TSTP Solution File: SCT171+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT171+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 : Mon Jul 18 22:04:26 EDT 2022
% Result : Theorem 0.95s 1.35s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT171+1 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 1 21:37:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.95/1.24 ============================== Prover9 ===============================
% 0.95/1.24 Prover9 (32) version 2009-11A, November 2009.
% 0.95/1.24 Process 23620 was started by sandbox2 on n011.cluster.edu,
% 0.95/1.24 Fri Jul 1 21:37:05 2022
% 0.95/1.24 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23467_n011.cluster.edu".
% 0.95/1.24 ============================== end of head ===========================
% 0.95/1.24
% 0.95/1.24 ============================== INPUT =================================
% 0.95/1.24
% 0.95/1.24 % Reading from file /tmp/Prover9_23467_n011.cluster.edu
% 0.95/1.24
% 0.95/1.24 set(prolog_style_variables).
% 0.95/1.24 set(auto2).
% 0.95/1.24 % set(auto2) -> set(auto).
% 0.95/1.24 % set(auto) -> set(auto_inference).
% 0.95/1.24 % set(auto) -> set(auto_setup).
% 0.95/1.24 % set(auto_setup) -> set(predicate_elim).
% 0.95/1.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.95/1.24 % set(auto) -> set(auto_limits).
% 0.95/1.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.95/1.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.95/1.24 % set(auto) -> set(auto_denials).
% 0.95/1.24 % set(auto) -> set(auto_process).
% 0.95/1.24 % set(auto2) -> assign(new_constants, 1).
% 0.95/1.24 % set(auto2) -> assign(fold_denial_max, 3).
% 0.95/1.24 % set(auto2) -> assign(max_weight, "200.000").
% 0.95/1.24 % set(auto2) -> assign(max_hours, 1).
% 0.95/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.95/1.24 % set(auto2) -> assign(max_seconds, 0).
% 0.95/1.24 % set(auto2) -> assign(max_minutes, 5).
% 0.95/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.95/1.24 % set(auto2) -> set(sort_initial_sos).
% 0.95/1.24 % set(auto2) -> assign(sos_limit, -1).
% 0.95/1.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.95/1.24 % set(auto2) -> assign(max_megs, 400).
% 0.95/1.24 % set(auto2) -> assign(stats, some).
% 0.95/1.24 % set(auto2) -> clear(echo_input).
% 0.95/1.24 % set(auto2) -> set(quiet).
% 0.95/1.24 % set(auto2) -> clear(print_initial_clauses).
% 0.95/1.24 % set(auto2) -> clear(print_given).
% 0.95/1.24 assign(lrs_ticks,-1).
% 0.95/1.24 assign(sos_limit,10000).
% 0.95/1.24 assign(order,kbo).
% 0.95/1.24 set(lex_order_vars).
% 0.95/1.24 clear(print_given).
% 0.95/1.24
% 0.95/1.24 % formulas(sos). % not echoed (322 formulas)
% 0.95/1.24
% 0.95/1.24 ============================== end of input ==========================
% 0.95/1.24
% 0.95/1.24 % From the command line: assign(max_seconds, 300).
% 0.95/1.24
% 0.95/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.95/1.24
% 0.95/1.24 % Formulas that are not ordinary clauses:
% 0.95/1.24 1 (all B_1_1 all B_2_1 is_fun917378774i_bool(cOMBC_277798809t_bool(B_1_1,B_2_1))) # label(gsy_c_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__Nat__) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 2 (all B_1_1 all B_2_1 (is_fun917378774i_bool(B_2_1) -> is_bool(inj_on24934938di_nat(B_1_1,B_2_1)))) # label(gsy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 3 (all B_1_1 all B_2_1 (is_fun917378774i_bool(B_1_1) -> is_fun959573582l_bool(pi_Arr688267935t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc_) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 4 (all B_1_1 all B_2_1 (is_fun959573582l_bool(B_1_1) -> is_fun631676118l_bool(pi_fun433100839t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 5 (all B_1_1 all B_2_1 (is_fun282293932t_bool(B_1_1) -> is_fun432044380l_bool(pi_Pro2135156861t_bool(B_1_1,B_2_1)))) # label(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oa) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 6 (all B_1_1 all B_2_1 (is_fun917378774i_bool(B_1_1) -> is_fun1016509681e_indi(hilber1792103167di_nat(B_1_1,B_2_1)))) # label(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____fjewxadnq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 7 (all B_1_1 (is_fun917378774i_bool(B_1_1) -> is_fun917378774i_bool(collec45183100e_indi(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 8 (all B_1_1 (is_fun959573582l_bool(B_1_1) -> is_fun959573582l_bool(collec1580242420t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oi) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 9 (all B_1_1 (is_fun631676118l_bool(B_1_1) -> is_fun631676118l_bool(collec1520786044t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewx) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 10 (all B_1_1 (is_fun432044380l_bool(B_1_1) -> is_fun432044380l_bool(collec874260222t_bool(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjew) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 11 (all B_1_1 (is_fun282293932t_bool(B_1_1) -> is_fun282293932t_bool(collec1711870802le_alt(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 12 (all B_1_1 all B_2_1 (is_Arr553848933le_alt(B_2_1) -> is_fun282293932t_bool(hAPP_A619995676t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 13 (all B_1_1 all B_2_1 (is_fun917378774i_bool(B_1_1) & is_Arr625519182e_indi(B_2_1) -> is_bool(hAPP_A1466488369i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__HOL__O) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 14 (all B_1_1 all B_2_1 (is_Arr625519182e_indi(B_2_1) -> is_fun959573582l_bool(hAPP_A1912483895l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 15 (all B_1_1 all B_2_1 (is_Arr625519182e_indi(B_2_1) -> is_fun631676118l_bool(hAPP_A1964572607l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_001) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 16 (all B_1_1 all B_2_1 (is_Arr625519182e_indi(B_2_1) -> is_fun432044380l_bool(hAPP_A1944296755l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_002) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 17 (all B_1_1 all B_2_1 (is_Arr625519182e_indi(B_2_1) -> is_fun282293932t_bool(hAPP_A1374816149t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_003) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 18 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 19 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun917378774i_bool(hAPP_b1018211123i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____fjew) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 20 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun959573582l_bool(hAPP_b1719629739l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 21 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun631676118l_bool(hAPP_b990649139l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 22 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun432044380l_bool(hAPP_b1965422783l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 23 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_fun282293932t_bool(hAPP_b1024867081t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 24 (all B_1_1 all B_2_1 (is_fun1016509681e_indi(B_1_1) -> is_Arr625519182e_indi(hAPP_n385347014e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oi) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 25 (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].
% 0.95/1.24 26 (all B_1_1 all B_2_1 (is_fun917378774i_bool(B_2_1) -> is_bool(hAPP_f919661787l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 27 (all B_1_1 all B_2_1 is_Arr625519182e_indi(hAPP_f1818473245e_indi(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__004) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 28 (all B_1_1 all B_2_1 (is_fun959573582l_bool(B_1_1) -> is_bool(hAPP_f1636546729l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__005) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 29 (all B_1_1 all B_2_1 is_fun917378774i_bool(hAPP_f749892423i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__006) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 30 (all B_1_1 all B_2_1 is_fun432044380l_bool(hAPP_f861484971l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__007) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 31 (all B_1_1 all B_2_1 is_fun282293932t_bool(hAPP_f695124765t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__008) # label(hypothesis) # label(non_clause). [assumption].
% 0.95/1.24 32 (all B_1_1 all 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].
