iple_a=1. hAPP_f1852971749l_bool=1. hAPP_f1872860171t_bool=1. hAPP_f1886543991t_bool=1. hAPP_f1900156034e_bool=1. hAPP_f1938783956a_bool=1. hAPP_f1951378235l_bool=1. hAPP_f2028971360e_bool=1. hAPP_f2085416313a_bool=1. hAPP_f2097660464ol_nat=1. hAPP_f2110185157t_bool=1. hAPP_f2116512939a_bool=1. hAPP_f228417655a_bool=1. hAPP_f254338943l_bool=1. hAPP_f260875897a_bool=1. hAPP_f343137017e_bool=1. hAPP_f376349141e_bool=1. hAPP_f414474559e_bool=1. hAPP_f421895915e_bool=1. hAPP_f446737578e_bool=1. hAPP_f472107739e_bool=1. hAPP_f536631715l_bool=1. hAPP_f556039215l_bool=1. hAPP_f633452666l_bool=1. hAPP_f635381775l_bool=1. hAPP_f682420871a_bool=1. hAPP_f698292281e_bool=1. hAPP_f759941367l_bool=1. hAPP_f816688069a_bool=1. hAPP_f843217465a_bool=1. hAPP_f874203478e_bool=1. hAPP_f883303749e_bool=1. hAPP_f915354021e_bool=1. hAPP_f922567064_state=1. hAPP_f924569416l_bool=1. hAPP_f934069744t_bool=1. hAPP_f953597140e_bool=1. hAPP_f957014749a_bool=1. hAPP_f963367678e_bool=1. hAPP_f992030835l_bool=1. hAPP_f998021053t_bool=1. hAPP_n1036200171_state=1. hAPP_n131076574a_bool=1. hAPP_n1753616192iple_a=1. hAPP_n2002774088l_bool=1. hAPP_n2011101340_state=1. hAPP_n362732366me_nat=1. hAPP_n525995272e_bool=1. hAPP_n60670500e_bool=1. hAPP_n766730025_state=1. hAPP_n83983309iple_a=1. hAPP_p105983054e_bool=1. hAPP_p1227342867iple_a=1. hAPP_p1331349103_state=1. hAPP_p1910214954l_bool=1. hAPP_p357103842_state=1. hAPP_p624562724a_bool=1. hAPP_p805859462iple_a=1. hAPP_s1226857760e_bool=1. hAPP_s1874344717e_bool=1. nat_case_bool=1. finite1171393829ol_nat=1. finite1443934175_pname=1. finite1750867337iple_a=1. finite183661956ol_nat=1. finite2098682953ol_nat=1. finite491497871ol_nat=1. finite576419631a_bool=1. finite658192434ol_nat=1. fun=1. hAPP_H1770360232iple_a=1. hAPP_f1023496418a_bool=1. hAPP_f1120848625l_bool=1. hAPP_f1319825314e_bool=1. hAPP_f1502860876e_bool=1. hAPP_f1659318414l_bool=1. hAPP_f1748906467a_bool=1. hAPP_f1847120l_bool=1. hAPP_f1874848592_state=1. hAPP_f21712077l_bool=1. hAPP_f230953622l_bool=1. hAPP_f447027986e_bool=1. hAPP_f540020688l_bool=1. hAPP_f631019661l_bool=1. nat_case_nat=1. f2=1. f3=1. f5=1. f6=1. f57=1. f58=1. f98=1. f99=1. f121=1. f122=1. f123=1. f124=1. f125=1. f128=1. f129=1. f130=1. f131=1. f132=1. f133=1. f134=1. f135=1. f136=1. f137=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f156=1. f157=1. f158=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. f204=1. f205=1. f206=1. f207=1. f208=1. f215=1. f216=1. f219=1. f220=1. f222=1. f223=1. f225=1. hoare_2102800559rivs_a=1. hoare_512830354_state=1. image_1738210978iple_a=1. image_185131637_state=1. evalc=1. image_nat_nat=1. cOMBB_1015721476ol_nat=1. cOMBB_675860798_pname=1. cOMBB_1866391387iple_a=1. cOMBB_703864541a_bool=1. cOMBB_2054374575_pname=1. image_pname_nat=1. cOMBB_2084106034_pname=1. image_2016317142a_bool=1. image_1865589340iple_a=1. cOMBB_1291456124_state=1. com_size=1. image_nat_pname=1. image_pname_pname=1. image_1153683671iple_a=1. image_1244540328_pname=1. image_1599849618