% 0.95/1.24 33 (all B_1_1 all B_2_1 is_bool(hAPP_f204273237l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 34 (all B_1_1 all B_2_1 is_bool(hAPP_f1012384989l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_009) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 35 (all B_1_1 all B_2_1 (is_fun959573582l_bool(B_2_1) -> is_bool(hAPP_f453661011l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_010) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 36 (all B_1_1 all B_2_1 is_Arr625519182e_indi(hAPP_f618619045e_indi(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_011) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 37 (all B_1_1 all B_2_1 (is_fun631676118l_bool(B_1_1) -> is_bool(hAPP_f785543729l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_012) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 38 (all B_1_1 all B_2_1 is_fun917378774i_bool(hAPP_f355113919i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_013) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 39 (all B_1_1 all B_2_1 is_bool(hAPP_f483434675l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_014) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 40 (all B_1_1 all B_2_1 is_bool(hAPP_f1018082273l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 41 (all B_1_1 all B_2_1 is_bool(hAPP_f1271180905l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 42 (all B_1_1 all B_2_1 is_bool(hAPP_f1550037191l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 43 (all B_1_1 all B_2_1 is_bool(hAPP_f1895985727l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 44 (all B_1_1 all B_2_1 is_bool(hAPP_f234874197l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 45 (all B_1_1 all B_2_1 is_bool(hAPP_f500145249l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_015) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 46 (all B_1_1 all B_2_1 (is_fun631676118l_bool(B_2_1) -> is_bool(hAPP_f213304539l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_016) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 47 (all B_1_1 all B_2_1 is_bool(hAPP_f1766869725l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 48 (all B_1_1 all B_2_1 is_bool(hAPP_f1279200745l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_017) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 49 (all B_1_1 all B_2_1 is_bool(hAPP_f592909149l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 50 (all B_1_1 all B_2_1 is_bool(hAPP_f526292585l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_018) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 51 (all B_1_1 all B_2_1 is_bool(hAPP_f460310451l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 52 (all B_1_1 all B_2_1 (is_fun432044380l_bool(B_2_1) -> is_bool(hAPP_f503012287l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje_019) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 53 (all B_1_1 all B_2_1 (is_fun282293932t_bool(B_2_1) -> is_Arr625519182e_indi(hAPP_f1659504677e_indi(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 54 (all B_1_1 all B_2_1 (is_fun432044380l_bool(B_1_1) & is_fun282293932t_bool(B_2_1) -> is_bool(hAPP_f745298353l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___020) # label(hypothesis) # label(non_clause). [assumption].
% 0.95/1.24 55 (all B_1_1 all B_2_1 (is_fun282293932t_bool(B_2_1) -> is_fun917378774i_bool(hAPP_f352490559i_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___021) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 56 (all B_1_1 all B_2_1 (is_fun282293932t_bool(B_2_1) -> is_fun432044380l_bool(hAPP_f2056167603l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___022) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 57 (all B_1_1 all B_2_1 (is_fun282293932t_bool(B_2_1) -> is_fun282293932t_bool(hAPP_f1673487381t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___023) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 58 (all B_1_1 all B_2_1 is_Arr625519182e_indi(hAPP_P2024088443e_indi(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 59 (all B_1_1 all B_2_1 (is_fun282293932t_bool(B_1_1) -> is_bool(hAPP_P2075002375t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__024) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 60 (all B_1_1 all B_2_1 is_fun917378774i_bool(hAPP_P907763049i_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__025) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 61 (all B_1_1 is_fun432044380l_bool(member1056080916le_alt(B_1_1))) # label(gsy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mt) # label(hypothesis) # label(non_clause). [assumption].
% 0.95/1.24 62 (all X_2 all Y_1 all L all Z_1 (is_Arr553848933le_alt(X_2) & is_Arr553848933le_alt(Y_1) & is_Arr553848933le_alt(Z_1) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,L),Z_1))) <-> Y_1 != Z_1 & (X_2 = Z_1 -> X_2 != Y_1) & (X_2 != Z_1 -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L)))))) # label(fact_4_in__mkbot) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 63 (all X_2 all Y_1 all L all Z_1 (is_Arr553848933le_alt(X_2) & is_Arr553848933le_alt(Y_1) & is_Arr553848933le_alt(Z_1) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,L),Z_1))) <-> X_2 != Z_1 & (Y_1 = Z_1 -> X_2 != Y_1) & (Y_1 != Z_1 -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L)))))) # label(fact_5_in__mktop) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 64 (all P_1 all Pa all A_8 all B_8 all Aa all Ba (is_Arr553848933le_alt(A_8) & is_Arr553848933le_alt(B_8) & is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) -> (Aa != Ba -> (A_8 != B_8 -> (Aa != B_8 -> (Ba != A_8 -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof)) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof)) -> ((all I (is_Arr625519182e_indi(I) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_8,B_8)),hAPP_A1374816149t_bool(P_1,I)))))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_8,B_8)),hAPP_f695124765t_bool(f,P_1))))))))))))) # label(fact_6__C2_C) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 65 (all P_1 all Pa all A_8 all B_8 all Aa all Ba (is_Arr553848933le_alt(A_8) & is_Arr553848933le_alt(B_8) & is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) -> (Aa != Ba -> (A_8 != B_8 -> (Aa != B_8 -> (Ba != A_8 -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof)) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof)) -> ((all I (is_Arr625519182e_indi(I) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_8,B_8)),hAPP_A1374816149t_bool(P_1,I)))))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa))) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_8,B_8)),hAPP_f695124765t_bool(f,P_1))))))))))))) # label(fact_7__C1_C) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 66 (all P_1 all Pa all Ca all Aa all Ba (is_Arr553848933le_alt(Ca) & is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) -> (Aa != Ba -> (Ba != Ca -> (Aa != Ca -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof)) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof)) -> ((all I (is_Arr625519182e_indi(I) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Ca)),hAPP_A1374816149t_bool(P_1,I)))))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Ca)),hAPP_f695124765t_bool(f,P_1)))))))))))) # label(fact_8__C4_C) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 67 (all P_1 all Pa all A_8 all B_8 all Aa all Ba (is_Arr553848933le_alt(A_8) & is_Arr553848933le_alt(B_8) & is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) -> (Aa != Ba -> (A_8 != B_8 -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof)) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof)) -> ((all I (is_Arr625519182e_indi(I) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_8,B_8)),hAPP_A1374816149t_bool(P_1,I)))))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_8,B_8)),hAPP_f695124765t_bool(f,P_1))))))))))) # label(fact_9_pairwise__neutrality) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 68 (all P_1 all Pa all Aa all Ba (is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof)) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof)) -> ((all I (is_Arr625519182e_indi(I) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Aa)),hAPP_A1374816149t_bool(P_1,I)))))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Aa)),hAPP_f695124765t_bool(f,P_1)))))))))) # label(fact_10__C3_C) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 69 (all I (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A1374816149t_bool(p,I))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,hAPP_A1374816149t_bool(p,I)),e)))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n)) -> (hAPP_A588601142di_nat(h,I) = n -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,hAPP_A1374816149t_bool(p,I)),c),e)))) & (hAPP_A588601142di_nat(h,I) != n -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,hAPP_A1374816149t_bool(p,I)),e))))))) # label(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 70 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) # label(fact_14_PW) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 71 (all Pa ((all X1 hBOOL(hAPP_P2075002375t_bool(Pa,X1))) <-> (all A_1 all B_1 (is_Arr553848933le_alt(A_1) & is_Arr553848933le_alt(B_1) -> hBOOL(hAPP_P2075002375t_bool(Pa,produc171383831le_alt(A_1,B_1))))))) # label(fact_15_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.24 