_state=1. cOMBB_188601460_state=1. cOMBB_923936821_pname=1. image_48635758_a_nat=1. image_533441733iple_a=1. cOMBB_1013749676a_bool=1. cOMBB_1269509967iple_a=1. cOMBB_1443236341_a_nat=1. cOMBB_1531938296te_nat=1. cOMBB_1799328076iple_a=1. cOMBB_989249001a_bool=1. hoare_293150257lids_a=1. hoare_919241616_state=1. image_1730813499_state=1. image_2037030074_pname=1. cOMBB_1355796797bool_a=1. cOMBB_1759179140_state=1. image_1590538908a_bool=1. image_299066104iple_a=1. image_821490176_state=1. cOMBB_1348041619bool_a=1. cOMBB_160679318_state=1. cOMBB_1757942702_state=1. cOMBB_1882975613iple_a=1. cOMBB_193631803a_bool=1. cOMBB_647938656_pname=1. cOMBB_800536526ol_nat=1. cOMBB_bool_bool_nat=1. image_1769043840ol_nat=1. image_2034400499a_bool=1. cOMBB_1063143712ol_nat=1. cOMBB_1141542387ol_nat=1. cOMBB_1209446585ol_nat=1. cOMBB_1212655066ol_nat=1. cOMBB_1282391997_state=1. cOMBB_1363536318_pname=1. cOMBB_1370228356ol_nat=1. cOMBB_1388879450_pname=1. cOMBB_1391527205iple_a=1. cOMBB_145932198bool_a=1. cOMBB_1467678496ol_nat=1. cOMBB_1481150806_pname=1. cOMBB_1524346879ol_nat=1. cOMBB_1575464575a_bool=1. cOMBB_1610959875iple_a=1. cOMBB_1722563443iple_a=1. cOMBB_181781758_pname=1. cOMBB_1824120853_pname=1. cOMBB_20296667_state=1. cOMBB_2115959324ol_nat=1. cOMBB_325909978_state=1. cOMBB_452540923_pname=1. cOMBB_523834888_pname=1. cOMBB_530759491_pname=1. cOMBB_542850580_pname=1. cOMBB_667059641_pname=1. cOMBB_734913733a_bool=1. cOMBB_85437587a_bool=1. cOMBB_955900739ol_nat=1. hoare_163978021_state=1. hoare_571935964size_a=1. hoare_Mirabelle_MGT=1. image_661047967_state=1. image_696316513a_bool=1. undefi17486888e_bool=1. undefined_pname=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f97=1. f100=1. f138=1. f139=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f159=1. f160=1. f161=1. f162=1. f163=1. f164=1. f165=1. f166=1. f167=1. f168=1. f209=1. f210=1. f211=1. f212=1. f213=1. f218=1. f221=1. f224=1. f226=1. evaln=1. cond=1. big_co2022808324_pname=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. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f101=1. f111=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f200=1. f201=1. f202=1. f203=1. f214=1. f217=1. f54=1. f55=1. f56=1. f79=1. f80=1. f81=1. f82=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f126=1. f184=1. f185=1. f186=1. f187=1. f188=1. f189=1. f190=1. f191=1. f192=1. f193=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f110=1. f127=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f112=1. f113=1. f114=1. f115=1. f116=1. f117=1. f118=1. f119=1. f120=1.
% 3.31/3.55
% 3.31/3.55 ============================== end of process initial clauses ========
% 3.31/3.55
% 3.31/3.55 ============================== CLAUSES FOR SEARCH ====================
% 3.31/3.55
% 3.31/3.55 ============================== end of clauses for search =============
% 3.31/3.55
% 3.31/3.55 ============================== SEARCH ================Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------