72 (all A_10 all B_10 all A_9 all B_9 (is_Arr553848933le_alt(A_10) & is_Arr553848933le_alt(B_10) & is_Arr553848933le_alt(A_9) & is_Arr553848933le_alt(B_9) -> (produc171383831le_alt(A_10,B_10) = produc171383831le_alt(A_9,B_9) -> -(A_10 = A_9 -> B_10 != B_9)))) # label(fact_21_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 73 (all Aa all Ba all A_8 all B_8 (is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) & is_Arr553848933le_alt(A_8) & is_Arr553848933le_alt(B_8) -> (produc171383831le_alt(Aa,Ba) = produc171383831le_alt(A_8,B_8) <-> Aa = A_8 & Ba = B_8))) # label(fact_22_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 74 (all Fa (hBOOL(hAPP_f785543729l_bool(arrow_1212118780le_IIA,Fa)) <-> (all X_1 (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof)) -> (all Xa (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Xa),arrow_413697182e_Prof)) -> (all A_1 all B_1 (is_Arr553848933le_alt(A_1) & is_Arr553848933le_alt(B_1) -> ((all I (is_Arr625519182e_indi(I) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(X_1,I))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(Xa,I)))))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,X_1))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,Xa))))))))))))) # label(fact_23_IIA__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 75 (all Fa (hBOOL(hAPP_f785543729l_bool(arrow_467566751nimity,Fa)) <-> (all X_1 (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof)) -> (all A_1 all B_1 (is_Arr553848933le_alt(A_1) & is_Arr553848933le_alt(B_1) -> ((all I (is_Arr625519182e_indi(I) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(X_1,I))))) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,X_1)))))))))) # label(fact_24_unanimity__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 76 (all X_2 hBOOL(hAPP_f745298353l_bool(top_to2005687013l_bool,X_2))) # label(fact_25_top1I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 77 (all X_2 hBOOL(hAPP_f1636546729l_bool(top_to1194196741l_bool,X_2))) # label(fact_26_top1I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 78 (all X_2 hBOOL(hAPP_f785543729l_bool(top_to40512653l_bool,X_2))) # label(fact_27_top1I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 79 (all X_2 hBOOL(hAPP_P2075002375t_bool(top_to2034604131t_bool,X_2))) # label(fact_28_top1I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 80 (all X_2 hBOOL(hAPP_A1466488369i_bool(top_to1256827021i_bool,X_2))) # label(fact_29_top1I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 81 (all X_2 hBOOL(hAPP_f387058535l_bool(member_bool(X_2),top_to1647826457l_bool))) # label(fact_30_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 82 (all X_2 hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),top_to1256827021i_bool))) # label(fact_31_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 83 (all X_2 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),top_to2034604131t_bool))) # label(fact_32_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 84 (all X_2 hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),top_to1194196741l_bool))) # label(fact_33_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 85 (all X_2 hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),top_to40512653l_bool))) # label(fact_34_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 86 (all X_2 hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),top_to2005687013l_bool))) # label(fact_35_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 87 (all X_2 hBOOL(hAPP_f387058535l_bool(member_bool(X_2),top_to1647826457l_bool))) # label(fact_36_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 88 (all X_2 hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),top_to1256827021i_bool))) # label(fact_37_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 89 (all X_2 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),top_to2034604131t_bool))) # label(fact_38_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 90 (all X_2 hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),top_to1194196741l_bool))) # label(fact_39_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 91 (all X_2 hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),top_to40512653l_bool))) # label(fact_40_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 92 (all X_2 hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),top_to2005687013l_bool))) # label(fact_41_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 93 (all X_2 (hBOOL(hAPP_f745298353l_bool(top_to2005687013l_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_42_top__apply) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 94 (all X_2 (hBOOL(hAPP_f1636546729l_bool(top_to1194196741l_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_43_top__apply) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 95 (all X_2 (hBOOL(hAPP_f785543729l_bool(top_to40512653l_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_44_top__apply) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 96 (all X_2 (hBOOL(hAPP_P2075002375t_bool(top_to2034604131t_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_45_top__apply) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 97 (all X_2 (hBOOL(hAPP_A1466488369i_bool(top_to1256827021i_bool,X_2)) <-> hBOOL(top_top_bool))) # label(fact_46_top__apply) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 98 (all Aa -hBOOL(hAPP_f503012287l_bool(hAPP_f1669465919l_bool(ord_le272605321l_bool,top_to2005687013l_bool),Aa))) # label(fact_47_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 99 (all Aa -hBOOL(hAPP_f453661011l_bool(hAPP_f1760255479l_bool(ord_le453141089l_bool,top_to1194196741l_bool),Aa))) # label(fact_48_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 100 (all Aa -hBOOL(hAPP_f213304539l_bool(hAPP_f281286919l_bool(ord_le1480133609l_bool,top_to40512653l_bool),Aa))) # label(fact_49_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 101 (all Aa -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa))) # label(fact_50_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 102 (all Aa -hBOOL(hAPP_f745298353l_bool(hAPP_f2056167603l_bool(ord_le227393471t_bool,top_to2034604131t_bool),Aa))) # label(fact_51_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 103 (all Aa -hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,top_to1256827021i_bool),Aa))) # label(fact_52_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 104 (all X_14 all Y_13 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_14),Y_13)) -> (X_14 != Y_13 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_13),X_14))))) # label(fact_53_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 105 (all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> -hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)))) # label(fact_54_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 106 (all X_13 all Y_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_12)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_13)))) # label(fact_55_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 107 (all Z_1 all Y_1 all X_2 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)) -> (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Z_1),Y_1)) -> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Z_1),X_2))))) # label(fact_56_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 108 (all Z_2 all Y_11 all X_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_11),X_12)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_12))))) # label(fact_57_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 109 (all Z_1 all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),Z_1)) -> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Z_1))))) # label(fact_58_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 110 (all Z all X_11 all Y_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_10),Z)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Z))))) # label(fact_59_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 111 (all Ca all Ba all Aa (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Aa)) -> (Ba = Ca -> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ca),Aa))))) # label(fact_60_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 112 (all C_3 all B_7 all A_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_7),A_7)) -> (B_7 = C_3 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),A_7))))) # label(fact_61_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 113 (all Ca all Aa all Ba (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ba)) -> (Ba = Ca -> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ca))))) # label(fact_62_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 114 (all C_2 all A_6 all B_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_6)) -> (B_6 = C_2 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),C_2))))) # label(fact_63_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 115 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ca),Ba)) -> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ca),Aa))))) # label(fact_64_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 116 (all C_1 all A_5 all B_5 (A_5 = B_5 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_1),B_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_1),A_5))))) # label(fact_65_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 117 (all Ca all Aa all Ba (Aa = Ba -> (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Ca)) -> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ca))))) # label(fact_66_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 118 (all C all A_4 all B_4 (A_4 = B_4 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_4),C)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),C))))) # label(fact_67_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 119 (all Ba all Aa (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Aa)) -> -hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ba)))) # label(fact_68_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 120 (all B_3 all A_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_3),A_3)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_3)))) # label(fact_69_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 121 (all Aa all Ba (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ba)) -> -hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Aa)))) # label(fact_70_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 122 (all A_2 all B_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_2),A_2)))) # label(fact_71_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 123 (all Pa all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)) -> hBOOL(Pa)))) # label(fact_72_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 124 (all Pa all X_2 all Y_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2)) -> hBOOL(Pa)))) # label(fact_73_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 125 (all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> Y_1 != X_2)) # label(fact_74_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 126 (all X_10 all Y_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_9)) -> Y_9 != X_10)) # label(fact_75_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 127 (all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> X_2 != Y_1)) # label(fact_76_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 128 (all X_9 all Y_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_8)) -> X_9 != Y_8)) # label(fact_77_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 129 (all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> -hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)))) # label(fact_78_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 130 (all X_8 all Y_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_7)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_7),X_8)))) # label(fact_79_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 131 (all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> -hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)))) # label(fact_80_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 132 (all X_7 all Y_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_6)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_6),X_7)))) # label(fact_81_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 133 (all X_2 all Y_1 (hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1)) -> X_2 != Y_1)) # label(fact_82_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 134 (all X_6 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_5)) -> X_6 != Y_5)) # label(fact_83_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 135 (all X_5 all Y_4 (X_5 != Y_4 -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_5),Y_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),X_5))))) # label(fact_84_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 136 (all Y_1 all X_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1)) <-> X_2 = Y_1))) # label(fact_85_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 137 (all X_4 all Y_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Y_3)) | X_4 = Y_3 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_4)))) # label(fact_86_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 138 (all X_2 all Y_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2)) | X_2 = Y_1)) # label(fact_87_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 139 (all X_2 all Y_1 (X_2 != Y_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2)))) # label(fact_88_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 140 (all X_2 -hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),X_2))) # label(fact_89_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 141 (all X_3 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_3),X_3))) # label(fact_90_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 142 (all S all R_1 (is_fun282293932t_bool(S) & is_fun282293932t_bool(R_1) -> ((all X_1 all Xa (is_Arr553848933le_alt(X_1) & is_Arr553848933le_alt(Xa) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Xa)),R_1)) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Xa)),S))))) <-> R_1 = S))) # label(fact_96_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 143 (all Aa (is_fun432044380l_bool(Aa) -> (Aa != top_to2005687013l_bool <-> hBOOL(hAPP_f503012287l_bool(hAPP_f1669465919l_bool(ord_le272605321l_bool,Aa),top_to2005687013l_bool))))) # label(fact_97_less__top) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 144 (all Aa (is_fun959573582l_bool(Aa) -> (Aa != top_to1194196741l_bool <-> hBOOL(hAPP_f453661011l_bool(hAPP_f1760255479l_bool(ord_le453141089l_bool,Aa),top_to1194196741l_bool))))) # label(fact_98_less__top) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 145 (all Aa (is_fun631676118l_bool(Aa) -> (Aa != top_to40512653l_bool <-> hBOOL(hAPP_f213304539l_bool(hAPP_f281286919l_bool(ord_le1480133609l_bool,Aa),top_to40512653l_bool))))) # label(fact_99_less__top) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 146 (all Aa (-(hBOOL(Aa) <-> hBOOL(top_top_bool)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)))) # label(fact_100_less__top) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 147 (all Aa (is_fun282293932t_bool(Aa) -> (Aa != top_to2034604131t_bool <-> hBOOL(hAPP_f745298353l_bool(hAPP_f2056167603l_bool(ord_le227393471t_bool,Aa),top_to2034604131t_bool))))) # label(fact_101_less__top) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 148 (all Aa (is_fun917378774i_bool(Aa) -> (Aa != top_to1256827021i_bool <-> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),top_to1256827021i_bool))))) # label(fact_102_less__top) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 149 (all X_2 all Y_1 all F (is_Arr625519182e_indi(X_2) -> (hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool)) -> (hAPP_A588601142di_nat(F,X_2) = Y_1 -> hAPP_n385347014e_indi(hilber1792103167di_nat(top_to1256827021i_bool,F),Y_1) = X_2)))) # label(fact_103_inv__f__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 150 (all X_2 all F (is_Arr625519182e_indi(X_2) -> (hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool)) -> hAPP_n385347014e_indi(hilber1792103167di_nat(top_to1256827021i_bool,F),hAPP_A588601142di_nat(F,X_2)) = X_2))) # label(fact_104_inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 151 (all X_2 all F all A (is_Arr625519182e_indi(X_2) -> (hBOOL(inj_on24934938di_nat(F,A)) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hAPP_n385347014e_indi(hilber1792103167di_nat(A,F),hAPP_A588601142di_nat(F,X_2)) = X_2)))) # label(fact_105_inv__into__f__f) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 152 (all Y_1 all X_2 all F all A (is_Arr625519182e_indi(X_2) -> (hBOOL(inj_on24934938di_nat(F,A)) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> (hAPP_A588601142di_nat(F,X_2) = Y_1 -> hAPP_n385347014e_indi(hilber1792103167di_nat(A,F),Y_1) = X_2))))) # label(fact_106_inv__into__f__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 153 (all X_2 all Y_1 all F (is_Arr625519182e_indi(X_2) & is_Arr625519182e_indi(Y_1) -> (hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool)) -> (hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1) <-> X_2 = Y_1)))) # label(fact_107_inj__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 154 (all F all A (hBOOL(inj_on24934938di_nat(F,A)) <-> (all X_1 (is_Arr625519182e_indi(X_1) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A)) -> (all Xa (is_Arr625519182e_indi(Xa) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Xa),A)) -> (hAPP_A588601142di_nat(F,X_1) = hAPP_A588601142di_nat(F,Xa) -> X_1 = Xa))))))))) # label(fact_108_inj__on__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 155 (all X_2 all Y_1 all F all A (is_Arr625519182e_indi(X_2) & is_Arr625519182e_indi(Y_1) -> (hBOOL(inj_on24934938di_nat(F,A)) -> (X_2 != Y_1 -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Y_1),A)) -> hAPP_A588601142di_nat(F,X_2) != hAPP_A588601142di_nat(F,Y_1))))))) # label(fact_109_inj__on__contraD) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 156 (all Y_1 all X_2 all F all A (is_Arr625519182e_indi(Y_1) & is_Arr625519182e_indi(X_2) -> (hBOOL(inj_on24934938di_nat(F,A)) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Y_1),A)) -> (hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1) <-> X_2 = Y_1)))))) # label(fact_110_inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 157 (all X_2 all Y_1 all F all A (is_Arr625519182e_indi(X_2) & is_Arr625519182e_indi(Y_1) -> (hBOOL(inj_on24934938di_nat(F,A)) -> (hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Y_1),A)) -> X_2 = Y_1)))))) # label(fact_111_inj__onD) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 158 (all X_2 all Y_1 all F (is_Arr625519182e_indi(X_2) & is_Arr625519182e_indi(Y_1) -> (hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool)) -> (hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1) -> X_2 = Y_1)))) # label(fact_112_injD) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 159 (all G all F (is_fun1016509681e_indi(G) -> (hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool)) -> ((all X_1 hAPP_A588601142di_nat(F,hAPP_n385347014e_indi(G,X_1)) = X_1) -> hilber1792103167di_nat(top_to1256827021i_bool,F) = G)))) # label(fact_113_inj__imp__inv__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 160 (all F ((all X_1 all Y_2 (is_Arr625519182e_indi(X_1) & is_Arr625519182e_indi(Y_2) -> (hAPP_A588601142di_nat(F,X_1) = hAPP_A588601142di_nat(F,Y_2) -> X_1 = Y_2))) -> hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool)))) # label(fact_114_injI) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 161 (all Aa all Ba all L (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),L)) -> -hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Aa)),L))))) # label(fact_118_Lin__irrefl) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 162 (all X_2 all Y_1 all L (is_Arr553848933le_alt(X_2) & is_Arr553848933le_alt(Y_1) -> (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) -> (X_2 != Y_1 -> (-hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L)) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Y_1,X_2)),L))))))) # label(fact_119_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 163 (all X_2 all A (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) <-> hBOOL(hAPP_A1466488369i_bool(A,X_2)))) # label(fact_120_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 164 (all X_2 all A (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) <-> hBOOL(hAPP_bool_bool(A,X_2)))) # label(fact_121_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 165 (all X_2 all A (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A)) <-> hBOOL(hAPP_P2075002375t_bool(A,X_2)))) # label(fact_122_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 166 (all X_2 all A (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) <-> hBOOL(hAPP_f1636546729l_bool(A,X_2)))) # label(fact_123_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 167 (all X_2 all A (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A)) <-> hBOOL(hAPP_f785543729l_bool(A,X_2)))) # label(fact_124_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 168 (all X_2 all A (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A)) <-> hBOOL(hAPP_f745298353l_bool(A,X_2)))) # label(fact_125_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 169 (all Pa (is_fun917378774i_bool(Pa) -> collec45183100e_indi(Pa) = Pa)) # label(fact_126_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 170 (all X_2 all L (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,L),X_2)),arrow_1239002508le_Lin)))) # label(fact_127_mktop__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 171 (all X_2 all L (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,L),X_2)),arrow_1239002508le_Lin)))) # label(fact_128_mkbot__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 172 (all L all X_2 all Y_1 (is_Arr553848933le_alt(X_2) & is_Arr553848933le_alt(Y_1) -> (X_2 != Y_1 -> (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,L),X_2),Y_1)),arrow_1239002508le_Lin)))))) # label(fact_129_above__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 173 (all L (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) -> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,L)),arrow_413697182e_Prof)))) # label(fact_130_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 174 (all X_2 all Y_1 all L all Aa all Ba (is_Arr553848933le_alt(X_2) & is_Arr553848933le_alt(Y_1) & is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,L),Aa),Ba))) <-> X_2 != Y_1 & (X_2 = Ba -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Y_1)),L))) & (X_2 != Ba -> (Y_1 = Ba -> X_2 = Aa | hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Aa)),L))) & (Y_1 != Ba -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L))))))))) # label(fact_131_in__above) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 175 (all I_1 all Fa (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(Fa),pi_fun433100839t_bool(arrow_413697182e_Prof,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,arrow_1239002508le_Lin)))) -> ((all X_1 (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof)) -> (all A_1 all B_1 (is_Arr553848933le_alt(A_1) & is_Arr553848933le_alt(B_1) -> (A_1 != B_1 -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(X_1,I_1))) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,X_1))))))))) -> hBOOL(hAPP_A1466488369i_bool(hAPP_f355113919i_bool(arrow_2061665457ctator,Fa),I_1))))) # label(fact_132_dictatorI) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 176 (all X_2 all F all A all B (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_2)),hAPP_P2127852789l_bool(B,X_2))) -> -hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A))))) # label(fact_133_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 177 (all X_2 all F all A all B (hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B))) -> (-hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_2)),hAPP_A1374816149t_bool(B,X_2))) -> -hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))))) # label(fact_134_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 178 (all X_2 all F all A all B (hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B))) -> (-hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_2)),hAPP_b1024867081t_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))))) # label(fact_135_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 179 (all X_2 all F all A all B (hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B))) -> (-hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_2)),hAPP_A1912483895l_bool(B,X_2))) -> -hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))))) # label(fact_136_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 180 (all X_2 all F all A all B (hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B))) -> (-hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_2)),hAPP_b1719629739l_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))))) # label(fact_137_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 181 (all X_2 all F all A all B (hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B))) -> (-hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_2)),hAPP_A1964572607l_bool(B,X_2))) -> -hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))))) # label(fact_138_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 182 (all X_2 all F all A all B (hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B))) -> (-hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_2)),hAPP_b990649139l_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))))) # label(fact_139_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 183 (all X_2 all F all A all B (hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B))) -> (-hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_2)),hAPP_b1965422783l_bool(B,X_2))) -> -hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))))) # label(fact_140_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 184 (all X_2 all F all A all B (hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B))) -> (-hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_2)),hAPP_P907763049i_bool(B,X_2))) -> -hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A))))) # label(fact_141_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 185 (all X_2 all F all A all B (hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B))) -> (-hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_2)),hAPP_f749892423i_bool(B,X_2))) -> -hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))))) # label(fact_142_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 186 (all X_2 all F all A all B (hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_2)),hAPP_f313042899l_bool(B,X_2))) -> -hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))))) # label(fact_143_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 187 (all X_2 all F all A all B (hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B))) -> (-hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_2)),hAPP_f355113919i_bool(B,X_2))) -> -hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A))))) # label(fact_144_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 188 (all X_2 all F all A all B (hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_2)),hAPP_f497468491l_bool(B,X_2))) -> -hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A))))) # label(fact_145_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 189 (all X_2 all F all A all B (hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B))) -> (-hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_2)),hAPP_f352490559i_bool(B,X_2))) -> -hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A))))) # label(fact_146_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 190 (all X_2 all F all A all B (hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B))) -> (-hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_2)),hAPP_f417299659l_bool(B,X_2))) -> -hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A))))) # label(fact_147_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 191 (all X_2 all F all A all B (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B))) -> (-hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_2)),hAPP_f861484971l_bool(B,X_2))) -> -hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))))) # label(fact_148_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 192 (all X_2 all F all A all B (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B))) -> (-hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_2)),hAPP_A1944296755l_bool(B,X_2))) -> -hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))))) # label(fact_149_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 193 (all Aa all Ba (is_Arr553848933le_alt(Aa) & is_Arr553848933le_alt(Ba) -> (Aa != Ba -> (exists X_1 (is_fun282293932t_bool(X_1) & hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),arrow_1239002508le_Lin)) & hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),X_1))))))) # label(fact_150_complete__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 194 (all Na hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(cOMBC_437064334t_bool(cOMBC_481590946t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),Na)),lab),lba)),arrow_413697182e_Prof))) # label(fact_151_PiProf) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 195 (all X_2 all F all A all B (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_2)),hAPP_P2127852789l_bool(B,X_2)))))) # label(fact_152_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 196 (all X_2 all F all A all B (hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_2)),hAPP_P907763049i_bool(B,X_2)))))) # label(fact_153_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 197 (all X_2 all F all A all B (hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B))) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_2)),hAPP_f749892423i_bool(B,X_2)))))) # label(fact_154_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 198 (all X_2 all F all A all B (hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B))) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_2)),hAPP_f313042899l_bool(B,X_2)))))) # label(fact_155_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 199 (all X_2 all F all A all B (hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B))) -> (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_2)),hAPP_f355113919i_bool(B,X_2)))))) # label(fact_156_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 200 (all X_2 all F all A all B (hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B))) -> (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_2)),hAPP_f497468491l_bool(B,X_2)))))) # label(fact_157_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 201 (all X_2 all F all A all B (hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B))) -> (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_2)),hAPP_f352490559i_bool(B,X_2)))))) # label(fact_158_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 202 (all X_2 all F all A all B (hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B))) -> (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_2)),hAPP_f417299659l_bool(B,X_2)))))) # label(fact_159_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 203 (all X_2 all F all A all B (hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_2)),hAPP_A1374816149t_bool(B,X_2)))))) # label(fact_160_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 204 (all X_2 all F all A all B (hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_2)),hAPP_b1024867081t_bool(B,X_2)))))) # label(fact_161_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 205 (all X_2 all F all A all B (hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_2)),hAPP_A1912483895l_bool(B,X_2)))))) # label(fact_162_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 206 (all X_2 all F all A all B (hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_2)),hAPP_b1719629739l_bool(B,X_2)))))) # label(fact_163_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 207 (all X_2 all F all A all B (hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_2)),hAPP_A1964572607l_bool(B,X_2)))))) # label(fact_164_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 208 (all X_2 all F all A all B (hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_2)),hAPP_b990649139l_bool(B,X_2)))))) # label(fact_165_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 209 (all X_2 all F all A all B (hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_2)),hAPP_b1965422783l_bool(B,X_2)))))) # label(fact_166_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 210 (all X_2 all F all A all B (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B))) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_2)),hAPP_f861484971l_bool(B,X_2)))))) # label(fact_167_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 211 (all X_2 all F all A all B (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_2)),hAPP_A1944296755l_bool(B,X_2)))))) # label(fact_168_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 212 (all X_2 all F all A all B (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,B)))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_2)),B))))) # label(fact_170_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 213 (all X_2 all F all A all B (hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,hAPP_f1970593179i_bool(cOMBK_100791596le_alt,B)))) -> (hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_2)),B))))) # label(fact_171_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 214 (all X_2 all F all A all B (hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,hAPP_f681113465i_bool(cOMBK_454107598t_bool,B)))) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_2)),B))))) # label(fact_172_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 215 (all X_2 all F all A all B (hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,hAPP_f219827985l_bool(cOMBK_886533338t_bool,B)))) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_2)),B))))) # label(fact_173_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 216 (all X_2 all F all A all B (hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,hAPP_f1677452273i_bool(cOMBK_1372975190t_bool,B)))) -> (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_2)),B))))) # label(fact_174_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 217 (all X_2 all F all A all B (hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,hAPP_f1235573641l_bool(cOMBK_1072228194t_bool,B)))) -> (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_2)),B))))) # label(fact_175_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 218 (all X_2 all F all A all B (hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,hAPP_f1903519657i_bool(cOMBK_2076140708t_bool,B)))) -> (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A)) -> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_2)),B))))) # label(fact_176_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 219 (all X_2 all F all A all B (hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,hAPP_f1667233577l_bool(cOMBK_1015076504t_bool,B)))) -> (hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A)) -> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_2)),B))))) # label(fact_177_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 220 (all X_2 all F all A all B (hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,B)))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_2)),B))))) # label(fact_178_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 221 (all X_2 all F all A all B (hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,hAPP_f1520552209t_bool(cOMBK_697786936l_bool,B)))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_2)),B))))) # label(fact_179_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 222 (all X_2 all F all A all B (hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,hAPP_f813556705l_bool(cOMBK_116240846e_indi,B)))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_2)),B))))) # label(fact_180_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 223 (all X_2 all F all A all B (hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,hAPP_f371807573l_bool(cOMBK_697604314l_bool,B)))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_2)),B))))) # label(fact_181_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 224 (all X_2 all F all A all B (hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,hAPP_f1697527281l_bool(cOMBK_1292462166e_indi,B)))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_2)),B))))) # label(fact_182_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 225 (all X_2 all F all A all B (hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,hAPP_f448497509l_bool(cOMBK_1268833122l_bool,B)))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_2)),B))))) # label(fact_183_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 226 (all X_2 all F all A all B (hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,hAPP_f2135750719l_bool(cOMBK_971068024l_bool,B)))) -> (hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_2)),B))))) # label(fact_184_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 227 (all X_2 all F all A all B (hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,B)))) -> (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_2)),B))))) # label(fact_185_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 228 (all X_2 all F all A all B (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,B)))) -> (hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) -> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_2)),B))))) # label(fact_186_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 229 (all Fa all I_1 (hBOOL(hAPP_A1466488369i_bool(hAPP_f355113919i_bool(arrow_2061665457ctator,Fa),I_1)) <-> (all X_1 (hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof)) -> hAPP_f695124765t_bool(Fa,X_1) = hAPP_A1374816149t_bool(X_1,I_1))))) # label(fact_187_dictator__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 230 (all A pi_Pro2135156861t_bool(A,hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,top_to1647826457l_bool)) = top_to2005687013l_bool) # label(fact_188_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 231 (all A pi_fun433100839t_bool(A,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,top_to2005687013l_bool)) = top_to40512653l_bool) # label(fact_189_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 232 (all A pi_Arr688267935t_bool(A,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,top_to2005687013l_bool)) = top_to1194196741l_bool) # label(fact_190_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 233 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),hAPP_f695124765t_bool(f,cOMBC_437064334t_bool(cOMBC_481590946t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),lab),lba)))) # label(fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 234 (all I ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,hAPP_A1374816149t_bool(p,I)),e)))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n)) -> (hAPP_A588601142di_nat(h,I) = n -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,hAPP_A1374816149t_bool(p,I)),c),e)))) & (hAPP_A588601142di_nat(h,I) != n -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,hAPP_A1374816149t_bool(p,I)),e))))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),lab))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n)) -> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),lba))))) # label(fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 235 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 236 (all X all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 237 (all X all Y (X != Y | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 238 (all P all Q (is_bool(P) -> hAPP_A1466488369i_bool(hAPP_b1018211123i_bool(cOMBK_1157044842e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____fje) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 239 (all P all Q all R hAPP_A1466488369i_bool(cOMBC_277798809t_bool(P,Q),R) = hAPP_nat_bool(hAPP_A1922697556t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 240 (all P all Q all R hAPP_A1922697556t_bool(cOMBB_317992461e_indi(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_A588601142di_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].
% 0.95/1.26 241 (all P all Q (is_bool(P) -> hAPP_P2075002375t_bool(hAPP_b1024867081t_bool(cOMBK_2069093696le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 242 (all X all Y (is_fun282293932t_bool(X) -> hAPP_f1673487381t_bool(hAPP_f159424297t_bool(hAPP_b1915039793t_bool(if_fun1419651289t_bool,fTrue),X),Y) = X)) # label(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 243 (all X all Y (is_fun282293932t_bool(Y) -> hAPP_f1673487381t_bool(hAPP_f159424297t_bool(hAPP_b1915039793t_bool(if_fun1419651289t_bool,fFalse),X),Y) = Y)) # label(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 244 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 245 (all P all Q (is_bool(P) -> hAPP_f745298353l_bool(hAPP_b1965422783l_bool(cOMBK_977355664t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 246 (all P all Q hAPP_P2127852789l_bool(hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 247 (all P all Q (is_fun282293932t_bool(P) -> hAPP_b1024867081t_bool(hAPP_f1520552209t_bool(cOMBK_697786936l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 248 (all P all Q hAPP_f417299659l_bool(hAPP_f1667233577l_bool(cOMBK_1015076504t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 249 (all P all Q (is_fun432044380l_bool(P) -> hAPP_b1965422783l_bool(hAPP_f2135750719l_bool(cOMBK_971068024l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 250 (all P all Q (is_fun917378774i_bool(P) -> hAPP_P907763049i_bool(hAPP_f1970593179i_bool(cOMBK_100791596le_alt,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 251 (all P all Q (is_fun282293932t_bool(P) -> hAPP_A1374816149t_bool(hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj_026) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 252 (all P all Q (is_bool(P) -> hAPP_f1636546729l_bool(hAPP_b1719629739l_bool(cOMBK_789167586t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 253 (all P all Q (is_fun917378774i_bool(P) -> hAPP_f352490559i_bool(hAPP_f1903519657i_bool(cOMBK_2076140708t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___027) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 254 (all P all Q (is_fun432044380l_bool(P) -> hAPP_A1944296755l_bool(hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_028) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 255 (all P all Q hAPP_f313042899l_bool(hAPP_f219827985l_bool(cOMBK_886533338t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_029) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 256 (all P all Q (is_fun959573582l_bool(P) -> hAPP_b1719629739l_bool(hAPP_f371807573l_bool(cOMBK_697604314l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 257 (all P all Q all R hAPP_A1374816149t_bool(cOMBC_1778077589t_bool(P,Q),R) = hAPP_A619995676t_bool(hAPP_A702630576t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_030) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 258 (all P all Q (is_fun917378774i_bool(P) -> hAPP_f749892423i_bool(hAPP_f681113465i_bool(cOMBK_454107598t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___031) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 259 (all P all Q (is_fun959573582l_bool(P) -> hAPP_A1912483895l_bool(hAPP_f813556705l_bool(cOMBK_116240846e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje_032) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 260 (all P all Q all R hAPP_A702630576t_bool(cOMBC_493523632t_bool(P,Q),R) = hAPP_A384644407t_bool(hAPP_A460042315t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_033) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 261 (all P all Q all R hAPP_A1374816149t_bool(cOMBC_437064334t_bool(P,Q),R) = hAPP_f1673487381t_bool(hAPP_A1333445289t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_034) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 262 (all P all Q all R hAPP_A1374816149t_bool(cOMBS_867867294t_bool(P,Q),R) = hAPP_f1673487381t_bool(hAPP_A1333445289t_bool(P,R),hAPP_A1374816149t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 263 (all P all Q (is_bool(P) -> hAPP_f785543729l_bool(hAPP_b990649139l_bool(cOMBK_580911210t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 264 (all P all Q (is_fun432044380l_bool(P) -> hAPP_f861484971l_bool(hAPP_f20355883l_bool(cOMBK_1088865252t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_035) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 265 (all P all Q hAPP_f497468491l_bool(hAPP_f1235573641l_bool(cOMBK_1072228194t_bool,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_036) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 266 (all P all Q (is_fun631676118l_bool(P) -> hAPP_b990649139l_bool(hAPP_f448497509l_bool(cOMBK_1268833122l_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 267 (all P all Q all R hAPP_A702630576t_bool(cOMBB_1292070696e_indi(P,Q),R) = hAPP_f1290184496t_bool(P,hAPP_A1374816149t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 268 (all P all Q (is_fun917378774i_bool(P) -> hAPP_f355113919i_bool(hAPP_f1677452273i_bool(cOMBK_1372975190t_bool,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___037) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 269 (all P all Q (is_fun631676118l_bool(P) -> hAPP_A1964572607l_bool(hAPP_f1697527281l_bool(cOMBK_1292462166e_indi,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_038) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 270 (all P all Q all R hAPP_A460042315t_bool(cOMBB_69933763e_indi(P,Q),R) = hAPP_f1336478923t_bool(P,hAPP_A1374816149t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj_039) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 271 (all P all Q all R hAPP_A1333445289t_bool(cOMBC_481590946t_bool(P,Q),R) = hAPP_f159424297t_bool(hAPP_A869356733t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_040) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 272 (all P all Q all R hAPP_A1333445289t_bool(cOMBS_102864562t_bool(P,Q),R) = hAPP_f159424297t_bool(hAPP_A869356733t_bool(P,R),hAPP_A1374816149t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_041) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.35 273 (all P all Q all R hAPP_A869356733t_bool(cOMBB_963584201e_indi(P,Q),R) = hAPP_b1915039793t_bool(P,hAPP_A1466488369i_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.35
% 0.95/1.35 ============================== end of process non-clausal formulas ===
% 0.95/1.35
% 0.95/1.35 ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.35
% 0.95/1.35 ============================== PREDICATE ELIMINATION =================
% 0.95/1.35 274 -is_fun1016509681e_indi(A) | is_Arr625519182e_indi(hAPP_n385347014e_indi(A,B)) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oi) # label(axiom). [clausify(24)].
% 0.95/1.35 275 -is_fun917378774i_bool(A) | is_fun1016509681e_indi(hilber1792103167di_nat(A,B)) # label(gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____fjewxadnq) # label(axiom). [clausify(6)].
% 0.95/1.35 Derived: is_Arr625519182e_indi(hAPP_n385347014e_indi(hilber1792103167di_nat(A,B),C)) | -is_fun917378774i_bool(A). [resolve(274,a,275,b)].
% 0.95/1.35 276 -is_fun1016509681e_indi(A) | -hBOOL(inj_on24934938di_nat(B,top_to1256827021i_bool)) | hAPP_A588601142di_nat(B,hAPP_n385347014e_indi(A,f22(A,B))) != f22(A,B) | hilber1792103167di_nat(top_to1256827021i_bool,B) = A # label(fact_113_inj__imp__inv__eq) # label(axiom). [clausify(159)].
% 0.95/1.35 Derived: -hBOOL(inj_on24934938di_nat(A,top_to1256827021i_bool)) | hAPP_A588601142di_nat(A,hAPP_n385347014e_indi(hilber1792103167di_nat(B,C),f22(hilber1792103167di_nat(B,C),A))) != f22(hilber1792103167di_nat(B,C),A) | hilber1792103167di_nat(top_to1256827021i_bool,A) = hilber1792103167di_nat(B,C) | -is_fun917378774i_bool(B). [resolve(276,a,275,b)].
% 0.95/1.35
% 0.95/1.35 ============================== end predicate elimination =============
% 0.95/1.35
% 0.95/1.35 Auto_denials: (non-Horn, no changes).
% 0.95/1.35
% 0.95/1.35 Term ordering decisions:
% 0.95/1.35 Function symbol KB weights: arrow_413697182e_Prof=1. f=1. p=1. e=1. ord_less_nat=1. c=1. h=1. n=1. d=1. arrow_1239002508le_Lin=1. arrow_812378712_above=1. top_to1256827021i_bool=1. arrow_2077223396_mkbot=1. if_fun1419651289t_bool=1. arrow_78446834_mktop=1. ord_le694128617i_bool=1. top_top_bool=1. arrow_1212118780le_IIA=1. a=1. b=1. top_to2005687013l_bool=1. lba=1. cOMBK_1088865252t_bool=1. fTrue=1. fequal_nat=1. top_to1194196741l_bool=1. top_to40512653l_bool=1. arrow_2061665457ctator=1. arrow_467566751nimity=1. top_to2034604131t_bool=1. lab=1. cOMBK_1158753900e_indi=1. fFalse=1. arrow_1812558424le_alt=1. cOMBK_1152753196e_indi=1. cOMBK_2008994872le_alt=1. ord_less_bool=1. top_to1647826457l_bool=1. cOMBK_100791596le_alt=1. cOMBK_1015076504t_bool=1. cOMBK_1072228194t_bool=1. cOMBK_1157044842e_indi=1. cOMBK_116240846e_indi=1. cOMBK_1268833122l_bool=1. cOMBK_1292462166e_indi=1. cOMBK_1372975190t_bool=1. cOMBK_2069093696le_alt=1. cOMBK_2076140708t_bool=1. cOMBK_454107598t_bool=1. cOMBK_580911210t_bool=1. cOMBK_697604314l_bool=1. cOMBK_697786936l_bool=1. cOMBK_789167586t_bool=1. cOMBK_886533338t_bool=1. cOMBK_971068024l_bool=1. cOMBK_977355664t_bool=1. arrow_2110637339e_indi=1. bool=1. ord_le1480133609l_bool=1. ord_le227393471t_bool=1. ord_le272605321l_bool=1. ord_le453141089l_bool=1. hAPP_f745298353l_bool=1. produc171383831le_alt=1. hAPP_f453661011l_bool=1. hAPP_A1374816149t_bool=1. hAPP_f695124765t_bool=1. hAPP_f919661787l_bool=1. hAPP_A619995676t_bool=1. hAPP_f503012287l_bool=1. hAPP_A588601142di_nat=1. hAPP_nat_bool=1. hAPP_n1699378549t_bool=1. hAPP_f785543729l_bool=1. hAPP_f387058535l_bool=1. hAPP_f213304539l_bool=1. hAPP_f1290184496t_bool=1. cOMBC_1778077589t_bool=1. hAPP_A384644407t_bool=1. hAPP_f1336478923t_bool=1. inj_on24934938di_nat=1. cOMBC_277798809t_bool=1. cOMBB_317992461e_indi=1. cOMBB_963584201e_indi=1. hAPP_A1466488369i_bool=1. cOMBB_1292070696e_indi=1. cOMBS_102864562t_bool=1. cOMBS_867867294t_bool=1. hAPP_f1710416135l_bool=1. hAPP_P2075002375t_bool=1. hAPP_f355113919i_bool=1. pi_fun433100839t_bool=1. hilber1792103167di_nat=1. hAPP_f1636546729l_bool=1. hAPP_f20355883l_bool=1. cOMBB_69933763e_indi=1. cOMBC_493523632t_bool=1. hAPP_b1024867081t_bool=1. hAPP_n385347014e_indi=1. hAPP_b1719629739l_bool=1. hAPP_b1965422783l_bool=1. hAPP_b990649139l_bool=1. hAPP_bool_bool=1. pi_Arr688267935t_bool=1. hAPP_f1673487381t_bool=1. pi_Pro2135156861t_bool=1. cOMBC_437064334t_bool=1. cOMBC_481590946t_bool=1. hAPP_A1333445289t_bool=1. hAPP_A1912483895l_bool=1. hAPP_A1944296755l_bool=1. hAPP_A1964572607l_bool=1. hAPP_P2024088443e_indi=1. hAPP_P907763049i_bool=1. hAPP_f1012384989l_bool=1. hAPP_f1018082273l_bool=1. hAPP_f1271180905l_bool=1. hAPP_f1279200745l_bool=1. hAPP_f1550037191l_bool=1. hAPP_f159424297t_bool=1. hAPP_f1659504677e_indi=1. hAPP_f1766869725l_bool=1. hAPP_f1818473245e_indi=1. hAPP_f1895985727l_bool=1. hAPP_f1979025587l_bool=1. hAPP_f204273237l_bool=1. hAPP_f234874197l_bool=1. hAPP_f352490559i_bool=1. hAPP_f460310451l_bool=1. hAPP_f483434675l_bool=1. hAPP_f500145249l_bool=1. hAPP_f526292585l_bool=1. hAPP_f592909149l_bool=1. hAPP_f618619045e_indi=1. hAPP_f749892423i_bool=1. hAPP_f861484971l_bool=1. hAPP_A1062826149t_bool=1. hAPP_A1594182429t_bool=1. hAPP_A1736628091le_alt=1. hAPP_A702630576t_bool=1. hAPP_A869356733t_bool=1. hAPP_P2127852789l_bool=1. hAPP_b1018211123i_bool=1. hAPP_b1817367815le_alt=1. hAPP_b1915039793t_bool=1. hAPP_b331122225t_bool=1. hAPP_b589554111l_bool=1. hAPP_b833696937t_bool=1. hAPP_f1507266205t_bool=1. hAPP_f1724001331l_bool=1. hAPP_f313042899l_bool=1. hAPP_f417299659l_bool=1. hAPP_f497468491l_bool=1. pi_Arr149813489le_alt=1. pi_Arr1511953043t_bool=1. pi_Arr372473371t_bool=1. pi_Pro437273841e_indi=1. pi_boo1877522301le_alt=1. pi_boo2007389459t_bool=1. pi_boo691944735t_bool=1. pi_boo71521447t_bool=1. pi_fun1494794527l_bool=1. pi_fun1727820731l_bool=1. pi_fun1736243859e_indi=1. pi_fun2075749915e_indi=1. pi_fun525942951l_bool=1. pi_fun972956463e_indi=1. hAPP_A1922697556t_bool=1. hAPP_A460042315t_bool=1. hAPP_f1235573641l_bool=1. hAPP_f1520552209t_bool=1. hAPP_f1667233577l_bool=1. hAPP_f1677452273i_bool=1. hAPP_f1697527281l_bool=1. hAPP_f1903519657i_bool=1. hAPP_f1970593179i_bool=1. hAPP_f2056167603l_bool=1. hAPP_f2135750719l_bool=1. hAPP_f219827985l_bool=1. hAPP_f371807573l_bool=1. hAPP_f448497509l_bool=1. hAPP_f681113465i_bool=1. hAPP_f813556705l_bool=1. fun=1. hAPP_f1669465919l_bool=1. hAPP_f1760255479l_bool=1. hAPP_f281286919l_bool=1. product_prod=1. f18=1. f19=1. f20=1. f21=1. f22=1. f25=1. f26=1. f27=1. f28=1. f29=1. member1056080916le_alt=1. member1277417654t_bool=1. member1965683644t_bool=1. member2074804542e_indi=1. member_bool=1. member1622429502t_bool=1. collec45183100e_indi=1. member1033316428l_bool=1. member1105181906e_indi=1. member1122398042e_indi=1. member1467476314t_bool=1. member1661336414l_bool=1. member1833291218t_bool=1. member1911067358t_bool=1. member2081512038t_bool=1. member329987264e_indi=1. member387398118l_bool=1. member42699324le_alt=1. member497701034t_bool=1. member765089840e_indi=1. member859582768le_alt=1. collec1520786044t_bool=1. collec1580242420t_bool=1. collec1711870802le_alt=1. collec874260222t_bool=1. finite120254591e_indi=1. undefi1301554228le_alt=1. undefi802509179t_bool=1. undefi818645567e_indi=1. f6=1. f7=1. f8=1. f10=1. f11=1. f12=1. f13=1. f15=1. f16=1. f17=1. f23=1. f24=1. f5=1. f14=1. f3=1. f9=1. f1=1. f2=1. f4=1.
% 0.95/1.35
% 0.95/1.35 ============================== PROOF =================================
% 0.95/1.35 % SZS status Theorem
% 0.95/1.35 % SZS output start Refutation
% 0.95/1.35
% 0.95/1.35 % Proof 1 at 0.16 (+ 0.00) seconds.
% 0.95/1.35 % Length of proof is 6.
% 0.95/1.35 % Level of proof is 3.
% 0.95/1.35 % Maximum clause weight is 43.000.
% 0.95/1.35 % Given clauses 0.
% 0.95/1.35
% 0.95/1.35 70 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) <-> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) # label(fact_14_PW) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.36 413 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) # label(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) # label(axiom). [assumption].
% 0.95/1.36 414 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) | -hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) # label(fact_14_PW) # label(axiom). [clausify(70)].
% 0.95/1.36 415 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))). [copy(414),unit_del(b,413)].
% 0.95/1.36 702 -hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) # label(conj_0) # label(negated_conjecture). [assumption].
% 0.95/1.36 703 $F. [copy(702),unit_del(a,415)].
% 0.95/1.36
% 0.95/1.36 % SZS output end Refutation
% 0.95/1.36 ============================== end of proof ==========================
% 0.95/1.36
% 0.95/1.36 ============================== STATISTICS ============================
% 0.95/1.36
% 0.95/1.36 Given=0. Generated=457. Kept=384. proofs=1.
% 0.95/1.36 Usable=0. Sos=0. Demods=24. Limbo=384, Disabled=460. Hints=0.
% 0.95/1.36 Megabytes=3.50.
% 0.95/1.36 User_CPU=0.16, System_CPU=0.00, Wall_clock=0.
% 0.95/1.36
% 0.95/1.36 ============================== end of statistics =====================
% 0.95/1.36
% 0.95/1.36 ============================== end of search =========================
% 0.95/1.36
% 0.95/1.36 THEOREM PROVED
% 0.95/1.36 % SZS status Theorem
% 0.95/1.36
% 0.95/1.36 Exiting with 1 proof.
% 0.95/1.36
% 0.95/1.36 Process 23620 exit (max_proofs) Fri Jul 1 21:37:05 2022
% 0.95/1.36 Prover9 interrupted
%------------------------------------------------------------------------------